by Matt Barsalou, guest blogger

I know that Thanksgiving is always on the last Thursday in November, but somehow I failed to notice it was fast approaching until the Monday before Thanksgiving. This led to frantically sending a last-minute invitation, and a hunt for a turkey.

I live in Germany and this greatly complicated the matter. Not only is Thanksgiving not celebrated, but also actual turkeys are rather difficult to find.

I looked at a large grocery store’s website and found 15 types of cat and dog food that contain turkey, but the only human food I could find was one jar of baby food.

Close, but not close enough. I wanted a whole turkey, not turkey puree.

The situation was even more complicated due to langue: Germans have one word for a male turkey and a different word for a female turkey. I did not realize there was a difference, so I wound up only looking for a male turkey. My conversation with the store clerk would sound like this if it were translated into English, where there is only one word commonly used for turkey:

Me: Do you carry turkey?

Clerk: No. We only have turkey.

Me: I don’t need turkey. I’m looking for turkey.

Clerk: Sorry, we don’t carry turkey, but we have turkey if you want it.

Me: No thank you. I need turkey, not turkey.

Eventually, I figured out what happened and returned to buy the biggest female turkey they had. It weighed 5 pounds.

This was not the first time I cooked a turkey, but my first attempt resulted in The Great Turkey Fireball of 1998. (Cooking tip: Don’t spray turkey juice onto the oven burner). My previous attempt resulted in a turkey that still had ice in it after five hours in the oven. (Life hack: The inside of a turkey is a good place to keep ice from melting.)

This year, to be safe, I contacted an old friend who explained how to properly cook a turkey, but I was told I would need to figure out the cooking time on my own. This was not a problem...or so I thought. I looked online and found turkey cooking times for a stuffed turkey, but my turkey was too light to be included in the table.

I may not know much about cooking, but I do know statistics, so I decided to run a regression analysis to determine the correct cooking time for my bird. The weights and times were in a table for ranges so I selected the times that corresponded to the low and high weight ranges and entered the data into a Minitab worksheet as shown in Figure 1.

Figure 1: Worksheet with weight and times

I like to look at my data before I analyze it so I created a scatterplot to see how time compares to weight. Go to Graph > Scatter Plot and select Simple. Enter Time as the Y variable and Weight as the X variable.

Visually, it looks as if there may be a relationship between weight and cooking time so I then performed a regression analysis (see Fig. 2).

Figure 2: Scatter plot of weight and times

Go to Stat > Regression > Regression > Fit Regression Model... and select Time for the response and Weight as the continuous predictor. Click on Graphs and select Four in One, then OK out of the dialogs.

The P-value is < 0.05 and the adjusted r-squared (adjusted) is 97.04% so it looks like I have a good model for time versus weight (See Fig. 3).

Figure 3: Session window for regression analysis for time versus weight

The residual plots for time shown in Figure 4 include a normal probability plot with residuals that look like they are normally distributed. My data did not need to follow the normal distribution, but the residuals should. But something seemed odd to me when I looked at the other three plots. Suddenly, I was not so sure my model was as good as I thought it was.

Figure 4: Residual plots for time

I then used the Minitab Assistant to perform a regression analysis. Since I was uncertain about my analysis, I could use the reports generated by the Assistant to better asses my data and the resulting analysis.

Go to Assistant > Regression and select Simple Regression. Select Time for the Y column and Weight for the X column and select OK.

The first report provided by the Minitab Assistant is the summary report, shown in Figure 5. The report indicates a statistically significant relationship between time and weight using an Alpha of 0.05. It also tells me that 99.8% of the variability in time is caused by weight. This does not match my previous results and I can see why: I previously performed linear regression and the Minitab Assistant identified a quadratic model for the data.

The regression equation is Y = 0.9281 +0.3738X -0.005902(X2).

Time = 0.9281 +0.3738(5) -0.005902(52) =

0.9281 + 1.869 – 1.8692 =

2.7971 – 0.0008708401 = 2.796 hours

That means the cooking time is 2 hours and 48 minutes.

Figure 5: Summary report for time versus weight

Figure 6 depicts the model selection report which includes a plot of the quadratic model and the r-squared (adjusted) for both the quadratic model and a linear model.

Figure 6: Model Selection report for time versus weight

The diagnostic report in Figure 7 is used to assess the residuals and guidance on the interpretation of the report is provided on the right side.

Figure 7: Diagnostic report for time versus weight

The prediction report in Figure 8 shows the prediction plot with the 95% prediction interval.

Figure 8: Prediction report for time versus weight

The report card shown in Figure 8 helps us to assess the suitability of the data. Here, I saw a problem: my sample size was only six. Minitab still provided me with results, but it warned me that the estimate for the strength of the relationship may not be very precise due to the low number if values I used. Minitab recommended I use 40 or more values. My data did not include any unusual data points, but using less than 15 values means the P-value could be incorrect if my results were not normally distributed.

Figure 9: Report card for time versus weight

It looks like my calculated cooking time may not be as accurate as I’d like it to be, but I don’t think it will be too far off since the relationship between weights and cooking time is so strong.

It is important to remember not to extrapolate beyond the data set when taking actions based on a regression model. My turkey weighs less than the lowest value used in the model, but I’m going to need to risk it. In such a situation, statistics alone will not provide us an answer on a platter (with stuffing and side items such as cranberry sauce and candied yams), but we can use the knowledge gained from the study to help us when making judgment calls based on expert knowledge or previous experience. I expect my turkey to be finished in around two and a half to three hours, but I plan to use a thermometer to help ensure I achieve the correct cooking time.

But first, it looks like I am going to need to perform a Type 1 Gage Study analysis, once I figure out how to use my kitchen thermometer.

Dear Readers,

As 2016 comes to a close, it’s time to reflect on the passage of time and changes. As I’m sure you’ve guessed, I love statistics and analyzing data! I also love talking and writing about it. In fact, I’ve been writing statistical blog posts for over five years, and it’s been an absolute blast. John Tukey, the renowned statistician, once said, “The best thing about being a statistician is that you get to play in everyone’s backyard.” I enthusiastically agree!

However, when I first started writing the blog, I wondered about being able to keep up a constant supply of fresh blog posts. And, when I first mentioned to some non-statistician friends that I’d be writing a statistical blog, I noticed a certain lack of enthusiasm. For instance, I heard a variety comments like, “So, you’ll be writing things along the lines of 9 out of 10 dentists recommend . . .” Would readers even be interested in what I had to say about statistics?

It turns out that with a curious mind, statistical knowledge, data, and a powerful tool like Minitab statistical software, the possibilities are endless. You can play in a wide variety of fascinating backyards! 

The most surprising statistic is that my blog posts have had over 5.5 million views in the past year alone. Never in my wildest dreams did I imagine so many readers when I wrote my first post! It’s a real testament to the growing importance of data analysis that so many people are interested in a blog dedicated to statistics. Thank you all for reading!

Some of the topics I've written about are out of this world. I’ve assessed dolphin communications and compared it to the search for extraterrestrial intelligence and analyzed exoplanet data in the search for the Earth’s twin! As an aside, my analysis showed that my writing style is similar to dolphin communications. I'll take that as a compliment!

For more Earthly subjects, I’ve studied the relationship between mammal size and their metabolic rate and longevity. I’ve analyzed raw research data to assess the effectiveness of flu shots first hand. I’ve downloaded economic data to assess patterns in both the U.S. GDP and U.S. job growth. For a Thanksgiving Day post, I analyzed world income data to answer the question of how thankful we should be statistically. As for Easter, I can tell you the date on which it falls in any of 2,517 years, along with which dates are the most and least common.

In the world of politics, I’ve used data to predict the 2012 U.S. Presidential election, analyzed the House Freedom Caucus and the search for the new Speaker of the House, assessed the factors that make a great President, and even helped Mitt Romney pick a running mate. Everyone talks about the weather, so of course I had to analyze that. My family loves the Mythbusters and it was fun applying statistical analyses to some of the myths that they tested (here and here). That's my family and I meeting them in the picture to the right!

Some of my posts have even been a bit surreal. I took my turn at attempting to explain the statistical illusion of the infamous Monty Hall problem. I’ve compared world travel to adjusting scales in graphs (seriously). I wrote a true story about how I drove a plane load of passengers 200 miles to their homes in the context of quality improvement! For Halloween themed posts, I showed how to go ghost hunting with a statistical mindset and how regression models can be haunted by phantom degrees of freedom. I analyzed the fatality rates in the original Star Trek TV series. I explored how some people can find so many four leaf clovers despite their rarity. And, I wondered whether a statistician can say that age is just a number?

See, not a mention of those dentists...well not until now. By this point, 9 out of 10 dentists are probably feeling neglected!

I’ve also written many posts aimed at helping those who are learning and performing statistical analyses. I described why statistics is cool based on my own personal experiences and how the whole field of statistics is growing in importance. I showed how anecdotal evidence is unreliable and explained why it fails so badly. And, I took a look forward at how statistical analyses are expanding into areas traditionally ruled by expert judgement.

I zoomed in to cover the details about how to perform and interpret statistical analyses. Some might think that covering the nitty gritty of statistical best practices is boring. Yet, you’d be surprised by the lively discussions we’ve had. We’ve had heated debates and philosophical discussions about how to correctly interpret p-values and what statistical significance does and does not tell you. This reached a fever pitch when a psychology journal actually banned p-values!

We had our difficult questions and surprising topics to grapple with. How high should R-squared be? Should I use a parametric or nonparametric analysis? How is it possible that a regression model can have significant variables but still have a low R-squared? I even had the nerve to suggest that R-squared is overrated! And, I made the unusual case that control charts are also very important outside the realm of quality improvement. Then, there is the whole frequentist versus Bayesian debate, but let’s not go there!

However, it’s true that not all topics about how to perform statistical analyses are riveting. I still love these topics. The world is becoming an increasingly data driven place and to produce trustworthy results, you must analyze your data correctly. After all, it’s surprisingly easy to make a costly mistake if you don’t know what you’re doing.

A data driven world requires an analyst to understand seemingly esoteric details such as: the different methods of fitting curves, the dangers of overfitting your model, assessing goodness-of-fit, checking your residual plots, and how to check for and correct multicollinearity and heteroscedasticity. How do you choose the best model? Do you need to standardize your variables before performing the analysis? Maybe you need a regression tutorial?

You may need to know how to identify the distribution of your data. And, just how do hypothesis tests work anyway? F-tests? T-tests? How do you test discrete data? Should you use a confidence interval, prediction interval, or a tolerance interval? How do you know when X causes a change in Y? Is a confounding variable distorting your results? What are the pros and cons of using a repeated measures design? Fisher’s or Welch’s ANOVA? ANOVA or MANOVA? Linear or nonlinear regression?

These may not be “sexy” topics but they are the meat and potatoes of being able to draw sound conclusions from your data. And, based on numerous blog comments, they have been well received by many people. In fact, the most rewarding aspect of writing blog posts has been the interactions I've had with all of you. I've communicated with literally hundreds and hundreds of students learning statistics and practitioners performing statistics in the field. I’ve had the pleasure of learning how you use statistical analyses, understanding the difficulties you face, and helping you resolve those issues.

It's been an amazing journey and I hope that my blog posts have allowed you to see statistics through my eyes―as a key that can unlock discoveries that are trapped in your data. After all, that's the reason why I titled my blog, Adventures in Statistics. Discovery is a bumpy road. There can be statistical challenges en route, but even those can be interesting, and perhaps even rewarding, to resolve. Sometimes it is the perplexing mystery in your data that prompts you to play detective and leads you to surprising new discoveries!

To close out the old year, it's good to remember that change is constant. There are bound to be many new and exciting adventures in the New Year. I wish you all the best in your endeavors. 

“We will open the book. Its pages are blank. We are going to put words on them ourselves. The book is called Opportunity and its first chapter is New Year's Day.”   ― Edith Lovejoy Pierce 

May you all find happiness in 2017! Onward and upward!

Jim

In Parts 1 and 2 of this blog series, I wrote about how statistical inference uses data from a sample of individuals to reach conclusions about the whole population. That’s a very powerful tool, but you must check your assumptions when you make statistical inferences. Violating any of these assumptions can result in false positives or false negatives, thus invalidating your results. 

The common data assumptions are: random samples, independence, normality, equal variance, stability, and that your measurement system is accurate and precise. I addressed random samples and statistical independence last time. Now let’s consider the assumptions of stability and measurement systems.

A stable process is one in which the inputs and conditions are consistent over time. When a process is stable, it is said to be “in control.” This means the sources of variation are consistent over time, and the process does not exhibit unpredictable variation. In contrast, if a process is unstable and changing over time, the sources of variation are inconsistent and unpredictable.  As a result of the instability, you cannot be confident in your statistical test results.

Use one of the various types of control charts available in Minitab Statistical Software to assess the stability of your data set. The Assistant menu can walk you through the choices to select the appropriate control chart based on your data and subgroup size. You can get advice about collecting and using data by clicking the “more” link.

In addition to preparing the control chart, Minitab tests for out-of-control or non-random patterns based on the Nelson Rules and provides an assessment in easy-to-read Summary and Stability reports. The Report Card, depending on the control chart selected, will automatically check your assumptions of stability, normality, amount of data, correlation, and will suggest alternative charts to further analyze your data.

All the other assumptions I’ve described “assume” the data reflects reality. But does it?

The measurement system is one potential source of variability when measuring a product or process. When a measurement system is poor, you lose the ability to truthfully “see” process performance. A poor measurement system leads to incorrect conclusions and flawed implementation. 

Minitab can perform a Gage R&R test for both measurement and appraisal data, depending on your measurement system. You can use the Assistant in Minitab to help you select the most appropriate test based on the type of measurement system you have.

There are two assumptions that should be satisfied when performing a Gage R&R for measurement data: 

1. The measurement device should be calibrated.
2. The parts to be measured should be selected from a stable process and cover approximately 80% of the possible operating range. 

When using a measurement device make sure it is properly calibrated and check for linearity, bias, and stability over time. The device should produce accurate measurements, compared to a standard value, through the entire range of measurements and throughout the life of the device. Many companies have a metrology or calibration department responsible for calibrating and maintaining gauges. 

Both these assumptions must be satisfied. If they are not, you cannot be sure that your data accurately reflect reality. And that means you’ll risk not understanding the sources of variation that influence your process outcomes. 

Collecting and analyzing data requires a lot of time and effort on your part. After all the work you put into your analysis, you want to be able to reach correct conclusions. Some analyses are robust to departures from these assumptions, but take the safe route and check! You want to be confident you can tell whether observed differences between data samples are simply due to chance, or if the populations are indeed different! 

It’s easy to put the cart before the horse and just plunge in to the data collection and analysis, but it’s much wiser to take the time to understand which data assumptions apply to the statistical tests you will be using, and plan accordingly.

Thank you for reading my blog.  I hope this information helps you with your data analysis mission!

Reliability analysis is the perfect tool for calculating the proportion of items that you can expect to survive for a specified period of time under identical operating conditions. Light bulbs—or lamps—are a classic example. Want to calculate the number of light bulbs expected to fail within 1000 hours? Reliability analysis can help you answer this type of question.

But to conduct the analysis properly, we need to understand the difference between the three types of censoring.

When you perform reliability analysis, you may not have exact failure times for all items. In fact, lifetime data are often "censored." Using the light bulb example, perhaps not all the light bulbs have failed by the time your study ends. The time data for those bulbs that have not yet failed are referred to as censored.

It is important to include the censored observations in your analysis because the fact that these items have not yet failed has a big impact on your reliability estimates.

Let’s move from light bulbs to newborns, inspired by my colleague who’s at the “you’re still here?” stage of pregnancy.

Suppose you’re conducting a study on pregnancy duration. You’re ready to complete the study and run your analysis, but some women in the study are still pregnant, so you don’t know exactly how long their pregnancies will last. These observations would be right-censored. The “failure,” or birth in this case, will occur after the recorded time.

Now suppose you survey some women in your study at the 250-day mark, but they already had their babies. You know they had their babies before 250 days, but don’t know exactly when. These are therefore left-censored observations, where the “failure” occurred before a particular time.

If we don’t know exactly when some babies were born but we know it was within some interval of time, these observations would be interval-censored. We know the “failure” occurred within some given time period. For example, we might survey expectant mothers every 7 days and then count the number who had a baby within that given week.

Once you set up your data, running the analysis is easy with Minitab Statistical Software. For more information on how to run the analysis and interpret your results, see this blog post, which—coincidentally—is baby-related, too.

If you’re familiar with Lean Six Sigma, then you’re familiar with DMAIC.

DMAIC is the acronym for Define, Measure, Analyze, Improve and Control. This proven problem-solving strategy provides a structured 5-phase framework to follow when working on an improvement project.

This is the first post in a five-part series that focuses on the tools available in Minitab Statistical Software that are most applicable to each phase, beginning with Define.

DMAIC begins once you have identified a problem to solve. The goal of this first phase is to define the project goals and customer deliverables. This includes developing a problem statement and identifying objectives, resources and project milestones.

Dear Readers,

As 2016 comes to a close, it’s time to reflect on the passage of time and changes. As I’m sure you’ve guessed, I love statistics and analyzing data! I also love talking and writing about it. In fact, I’ve been writing statistical blog posts for over five years, and it’s been an absolute blast. John Tukey, the renowned statistician, once said, “The best thing about being a statistician is that you get to play in everyone’s backyard.” I enthusiastically agree!

However, when I first started writing the blog, I wondered about being able to keep up a constant supply of fresh blog posts. And, when I first mentioned to some non-statistician friends that I’d be writing a statistical blog, I noticed a certain lack of enthusiasm. For instance, I heard a variety of comments like, “So, you’ll be writing things along the lines of 9 out of 10 dentists recommend . . .” Would readers even be interested in what I had to say about statistics?

It turns out that with a curious mind, statistical knowledge, data, and a powerful tool like Minitab statistical software, the possibilities are endless. You can play in a wide variety of fascinating backyards! 

The most surprising statistic is that my blog posts have received over 5.5 million views in the past year alone. Never in my wildest dreams did I imagine so many readers when I wrote my first post! It’s a real testament to the growing importance of data analysis that so many people are interested in a blog dedicated to statistics. Thank you all for reading!

Some of the topics I've written about are out of this world. I’ve assessed dolphin communications and compared it to the search for extraterrestrial intelligence and analyzed exoplanet data in the search for the Earth’s twin! (As an aside, my analysis showed that my writing style is similar to dolphin communications. I'll take that as a compliment!)

For more Earthly subjects, I’ve studied the relationship between mammal size and their metabolic rate and longevity. I’ve analyzed raw research data to assess the effectiveness of flu shots first hand. I’ve downloaded economic data to assess patterns in both the U.S. GDP and U.S. job growth. For a Thanksgiving Day post, I analyzed world income data to answer the question of how thankful we should be statistically. As for Easter, I can tell you the date on which it falls in any of 2,517 years, along with which dates are the most and least common.

In the world of politics, I’ve used data to predict the 2012 U.S. Presidential election, analyzed the House Freedom Caucus and the search for the new Speaker of the House, assessed the factors that make a great President, and even helped Mitt Romney pick a running mate. Everyone talks about the weather, so of course I had to analyze that. My family loves the Mythbusters and it was fun applying statistical analyses to some of the myths that they tested (here and here). That's my family and I meeting them in the picture to the right!

Some of my posts have even been a bit surreal. I took my turn at attempting to explain the statistical illusion of the infamous Monty Hall problem. I’ve compared world travel to adjusting scales in graphs (seriously). I wrote a true story about how I drove a plane load of passengers 200 miles to their homes in the context of quality improvement! For Halloween-themed posts, I showed how to go ghost hunting with a statistical mindset and how regression models can be haunted by phantom degrees of freedom. I analyzed the fatality rates in the original Star Trek TV series. I explored how some people can find so many four leaf clovers despite their rarity. And, I wondered whether a statistician can say that age is just a number?

See, not a mention of those dentists...well, not until now. By this point, 9 out of 10 dentists are probably feeling neglected!

I’ve also written many posts aimed at helping those who are learning and performing statistical analyses. I described why statistics is cool based on my own personal experiences and how the whole field of statistics is growing in importance. I showed how anecdotal evidence is unreliable and explained why it fails so badly. And, I took a look forward at how statistical analyses are expanding into areas traditionally ruled by expert judgement.

I zoomed in to cover the details about how to perform and interpret statistical analyses. Some might think that covering the nitty gritty of statistical best practices is boring. Yet, you’d be surprised by the lively discussions we’ve had. We’ve had heated debates and philosophical discussions about how to correctly interpret p-values and what statistical significance does and does not tell you. This reached a fever pitch when a psychology journal actually banned p-values!

We had our difficult questions and surprising topics to grapple with. How high should R-squared be? Should I use a parametric or nonparametric analysis? How is it possible that a regression model can have significant variables but still have a low R-squared? I even had the nerve to suggest that R-squared is overrated! And, I made the unusual case that control charts are also very important outside the realm of quality improvement. Then, there is the whole frequentist versus Bayesian debate, but let’s not go there!

However, it’s true that not all topics about how to perform statistical analyses are riveting. I still love these topics. The world is becoming an increasingly data-driven place, and to produce trustworthy results, you must analyze your data correctly. After all, it’s surprisingly easy to make a costly mistake if you don’t know what you’re doing.

A data-driven world requires an analyst to understand seemingly esoteric details such as: the different methods of fitting curves, the dangers of overfitting your model, assessing goodness-of-fit, checking your residual plots, and how to check for and correct multicollinearity and heteroscedasticity. How do you choose the best model? Do you need to standardize your variables before performing the analysis? Maybe you need a regression tutorial?

You may need to know how to identify the distribution of your data. And just how do hypothesis tests work anyway? F-tests? T-tests? How do you test discrete data? Should you use a confidence interval, prediction interval, or a tolerance interval? How do you know when X causes a change in Y? Is a confounding variable distorting your results? What are the pros and cons of using a repeated measures design? Fisher’s or Welch’s ANOVA? ANOVA or MANOVA? Linear or nonlinear regression?

These may not be “sexy” topics but they are the meat and potatoes of being able to draw sound conclusions from your data. And, based on numerous blog comments, they have been well received by many people. In fact, the most rewarding aspect of writing blog posts has been the interactions I've had with all of you. I've communicated with literally hundreds and hundreds of students learning statistics and practitioners performing statistics in the field. I’ve had the pleasure of learning how you use statistical analyses, understanding the difficulties you face, and helping you resolve those issues.

It's been an amazing journey and I hope that my blog posts have allowed you to see statistics through my eyes―as a key that can unlock discoveries that are trapped in your data. After all, that's the reason why I titled my blog Adventures in Statistics. Discovery is a bumpy road. There can be statistical challenges en route, but even those can be interesting, and perhaps even rewarding, to resolve. Sometimes it is the perplexing mystery in your data that prompts you to play detective and leads you to surprising new discoveries!

To close out the old year, it's good to remember that change is constant. There are bound to be many new and exciting adventures in the New Year. I wish you all the best in your endeavors. 

“We will open the book. Its pages are blank. We are going to put words on them ourselves. The book is called Opportunity and its first chapter is New Year's Day.”   ― Edith Lovejoy Pierce 

May you all find happiness in 2017! Onward and upward!

Jim

The line plot is an incredibly agile but frequently overlooked tool in the quest to better understand your processes.

In any process, whether it's baking a cake or processing loan forms, many factors have the potential to affect the outcome. Changing the source of raw materials could affect the strength of plywood a factory produces. Similarly, one method of gluing this plywood might be better or worse than another.

But what is even more complicated to consider is how these factors might interact. In this case, plywood made with materials obtained from supplier “A” might be strongest when glued with one adhesive, while plywood that uses material from supplier “B” might be strongest when you glued with a different adhesive.

Understanding these kinds of interactions can help you maintain quality when conditions change. But where do you begin? Try starting with a line plot.

Line plots created with Minitab Statistical Software are flexible enough to help you find interactions and response patterns whether you have 2 factors or 20. But while the graph is always created the same way, such changes in scale produce two seemingly distinct types of graph.

With just a few groups…the focus is on interaction effects. In the graph below, a paint company that wants to improve the performance of its products has created a line plot that finds a strong interaction between spray paint formulation and the pressure at which it’s applied.

An interaction is present where the lines are not parallel.

With many groups…the focus is on deviations from an expected response profile. (That's why in the chemical industry this is sometimes called a profile graph.) The line plot below shows a comparison of chemical profiles of a drug from three different manufacturing lines.

Any profile that deviates from the established pattern could suggest quality problems with that production line, but these three profiles look quite similar.

If you’re an experienced Minitab user, these examples may seem familiar. In its various incarnations, the line plot is similar to the interaction plot, to "Calculated X" plots used in PLS, and even to time series plots that appear with more advanced analyses. But the line plot gives you many more options for exploring your data. Here’s another example.

A line plot of the mean sales from a call center shows little interaction between the call script and whether the operators received sales training because the lines are parallel.

But because line plot allows us to examine functions other than the mean, we can see that there is, in fact, an interaction effect in terms of standard deviation. The lines are not parallel. For some reason, the variability in sales seems to be affected by the combination of script and training.

Creating a line plot in Minitab is simple. For example, suppose that your company makes pipes. You’re concerned about the mean diameter of pipes that are produced on three manufacturing lines with raw materials from two suppliers.

Because you’re examining only two factors­—line and supplier—a With Symbols option is appropriate. Use Without Symbols options when you have many groups to consider. Symbols may clutter the graph. Within these categories, you have your choice of data arrangement.

Choose Graph > Line Plot > With Symbols, One Y.
Click OK.

Now, enter the variables to graph. Note that Line Plot allows you to graph a number of different functions apart from the mean.

In Graph variables, enter 'Diameter'.
In Categorical variable for X-scale grouping, enter Line.
In Categorical variable for legend grouping, enter Supplier.
Click OK.

The line plot shows a clear interaction between the supplier and the line that manufacture the pipe. 

The line plot is an ideal way to get a first glimpse into the data behind your processes. The line plot resembles a number of graphs, particularly the interaction plots used with DOE or ANOVA analyses. But, while the function of line plots may be similar, their simplicity makes them an especially appropriate starting point.

It can highlight the variables and the interactions that are worth exploration. Its powerful graphing features also allow you to analyze subsets of your data or to graph different functions of your measurement variable, like standard deviation or count.

Want to learn some simple tricks for preparing your graphs for presentation—specifically, how to add footnotes to your graphs, display your graphs in one layout, and add objects (shapes, text, etc.) to make your graphs easier to interpret? Below I’ll share three tips that can help you get your Minitab graphs presentation-ready!

If you’re looking to add a footnote while you’re in the process of creating a graph, in the dialog box for the graph you are creating, click Labels:

Then you can type your footnote (or modify your graph title and even add a subtitle):

If you’ve already got your graph created and want to add a footnote, just make sure the existing graph is active, then choose Editor> Add:

Note that you can also change the text, font, size, color, or alignment of your footnote (or title or subtitle) by double-clicking it, and then you can move it by dragging and dropping it to a new location on your graph.

Bonus Tip! You can display the project name, worksheet name, date, time, or custom text (such as your company's name) automatically on all the graphs you create. Choose Tools> Options> Graphics> Annotation> My Footnote and select the items that you want to include.

If you want to compare or contrast different graphs or perhaps emphasize a group of graphs for your report or presentation, then the graph layout options in Minitab are for you! Use this option to organize multiple graphs from the same project on one page. Here’s how to do it:

1. With one of the graphs you want to include in the layout active, choose Editor> Layout Tool (the active graph is copied to the first cell in the layout):

2. In Rows, enter the number of rows for the layout.
3. In Columns, enter the number of columns for the layout.
4. To copy graphs to the layout, click the cell where you want to copy the graph and do one of the following:

• In the list box, double-click a graph name.
• In the list box, click a graph name and then click the right arrow button.
• Double-click the image of the selected item below the list box.

5. Click Finish.

Here’s sample of a 2 rows by 1 column graph layout:

And here’s a sample of a 2 rows by 2 column graph layout:

In the time series plot below, a rectangle, comment bubble, text and lines were added to show when a new product was released:

To do this in Minitab, use the Graph Annotation Tools toolbar:

With the graph active, click the item you’d like to add from the toolbar (text, a shape, marker symbols, etc.), and then click and drag on the graph to place item. To edit one the items you’ve already placed on the graph, select it and double-click it.

Looking for more tips for making your graphs presentation-worthy? Check out this topic on the Minitab Support site: Preparing your graphs for presentation

Did you ever get a pair of jeans or a shirt that you liked, but didn't quite fit you perfectly? That happened to me a few months ago. The jeans looked good, and they were very well made, but it took a while before I was comfortable wearing them.

I much prefer it when I can get a pair with a perfect fit, that feel like I was born in them, with no period of "adjustment." 

So which pair do you think I wear more often...the older pair that fits me like a glove, or the newer ones that aren't quite as comfortable? You already know the answer, because I'll bet you have a favorite pair of jeans, too. 

So what does all this have to do with statistical software? Just this: if you can get statistical software that's perfectly matched to how you're going to use it, you're going to feel more comfortable, confident, and at ease when from the second you open it. 

We do strive to make Minitab Statistical Software very easy to use from the first time you launch it. Our roots lie in providing tools that make data analysis easier, and that's still our mission today. But we know a little bit of tailoring can make a garment that feels very good into one that feels great. 

So if you want to tailor your Minitab software to fit you perfectly, we also make that easy—even if you have multiple people using Minitab on the same computer. 

If you're like most people, you want software that gives you the options you want, when you want them. You want a menu has everything organized just the way you like it. And while we're at it, how about a toolbar that gives you immediate access to the tools you know you'll be using most frequently? 

We don't think that's too much to ask. 

In my job, I frequently need to perform a series of analyses on data about marketing and online traffic. It's easy enough to access those tools through Minitab's default menus, but one day I realized I didn't even need to do that—I could just make myself a menu in Minitab that includes the tools I use most frequently. 

Taking this thought from idea to execution was a breeze. I simply right-clicked on the menu bar and selected the "Customize" option. 

There are many more ways you can customize Minitab to suit your needs, including the creation of customized toolbars and individual profiles, which are great if you share your computer with someone who would like to have Minitab customized to their preferences, too. 

Let us know what you've done to customize Minitab so it fits you perfectly!

by Matthew Barsalou, guest blogger

The great Dr. Seuss tells of Mr. Plunger who is the custodian at Diffendoofer School on the corner of Dinkzoober and Dinzott in the town of Dinkerville. The good Mr. Plunger “keeps the whole school clean” using a supper-zooper-flooper-do.

Unfortunately, Dr. Seuss fails to tell us where the supper-zooper-flooper-do came from and if the production process was capable.

Let’s assume the broom boom length was the most critical dimension on the supper-zooper-flooper-do. The broom boom length drawing calls for a length of 55.0 mm with a tolerance of +/- 0.5 mm. The quality engineer has checked three supper-zooper-flooper-do broom booms and all were in specification, so he concludes that there is no reason to worry about the process producing out of specification parts. But we know this not true. Perhaps the fourth supper-zooper-flooper-do broom boom will be out of specification. Or maybe the 1,000th.

It’s time for a capability study, but don’t fire up your Minitab Statistical Software just yet. First we need to plan the capability study. Each day the supper-zooper-flooper-do factory produces supper-zooper-flooper-do broom booms with a change in broom boom material batch every 50th part. A capability study should have a minimum of 100 values and 25 subgroups. The subgroups should be rational: that means the variability within each subgroup should be less than the variability between subgroups. We can anticipate more variation between material batches than within a material batch so we will use the batches as subgroups, with a sample size of four.

Once the data has been collected, we can crank up our Minitab and perform a capability study by going to Stat > Quality Tools > Capability Analysis > Normal. Enter the column containing the measurement values. Then either enter the column containing the subgroup or type the size of the subgroup. Enter the lower specification limit and the upper specification limit, and click OK.

We now have the results for the supper-zooper-flooper-do broom boom lengths, but can we trust our results? A capability study has requirements that must be met. We should have a minimum of 100 values and 25 subgroups, which we have. But the data should also be normally distributed and in a state of statistical control; otherwise, we either need to transform the data, or identify the distribution of the data and perform capability study for nonnormal data.

Dr. Seuss has never discussed transforming data so perhaps we should be hesitant if the data do not fit a distribution. Before performing a transformation, we should determine if there is a reason the data do not fit any distribution.

We can use the Minitab Capability Sixpack to determine if the data is normally distributed and in a state of statistical control. Go to Stat > Quality Tools > Capability Sixpack > Normal. Enter the column containing the measurement values. Then either enter the column containing the subgroup or type the size of the subgroup. Enter the lower specification limit and the upper specification limit and click OK.

There are no out-of-control points in the control chart and the P value is greater than 0.05 so we can reject the null hypothesis of “The data is not normally distributed.” The data is suitable for a capability study.

The within subgroup variation is also known as short term capability and is indicated by Cp and Cpk. The between subgroup variability is also known as long term capability is given as Pp and Ppk. The Cp and Cpk fail to account for the variability that will occur between batches;  Pp and Ppk tell us what we can expect from the process over time.

Both Cp and Pp tell us how well the process conforms to the specification limits. In this case, a Cp of 1.63 tells us the spread of the data is much narrower than the width of the specification limits, and that is a good thing. But Cp and Pp alone are not sufficient. The Cpk and Ppk indicate how spread out the data is relative to the center of the specification limits. There is an upper and lower Cpk and Ppk; however, we are generally only concerned with the lower of the two values.

In the supper-zooper-flooper-do broom boom length example, a Cpk of 1.10 is an indication that the process is off center. The Cpk is 1.63, so we can reduce the number of potentially out-of-specification supper-zooper-flooper-do broom booms if we shift the process mean down to center the process while maintaining the current variation. This is a fortunate situation as it is often easier to shift the process mean than to reduce the process variation.

Once improvements are implemented and verified, we can be sure that the next supper-zooper-flooper-do the Diffendoofer School purchases for Mr. Plunger will have a broom boom that is in specification if only common cause variation is present.

Ahoy, matey! Ye’ve come to the right place to learn about Value Stream Maps (VSM).  Just as a treasure map can lead a band o’ pirates to buried treasures, so too can the VSM lead a process improvement bilge rat to the loot buried deep inside a process! Minitab’s Quality Companion has an easy-to-use VSM tool to guide yer way.

Use a value stream map to illustrate the flow of materials and information as a product or service moves through the value stream. A value stream is the collection of all activities, both value-added and non-value added, that generate a product or service.  The VSM is one of the most useful tools in your tool bag because it helps document the process, identify wasteful activities and spot opportunities to improve.

In this blog post, I look at five reasons why a VSM is like a pirate’s treasure map and one reason why it is not!

Maps have been around since ancient times and are often associated with pirates.  When pirates buried their treasure on a remote island, they relied on the treasure map to lead them back to that crucial spot. 

In Lean, the crucial spot is called the GEMBA.  It’s where the ‘activity is happening,’ so it is the ‘place to be’!  When pirates created their map, they usually started where they buried the gold and drew the map backward. Process improvement practitioners often do just that when creating a value stream map: start at the end of the process and work backward. But whether you start at the end or the beginning, to accurately capture the process and all rework loops, you must go to the GEMBA, walk the process and talk to the operators.

When pirates created a map, they used a scrap of parchment and an ink quill to draw the most important landmarks leading them back to their treasure. Take a cue from the pirates and use pencil and paper to start your VSM. That way you can draw the map fairly quickly and change it easily as you learn more about the process. If you do projects with Quality Companion, you can then create the final map in the VSM tool so you can capture data pertaining to each process step, such as inventory levels, defect rate, and cycle or takt time.

Unless you’re a scallywag, you will notice that pirates use symbols to identify important landmarks on their maps. Mountains are upside-down V’s, a wavy circle is a lake, a skull-and-crossbones represents danger, a dashed line charts the path to follow, and so on, until X marks the spot. 

Similarly, a VSM uses symbols to illustrate the important parts of the value stream such as the process steps, suppliers/customers, inventory, transportation, product/information flow, and so on.

Quality Companion uses these standard, industry-recognized symbols so that everyone in your organization will be able to read and understand your VSM. For a full listing of the symbols available in the Quality Companion VSM tool, press the F1 key to open Help on the web and navigate to the Value Stream Map Shapes section.

Pirates worried that someone could steal their maps and find their loot before they returned to retrieve it. They set traps and used arcane clues to mislead potential thieves.

Like a pirate map, a VSM may seem difficult to decipher at first. But if you pull out your spyglass and look hard for clues, you will find the hidden gold. As you follow the map, keep on the lookout for the dangers: process waste! 

The easiest signs of waste to decipher include the piles of inventory just prior to the bottleneck step, excessive non-value added time, push instead of pull hand-offs, defect rate, scrap rate, equipment downtime, and excessive set-up times—to name a few. Look hard and ask lots of questions of the operators in the process. Often you don’t need to dig deep to find these improvement opportunities.

Shiver me timbers! On the pirate’s treasure map you will find the gold hidden under the big X! Same with VSMs: once you identify the improvement opportunities, use a Kaizen burst symbol to mark that spot. Gather your team of knowledgeable folks and start digging into the process. Look for the sources of waste, broken hand-offs, unclear decision points, rework loops, excessive activities and opportunities for simplification. 

“Dead men tell no tales!” When pirates journeyed back to the site of the hidden treasure, a lot of backstabbing and trickery ensued. Typically, only one pirate arrived alive to claim the loot.

This should not be the case for your VSM effort.

Rarely does one person know all the details about a process!  Work as a team to document the process, collect and validate the data, and then interpret the map and brainstorm solutions together. Finding gold with a VSM is a team effort, not an individual effort.

Next time your process makes you feel like you want to walk the plank, pull out your VSM tools, weigh anchor, and hoist the mizzen! You’ll be glad you did!

Process validation is vital to the success of companies that manufacture drugs and biological products for people and animals. According to the FDA guidelines published by the U.S. Department of Health and Human Services:

“Process validation is defined as the collection and evaluation of data, from the process design state through commercial production, which establishes scientific evidence that a process is capable of consistently delivering quality product.”
— Food and Drug Administration

The FDA recommends three stages for process validation. In this 3-part series, we will briefly explore the stage goals and the types of activities and statistical techniques typically conducted within each. For complete FDA guidelines, see www.fda.gov. 

The goal of this stage is to design a process suitable for routine commercial manufacturing that can consistently deliver a product that meets its quality attributes. It is important to demonstrate an understanding of the process and characterize how it responds to various inputs within Process Design.

Suppose you need to identify the critical process parameters for an immediate-release tablet. There are three process input variables that you want to examine: filler%, disintegrant%, and particle size. You want to find which inputs and input settings will maximize the dissolution percentage at 30 minutes.

To conduct this analysis, you can use design of experiments (DOE). DOE provides an efficient data collection strategy, during which inputs are simultaneously adjusted, to identify if relationships exist between inputs and output(s). Once you collect the data and analyze it to identify important inputs, you can then use DOE to pinpoint optimal settings.

The first step in DOE is to identify the inputs and corresponding input ranges you want to explore. The next step is to use statistical software, such as Minitab, to create an experimental design that serves as your data collection plan.

According to the design shown below, we first want to use a particle size of 10, disintegrant of 1%, and MCC at 33.3%, and then record the corresponding average dissolution% using six tablets from a batch:

Using Minitab’s DOE analysis and p-values, we are ready to identify which X's are critical. Based on the bars that cross the red significance line, we can conclude that particle size and disintegrant% significantly affect the dissolution%, as does the interaction between these two factors. Filler% is not significant.

Optimizing Product Quality

Now that we've identified the critical X's, we're ready to determine the optimal settings for those inputs. Using a contour plot, we can easily identify the process window for the particle size and disintegrant% settings needed to achieve a percent dissolution of 80% or greater.

And that's how you can use design of experiments to conduct the Process Design stage. Next in this series, we'll look at the statistical tools and techniques commonly used for Process Qualification!

Opinions, they say, are like certain anatomical features: everybody has one. Usually that's fine—if everybody thought the same way, life would be pretty boring—but many business decisions are based on opinion. And when different people in an organization reach different conclusions about the same business situation, problems follow. 

Inconsistency and poor quality result when people being asked to make yes / no, pass / fail, and similar decisions don't share the same opinions, or base their decisions on divergent standards. Consider the following examples. 

Manufacturing: Is this part acceptable? 

Billing and Purchasing: Are we paying or charging an appropriate amount for this project? 

Lending: Does this person qualify for a new credit line? 

Supervising: Is this employee's performance satisfactory or unsatisfactory? 

Teaching: Are essays being graded consistently by teaching assistants?

It's easy to see how differences in judgment can have serious impacts. I wrote about a situation encountered by the recreational equipment manufacturer Burley. Pass/fail decisions of inspectors at a manufacturing facility in China began to conflict with those of inspectors at Burley's U.S. headquarters. To make sure no products reached the market unless the company's strict quality standards were met, Burley acted quickly to ensure that inspectors at both facilities were making consistent decisions about quality evaluations. 

Sometimes We Can't Just Agree to Disagree

The challenge is that people can have honest differences of opinion about, well, nearly everything—including different aspects of quality. So how do you get people to make business decisions based on a common viewpoint, or standard?

Fortunately, there's a statistical tool that can help businesses and other organizations figure out how, where, and why people evaluate the same thing in different ways. From there, problematic inconsistencies can be minimized. Also, inspectors and others who need to make tough judgment calls can be confident they are basing their decisions on a clearly defined, agreed-upon set of standards. 

That statistical tool is called "Attribute Agreement Analysis," and using it is easier than you might think—especially with data analysis software such as Minitab. 

What Does "Attribute Agreement Analysis" Mean? 

Statistical terms can be confusing, but "attribute agreement analysis" is exactly what it sounds like: a tool that helps you gather and analyze data about how much agreement individuals have on a given attribute.

So, what is an attribute? Basically, any characteristic that entails a judgment call, or requires us to classify items as this or that. We can't measure an attribute with an objective scale like a ruler or thermometer. The following statements concern such attributes:

• This soup is spicy.
• The bill for that repair is low. 
• That dress is red. 
• The carpet is rough. 
• That part is acceptable. 
• This candidate is unqualified. 

Attribute agreement analysis uses data to understand how different people assess a particular item's attribute, how consistently the same person assesses the same item on multiple occasions, and compares both to the "right" assessment. 

This method can be applied to any situation where people need to appraise or rate things. In a typical quality improvement scenario, you might take a number of manufactured parts and ask multiple inspectors to assess each part more than once. The parts being inspected should include a roughly equal mix of good and bad items, which have been identified by an expert such as a senior inspector or supervisor. 

In my next post, we'll look at an example from the financial industry to see how a loan department used this statistical method to make sure that applications for loans were accepted or rejected appropriately and consistently. 

In my last post on DMAIC tools for the Define phase, we reviewed various graphs and stats typically used to define project goals and customer deliverables. Let’s now move along to the tools you can use in Minitab Statistical Software to conduct the Measure phase.

The goal of this phase is to measure the process to determine its current performance and quantify the problem. This includes validating the measurement system and establishing a baseline process capability (i.e., sigma level).

Before you analyze your data, you should first make sure you can trust it, which is why successful Lean Six Sigma projects begin the Measure phase with Gage R&R. This measurement systems analysis tool assesses if measurements are both repeatable and reproducible. And there are Gage R&R studies available in Minitab for both destructive and non-destructive tests.

Minitab location:Stat > Quality Tools > Gage Study > Gage R&R Study OR Assistant > Measurement Systems Analysis.

When assessing the validity of our data, we need to consider both precision and accuracy. While Gage R&R assesses precision, it’s Gage Linearity and Bias that tells us if our measurements are accurate or are biased.

Minitab location: Stat > Quality Tools > Gage Study > Gage Linearity and Bias Study.

Many statistical tools and p-values assume that your data follow a specific distribution, commonly the normal distribution, so it’s good practice to assess the distribution of your data before analyzing it. And if your data don’t follow a normal distribution, do not fear as there are various techniques for analyzing non-normal data.

Minitab location: Stat > Basic Statistics > Normality Test OR Stat > Quality Tools > Individual Distribution Identification.

Capability analysis is arguably the crux of “Six Sigma” because it’s the tool for calculating your sigma level. Is your process at a 1 Sigma, 2 Sigma, etc.? It reveals just how good or bad a process is relative to specification limit(s). And in the Measure phase, it’s important to use this tool to establish a baseline before making any improvements.

Minitab location: Stat > Quality Tools > Capability Analysis/SixpackOR Assistant > Capability Analysis.

Like Gage R&R and Gage Linearity and Bias studies mentioned above for continuous measurements, this tool helps you assess if you can trust categorical measurements, such as pass/fail ratings. This tool is available for binary, ordinal, and nominal data types.

Minitab location: Stat > Quality Tools > Attribute Agreement AnalysisOR Assistant > Measurement Systems Analysis.

If you’re counting the number of defective items, where each item is classified as either pass/fail, go/no-go, etc., and you want to compute parts per million (PPM) defective, then you can use binomial capability analysis to assess the current state of the process.

Or if you’re counting the number of defects, where each item can have multiple flaws, then you can use Poisson capability analysis to establish your baseline performance.

Minitab location:Stat > Quality Tools > Capability Analysis OR Assistant > Capability Analysis.

As I mentioned in my last post on the Define phase, Six Sigma projects can vary. Every project does not necessarily use the same identical tool set every time, so the tools above merely serve as a guide to the types of analyses you may need to use. And there are other tools to consider, such as flowcharts to map the process, which you can complete using Minitab’s cousin, Quality Companion.

While there are many graph options available in Minitab’s Graph menu, there is no direct option to generate a waterfall chart. This type of graph helps visualize the cumulative effect of sequentially introducing positive or negative values.

In this post, I’ll show you the steps to follow to make Minitab display a waterfall chart even without a "waterfall chart" tool. If you don’t already have Minitab 17, you can download a free 30-day trial here.

For the purpose of this post, I’ll replicate this sample waterfall chart that I found in Wikipedia:

In Minitab, we’ll need to set up the data in table form. Here is how I’ve set up the data in my Minitab 17 worksheet:

The tricky part is adding and subtracting to make sure that each section on each of the five bars is the right height. For example, the height of the Services Revenue bar is 630 (that’s 420 + 210 = 630).

To make the Fixed Costs bar reflect a $170 decrease from $630, we enter Fixed Costs twice in the worksheet with values of 460 and 170 (that’s 630 - 170 = 460). We will sum the two values together when we create the bar chart, and we will use column C3 to make one bar with two sections representing those two values.

To make the graph, go to Graph> Bar chart> A function of a variable> One Y Stack:

Complete the new window like this:

When you click OK in the window above, Minitab will create a graph that looks similar to the one below:

To get the final waterfall chart, the graph above will need to be manually edited. In the example below, I’ve hidden the sections of the bar chart that I don’t want to see. To hide a section of the bar chart, make sure only that section is selected (single-click on the bar you want to edit until only that section is selected) and then double-click to bring up the Edit Bars window. Next, make the selections show in the image below:

In the example below, I repeated the steps above to remove the section of each bar that I wanted to hide. I’ve also manually deleted the legend:

The graph above is almost ready, but to match our initial example I’ll make a few more manual edits as detailed below:

1. Delete the Y-axis Label Sum of Profits by clicking on the label and using the Delete key on the keyboard. I also changed the title of the graph by clicking on the current title and typing in the title I wanted to see.
2. Adjust the Y-axis tick labels to the values in the example by double-clicking on the Y-axis scale to bring up the Edit Scale window, selecting Position of ticks and typing in the values I’d like to see on the Y-axis: 0, 140, 280, 420, 560, 700.
3. Manually change the colors of the Product Revenue and Services Revenue to green by selecting each bar individually, double-clicking to bring up the Edit Bars window and changing the Fill Pattern Background color.
4. Add horizontal gridlines by right-clicking on the graph and choosing Add> Gridlines and selecting Y major ticks. I also double-clicked on one of the gridlines to bring up the Edit Gridlines window and changed the Major Gridlines to Custom and selected a solid line (instead of the default dotted line) so I could match the example more closely.
5. Use the Graph Annotation toolbar to insert a text box (look for a button that looks like a capital T in the toolbars at the top), placing the text box for each bar where I want to see it, typing in the value I want to display ($420K, $210K, $-170K, etc.), and clicking OK. Finally, I double-clicked on each label to bring up the Edit Text window where I used the Font tab to change the font color from black to white.

The final result looks very much like the example shown at the beginning of this post:

I hope you’ve enjoyed reading this post! For more information about editing graphs in Minitab 17, take a look at this online support page.

Previously, I discussed how business problems arise when people have conflicting opinions about a subjective factor, such as whether something is the right color or not, or whether a job applicant is qualified for a position. The key to resolving such honest disagreements and handling future decisions more consistently is a statistical tool called attribute agreement analysis. In this post, we'll cover how to set up and conduct an attribute agreement analysis. 

A busy loan office for a major financial institution processed many applications each day. A team of four reviewers inspected each application and categorized it as Approved, in which case it went on to a loan officer for further handling, or Rejected, in which case the applicant received a polite note declining to fulfill the request. 

The loan officers began noticing inconsistency in approved applications, so the bank decided to conduct an attribute agreement analysis on the application reviewers.

Two outcomes were possible: 

1. The reviewers make the right choice most of the time. If this is the case, loan officers can be confident that the reviewers do a good job, rejecting risky applicants and approving applicants with potential to be good borrowers. 

2. The reviewers too often choose incorrectly. In this case, the loan officers might not be focusing their time on the best applications, and some people who may be qualified may be rejected incorrectly. 

One particularly useful thing about an attribute agreement analysis: even if reviewers make the wrong choice too often, the results will indicate where the reviewers make mistakes. The bank can then use that information to help improve the reviewers' performance. 

A typical attribute agreement analysis asks individual appraisers to evaluate multiple samples, which have been selected to reflect the range of variation they are likely to observe. The appraisers review each sample item several times each, so the analysis reveals how not only how well individual appraisers agree with each other, but also howl consistently each appraiser evaluates the same item. 

For this study, the loan officers selected 30 applications, half of which the officers agreed should receive approval and half which should be rejected. These included both obvious and borderline applications. 

Next, each of the four reviewers was asked to approve or reject the 30 applications two times. These evaluation sessions took place one week apart, to make it less likely they would remember how they'd classified them the first time. The applications were randomly ordered each time.

The reviewers did not know how the applications had been rated by the loan officers. In addition, they were asked not to talk about the applications until after the analysis was complete, to avoid biasing one another. 

You don't need to use software to perform an Attribute Agreement Analysis, but a program like Minitab does make it easier both to plan the study and gather the data, as well as to analyze the data after you have it. There are two ways to set up your study in Minitab. 

The first way is to go to Stat > Quality Tools > Create Attribute Agreement Analysis Worksheet... as shown here: 

This option calls up an easy-to-follow dialog box that will set up your study, randomize the order of reviewer evaluations, and permit you to print out data collection forms for each evaluation session. 

But it's even easier to use Minitab's Assistant. In the menu, select Assistant > Measurement Systems Analysis..., then click the Attribute Agreement Worksheet button:

That brings up the following dialog box, which walks you through setting up your worksheet and printing out data collection forms, if desired. For this analysis, the Assistant dialog box is filled out as shown here: 

After you press OK, Minitab creates a worksheet for you and gives you the option to print out data collection forms for each reviewer and each trial. As you can see in the "Test Items" column below, Minitab randomizes the order of the observed items in each trial automatically, and the worksheet is arranged so you need only enter the reviewers' judgments in the the "Results" column. 

In my next post, we'll analyze the data collected in this attribute agreement analysis. 

T'was the season for toys recently, and Christmas day found me playing around with a classic, the Etch-a-Sketch. As I noodled with the knobs, I had a sudden flash of recognition: my drawing reminded me of the Empirical CDF Plot in Minitab Statistical Software. Did you just ask, "What's a CDF plot? And what's so empirical about it?" Both very good questions. Let's start with the first, and we'll save that second question for a future post.

The acronym CDF stands for Cumulative Distribution Function. If, like me, you're a big fan of failures, then you might be familiar with the cumulative failure plot that you can create with some Reliability/Survival tools in Minitab. (For an entertaining and offbeat example, check out this excellent post, What I Learned from Treating Childbirth as a Failure.) The cumulative failure plot is a CDF.

Even if you're not a fan of failure plots and CDFs, you're likely very familiar with the CDF's famous cousin, the PDF or Probability Density Function. The classic "bell curve" is no more (and no less) than a PDF of a normal distribution.

For example, here's a histogram with a fitted normal PDF for PinLength.MTW, from Minitab's online Data Set Library.

To create this plot, do the following:

1. Download the data file, PinLength.MTW, and open it in Minitab.
2. Choose Graph > Histogram > With Fit, and click OK.
3. In Graph variables, enter Length.
4. Click the Scale button.
5. On the Y-Scale Type tab, choose Percent.
6. Click OK in each dialog box.

The data are from a sample of 100 connector pins. The histogram and fitted line show that the lengths of the pins (shown on the x-axis) roughly follow a normal distribution with a mean of 19.26 and a standard deviation of 2.154. You can get the specifics for each bin of the histogram by hovering over the corresponding bar.

The height of each bar represents the percentage of observations in the sample that fall within the specified lengths. For example, the fifth bar is the tallest. Hovering over the fifth bar reveals that 18% of the bins have lengths that fall between 18.5 mm to 19.5 mm. Remember that for a moment.

Now let's try something a little different.

1. Double-click the y-axis.
2. On the Type tab, select Accumulate values across bins.
3. Click OK.

It looks very different, but it's the exact same data. The difference is that the bar heights now represent cumulative percentages. In other words, each bar represents the percentage of pins with the specified lengths or smaller.

For example, the height of the fifth bar indicates that 55% of the pin lengths are less than 19.5 mm. The height of the fourth bar indicates that 37% of pin lengths are 18.5 or less. The difference in height between the 2 bars is 18, which tells us that 18% of the pins have lengths between 18.5 and 19.5. Which, if you remember, we already knew from our first graph. So the cumulative bars look different, but it's just another way of conveying the same information.

You may have also noticed that the fitted line no longer looks like a bell curve. That's because when we changed to a cumulative y-axis, Minitab changed the fitted line from a PDF to... you guessed it, a cumulative distribution function (CDF). Like the cumulative bars, the cumulative distribution function represents the cumulative percentage of observations that have values less than or equal to X. Basically, the CDF of a distribution gives us the cumulative probabilities from the PDF of the same distribution.

I'll show you what I mean. Choose Graph > Probability Distribution Plot > View Probability, and click OK. Then enter the parameters and x-value as shown here, and click OK.

The "Left Tail" probabilities are cumulative probabilities. The plot tells us that the probability of obtaining a random value that is less than or equal to 16 is about 0.065. That's another way of saying that 6.5% of the values in this hypothetical population are less than or equal to 16.

Now we can create a CDF using the same parameters:

1. Choose Graph > Empirical CDF > Single and click OK.
2. In Graph variables, enter Length.
3. Click the Distribution button.
4. On the Data Display tab, select Distribution fit only.
5. Click OK, then click the Scale button.
6. On the Percentile Lines tab, under Show percentile lines at data values, enter 16.

The CDF tells us that 6.5% of the values in this distribution are less than or equal to 16, as did the PDF.

Let's try another. Double-click the shaded area on the PDF and change x to 19.26, which is the mean of the distribution.

Naturally, because we're dealing with a perfect theoretical normal distribution here, half of the values in the hypothetical population are less than or equal to the mean. You can also visualize this on the CDF by adding another percentile line. Click the CDF and choose Editor > Add > Percentile Lines. Then enter 19.26 under Show percentile lines at data values.

There's a little bit of rounding error, but the CDF tells us the same thing that we learned from the PDF, namely that 50% of the values in the distribution are less than or equal to the mean.

Finally, let's input a probability and determine the associated x-value. Double-click the shaded area on the PDF, but this time enter a probability of 0.95 as shown:

The PDF shows that the x-value that is associated with a cumulative probability of 0.5 is 22.80. Now right-click the CDF and choose Add > Percentile Lines. This time, under Show percentile lines at Y values, enter 95 for 95%.  

Once again, other than a little rounding error, the CDF tells us the same thing as the PDF.

For most people (maybe everyone?), the PDF is an easier way to visualize the shape of a distribution. But the nice thing about the CDF is that there's no need to look up probabilities for each x-value individually: all of the x-values in the distribution and the associated cumulative probabilities are right there on the curve.

Did you ever wonder why statistical analyses and concepts often have such weird, cryptic names?

One conspiracy theory points to the workings of a secret committee called the ICSSNN. The International Committee for Sadistic Statistical Nomenclature and Numerophobia was formed solely to befuddle and subjugate the masses. Its mission: To select the most awkward, obscure, and confusing name possible for each statistical concept.

A whistle-blower recently released the following transcript of a secretly recorded ICSSNN meeting:

"This statistical analysis seems pretty straightforward…"

“What does it do?”

“It describes the relationship between one or more 'input' variables and an 'output' variable. It gives you an equation to predict values for the 'output' variable, by plugging in values for the input variables."

“Oh dear. That sounds disturbingly transparent.”

“Yes. We need to fix that—call it something grey and nebulous. What do you think of 'regression'?”

“What’s 'regressive' about it? 

“Nothing at all. That’s the point!”

“Re-gres-sion. It does sound intimidating. I’d be afraid to try that alone.”

“Are you sure it’s completely unrelated to anything?  Sounds a lot like 'digression.' Maybe it’s what happens when you add up umpteen sums of squares…you forget what you were talking about.”

“Maybe it makes you regress and relive your traumatic memories of high school math…until you  revert to a fetal position?”

“No, no. It’s not connected with anything concrete at all.”

“Then it’s perfect!”

In the first part of this series, we saw how conflicting opinions about a subjective factor can create business problems. In part 2, we used Minitab's Assistant feature to set up an attribute agreement analysis study that will provide a better understanding of where and when such disagreements occur. 

We asked four loan application reviewers to reject or approve 30  selected applications, two times apiece. Now that we've collected that data, we can analyze it. If you'd like to follow along, you can download the data set here.

As is so often the case, you don't need statistical software to do this analysis—but with 240 data points to contend with, a computer and software such as Minitab will make it much easier. 

Last time, we showed that the only data we need to record is whether each appraiser approved or rejected the sample application in each case. Using the data collection forms and the worksheet generated by Minitab, it's very easy to fill in the Results column of the worksheet. 

The next step is to use statistics to better understand how well the reviewers agree with each others' assessments, and how consistently they judge the same application when they evaluate it again. Choose Assistant > Measurement Systems Analysis (MSA)... and press the Attribute Agreement Analysis button to bring up the appropriate dialog box: 

The resulting dialog couldn't be easier to fill out. Assuming you used the Assistant to create your worksheet, just select the columns that correspond to each item in the dialog box, as shown: 

If you set up your worksheet manually, or renamed the columns, just choose the appropriate column for each item. Select the value for good or acceptable items—"Accept," in this case—then press OK to analyze the data.  

Minitab's Assistant generates four reports as part of its attribute agreement analysis. The first is a summary report, shown below: 

The green bar at top left of the report indicates that overall, the error rate of the application reviewers is 15.8%. That's not as bad as it could be, but it certainly indicates that there's room for improvement! The report also shows that 13% of the time, the reviewers rejected applications that should be accepted, and they accepted applications that should be rejected 18% of the time. In addition, the reviewers rated the same item two different ways almost 22% of the time.

The bar graph in the lower left indicates that Javier and Julia have the lowest accuracy percentages among the reviewers at 71.7% and 78.3%, respectively. Jim has the highest accuracy, with 96%, followed by Jill at 90%.

The second report from the Assistant, shown below, provides a graphic summary of the accuracy rates for the analysis.

This report illustrates the 95% confidence intervals for each reviewer in the top left, and further breaks them down by standard (accept or reject) in the graphs on the right side of the report. Intervals that don't overlap are likely to be different. We can see that overall, Javier and Jim have different overall accuracy percentages. In addition, Javier and Jim have different accuracy percentages when it comes to assessing those applications that should be rejected. However, most of the other confidence intervals overlap, suggesting that the reviewers share similar abilities. Javier clearly has the most room for improvement, but none of the reviewers are performing terribly when compared to the others. 

The Assistant's third report shows the most frequently misclassified items, and individual reviewers' misclassification rates:

This report shows that App 9 gave the reviewers the most difficulty, as it was misclassified almost 80% of the time. (A check of the application revealed that this was indeed a borderline application, so the fact that it proved challenging is not surprising.) Among the reject applications that were mistakenly accepted, App 5 was misclassified about half of the time. 

The individual appraiser misclassification graphs show that Javier and Julia both misclassified acceptable applications as rejects about 20% of the time, but Javier accepted "reject" applications nearly 40% of the time, compared to roughly 20% for Julia. However, Julia rated items both ways nearly 40% of the time, compared to 30% for Javier. 

The last item produced as part of the Assistant's analysis is the report card:

This report card provides general information about the analysis, including how accuracy percentages are calculated. It also can alert you to potential problems with your analysis (for instance, if there were an imbalance in the amount of acceptable to rejectable items being evaluated); in this case, there are no alerts we need to be concerned about. 

The results of this attribute agreement analysis give the bank a clear indication of how the reviewers can improve their overall accuracy. Based on the results, the loan department provided additional training for Javier and Julia (who also were the least experienced reviewers on the team), and also conducted a general review session for all of the reviewers to refresh their understanding about which factors on an application were most important. 

However, training may not always solve problems with inconsistent assessments. In many cases, the criteria on which decisions should be based are either unclear or nonexistent. "Use your common sense" is not a defined guideline! In this case, the loan officers decided to create very specific checklists that the reviewers could refer to when they encountered borderline cases. 

After the additional training sessions were complete and the new tools were implemented, the bank conducted a second attribute agreement analysis, which verified improvements in the reviewers' accuracy. 

If your organization is challenged by honest disagreements over "judgment calls," an attribute agreement analysis may be just the tool you need to get everyone back on the same page. 

Have you ever wished your control charts were better?  More effective and user-friendly?  Easier to understand and act on?  In this post, I'll share some simple ways to make SPC monitoring more effective in Minitab.

I worked for several years in a large manufacturing plant in which control charts played a very important role. Virtually thousands of SPC (Statistical Process Control) charts were used to monitor processes, contamination in clean rooms, monitor product thicknesses and shapes as well as critical equipment process parameters. Process engineers regularly checked the control charts of the processes they were responsible for. Operators were expected to stop using equipment as soon as an out of control alert appeared and report this incident back to their team leader.

But some of the problems we faced had little to do with statistics. For example, comments entered by the operators were often not explicit at all. Control chart limits were not updated regularly and were sometimes not appropriate due to process changes in time. Also, there was confusion about the difference between control limits and specification limits, so even when drifts from the target were clearly identifiable, some process engineers were reluctant to take action as long as their data remained within specifications.

Other problems could be solved with a better knowledge of statistics. For example, some processes were cyclical in nature, and therefore the way subgroups were defined was critical. Also, since the production was based on small batches of similar parts, the within-batch variability was often much smaller than the between-batch variability (simply because the parts within a batch had been processed in very similar conditions). This lead to inappropriate control limits when standard X-bar control charts were used.

Let's look at some simple ways to make SPC monitoring more effective in Minitab. In addition to creating standard control charts, you can use Minitab to:

1. Import data quickly to identify drifts as soon as possible.
2. Create Pareto charts to prevent special causes from reoccurring.
3. Account for atypical periods to avoid inflating your control limits.
4. Visually manage SPC alerts to quickly identify the out-of-control points.
5. Choose the right type of charts for your process.

To ensure that your control charts are up to date in Minitab, you can right click on them and choose “Automatically update Graphs.” However, Minitab is not always available on the shop floor, so the input data often must be saved in an Excel file or in a database.

Suppose that the measurement system generates an XML, Excel or text file, and that this data needs to be reconfigured and manipulated in order to be processed in an SPC chart in Minitab. You can automate these using a Minitab macro.

This macro might automatically retrieve data from an XML or a Text file or from a database (using Minitab's ODBC “Open Data Base Connectivity” functionality) into a Minitab worksheet, or transpose rows into columns, stack columns, or merge several files into one etc. This macro would enable you to obtain a continuously updated Minitab worksheet -- and consequently a continuously updated control chart.

You could easily launch the macro just by clicking on a customized icon or menu in Minitab (see the graph below) in order to update the resulting control chart.

Alternatively, if the macro is named Startup.mac, it will launch whenever you launch Minitab. If you're using Minitab to enable process operators or engineers to monitor control charts, you could also customize Minitab's toolbars and icons in order to show only the relevant toolbars and icons and focus on SPC.

The product support section of our website has information on adding a button to a menu or toolbar that will update data from a file or a database.

Statistical Process Control may be used to identify the true root causes (the so-called special causes) of quality problems from the surrounding process noise (the so-called common causes). The root causes of quality issues need to be truly understood in order to prevent reoccurrence.

A Pareto chart of the causes for out-of-control points might be very useful to identify which special causes occur most frequently.

Comments can be entered in a column of the Minitab worksheet for each out-of-control point. These comments should be standardized for each type of problem. A list of keywords displayed in the Minitab worksheet would help operators enter meaningful keywords, instead of comments that differ each time. Then a Pareto chart could be used to identify the 20% causes that generate 80% of your problems, based on the (standardized) comments entered in the worksheet.

Comments can even be displayed in the SPC chart by using the annotation toolbar.  Click on the T (text) icon of the Graph Annotation toolbar.

Atypical periods (due to measurement issues, outliers, or a quality crisis) may artificially inflate your control chart limits. In Minitab, control limits may be calculated according to a reference period (one with standard, stable /predictable behavior), or the atypical period may be omitted so that control limits are not affected.

In Minitab, go to Options in the control chart dialogue box, look for the Estimate Tab and select the subgroups to be omitted (untypical behavior, outliers), or use only some specified sub-groups to set reference periods. Although the atypical period will still get displayed on the control chart, it won't affect the way your control limits are estimated.

If a reference period has been selected, you will probably need to update it after a certain period of time to ensure that this selection is still relevant.

If the number of control charts you deal with is very large, and you need to quickly identify processes that are drifting away from the target, your could display all control charts in a Tile format (go to Window > Tile). When the latest data (i.e., the last row of the worksheet) generates an out-of-control warning, you can have the control chart become completely red, as shown in the picture below:

You can do this by going to Tools > Options. Select “Control Charts and Quality Tools” on the list, then choose Other. Under the words “When last row of data causes a new test failure for any point,” check the box that says "Change color of chart." Note that the color will change according to the last row (latest single value) not according to the latest subgroup, so this option is more effective when collecting individual values.

When it comes to control charts, one size does not fit all. That's why you'll see a wide array of options when you select Stat > Control Charts. Be sure that you're matching the control chart you're using to the type of data and information you want to monitor. For example, if your subgroups are based on batches of products, I-MR-R/S (within/between) charts are probably best suited to monitor your process.

If you're not sure which control chart to use, you can get details about each type from the Help menu in Minitab, or try using the Assistant menu to direct you to the best test for your situation.