Category Archives: Lean Six Sigma

Why the Ban on P-Values? And What Now?

Just recently, the editors of the academic journal Basic and Applied Social Psychology have decided to ban p-values: that’s right, the nexus for inferential decision making… gone! This has created quite a fuss among anyone who relies on significance testing and p-values to do research (especially those, presumably, in social psychology who were hoping to submit a paper to that journal any time soon). The Royal Statistical Society even shared six interesting letters from academics to see how they felt about the decision.

These letters all tell a similar story: yes, p-values can be mis-used and mis-interpreted, and we need to be more careful about how we plan for — and interpret the results of — just one study! But not everyone advocated throwing out the method in its entirety. I think a lot of the issues could be avoided if people had a better gut sense of what sampling error is… and how easy it is to encounter (and as a result, how easy it can be to accidentally draw a wrong conclusion in an inference study just based on sampling error). I wanted to do a simulation study to illustrate this for my students.

The Problem

You’re a student at a university in a class full of other students. I tell you to go out and randomly sample 100 students, asking them what their cumulative GPA is. You come back to me with 100 different values, and some mean value that represents the average of all the GPAs you went out and collected. You can also find the standard deviation of all the values in your sample of 100. Everyone has their own unique sample.

“It is misleading to emphasize the statistically significant findings of any single team. What matters is the totality of the evidence.” – John P. A. Ioannidis in Why Most Published Research Findings are False

It’s pretty intuitive that everyone will come back with a different sample… and thus everyone will have a different point estimate of the average GPA that students have at your university. But, according to the central limit theorem, we also know that if we take the collection of all the average GPAs and plot a histogram, it will be normally distributed with a peak around the real average GPA. Some students’ estimates will be really close to the real average GPA. Some students’ estimates will be much lower (for example, if you collected the data at a meeting for students who are on academic probation). Some students’ estimates will be much higher (for example, if you collected the data at a meeting for honors students). This is sampling error, which can lead to incorrect inferences during significance testing.

Inferential statistics is good because it lets us make decisions about a whole population just based on one sample. It would require a lot of time, or a lot of effort, to go out and collect a whole bunch of samples. Inferential statistics is bad if your sample size is too small (and thus you haven’t captured the variability in the population within your sample) or have one of these unfortunate too-high or too-low samples, because you can make incorrect inferences. Like this.

The Input Distribution

Let’s test this using simulation in R. Since we want to randomly sample the cumulative GPAs of students, let’s choose a distribution that reasonably reflects the distribution of all GPAs at a university. To do this, I searched the web to see if I could find data that might help me get this distribution. I found some data from the University of Colorado Boulder that describes GPAs and their corresponding percentile ranks. From this data, I could put together an empirical CDF, and then since the CDF is the integral of the PDF, I approximated the PDF by taking the derivatives of the CDF. (I know this isn’t the most efficient way to do it, but I wanted to see both plots):

score <- c(.06,2.17,2.46,2.67,2.86,3.01,3.17,3.34,3.43,3.45,
perc.ranks <- c(0,10,20,30,40,50,60,70,75,76,77,78,79,80,81,
fn <- ecdf(perc.ranks)
xs <- score
ys <- fn(perc.ranks)
slope <- rep(NA,length(xs))
for (i in 2:length(xs)) {
 slope[i] <- (ys[i]-ys[i-1])/(xs[i]-xs[i-1])
slope[1] <- 0
slope[length(xs)] <- slope[length(xs)-1]

Then, I plotted them both together:

plot(xs,slope,type="l",main="Estimated PDF")
plot(xs,ys,type="l",main="Estimated CDF")


I looked around for a distribution that might approximate what I saw. (Yes, I am eyeballing.) I found the Stable Distribution, and then played around with the parameters until I plotted something that looked like the empirical PDF from the Boulder data:

x <- seq(0,4,length=100)
hx <- dstable(x, alpha=0.5, beta=0.75, gamma=1, delta=3.2)


The Simulation

First, I used pwr.t.test to do a power analysis to see what sample size I needed to obtain a power of 0.8, assuming a small but not tiny effect size, at a level of significance of 0.05. It told me I needed at least 89. So I’ll tell my students to each collect a sample of 100 other students.

Now that I have a distribution to sample from, I can pretend like I’m sending 10,000 students out to collect a sample of 100 students’ cumulative GPAs. I want each of my 10,000 students to run a one-sample t-test to evaluate the null hypothesis that the real cumulative GPA is 3.0 against the alternative hypothesis that the actual cumulative GPA is greater than 3.0. (Fortunately, R makes it easy for me to pretend I have all these students.)

sample.size <- 100
numtrials <- 10000
p.vals <- rep(NA,numtrials)
gpa.means <- rep(NA,numtrials) <- 3.00
for (j in 1:numtrials) {
     r <- rstable(n=1000,alpha=0.5,beta=0.75,gamma=1,delta=3.2)
     meets.conds <- r[r>0 & r<4.001]
     my.sample <- round(meets.conds[1:sample.size],3)
     gpa.means[j] <- round(mean(my.sample),3)
     p.vals[j] <- t.test(my.sample,,alternative="greater")$p.value
     if (p.vals[j] < 0.02) {
          # capture the last one of these data sets to look at later
     capture <- my.sample

For all of my 10,000 students’ significance tests, look at the spread of p-values! They are all over the place! And there are 46 students whose p-values were less than 0.05… and they rejected the null. One of the distributions of observed GPAs for a student who would have rejected the null is shown below, and it looks just fine (right?) Even though the bulk of the P-Values are well over 0.05, and would have led to the accurate inference that you can’t reject the null in this case, there are still plenty of values that DO fall below that 0.05 threshold. 

> summary(p.vals)
 Min. 1st Qu. Median Mean 3rd Qu. Max. 
0.005457 0.681300 0.870900 0.786200 0.959300 1.000000 
> p.vals.under.pointohfive <- p.vals[p.vals<0.05]
> length(p.vals.under.pointohfive)
[1] 46
> par(mfrow=c(1,2))
> hist(capture,main="One Rogue Sample",col="purple")
> boxplot(p.vals,main="All P-Values")


Even though the p-value shouted “reject the null!” from this rogue sample, a 99% confidence interval shows that the value I’m testing against… that average cumulative GPA of 3.0… is still contained within the confidence interval. So I really shouldn’t have ruled it out:

> mean(capture) + c(-1*qt(0.995,df=(sample.size-1))*(sd(capture)/sqrt(sample.size)),
+ qt(0.995,df=(sample.size-1))*(sd(capture)/sqrt(sample.size)))
[1] 2.989259 3.218201
> t.test(capture,,alternative="greater")$p.value
[1] 0.009615011

If you’re doing real research, how likely are you to replicate your study so that you know if this happened to you? Not very likely at all, especially if collecting more data is costly (in terms of money or effort). Replication would alleviate the issues that can arise due to the inevitable sampling error… it’s just that we don’t typically do it ourselves, and we don’t make it easy for others to do it. Hence the p-value controversy.

What Now?

What can we do to improve the quality of our research so that we avoid the pitfalls associated with null hypothesis testing completely, or, to make sure that we’re using p-values more appropriately?

  • Make sure your sample size is big enough. This usually involves deciding what you want the power of the test to be, given a certain effect size that you’re trying to detect. A power of 0.80 means you’ll have an 80% chance of detecting an effect that’s actually there. However, knowing what your effect size is prior to your research can be difficult (if not impossible).
  • Be aware of biases that can be introduced by not having a random enough or representative enough sample.
  • Estimation. In our example above we might ask “How much greater than 3.0 is the average cumulative GPA at our university?” Check out Geoff Cummings’ article entitled “The New Statistics: Why and How” for a roadmap that will help you think more in terms of estimation (using effect sizes, confidence intervals, and meta-analysis).
  • Support open science. Make it easy for others to replicate your study. If you’re a journal reviewer, consider accepting more articles that replicate other studies, even if they aren’t “novel enough”.

I am certain that my argument has holes, but it seems to be a good example for students to better embrace the notion of sampling error (and become scared of it… or at least more mindful). Please feel free to suggest alternatives that could make this a more informative example. Thank you!

[ALSO… this xkcd cartoon pretty much nails the whole process of why p-values can be misleading. Enjoy.]

Top 10 Statistics Topics for the Six Sigma Black Belt (CSSBB) Exam

Image Credit: Doug Buckley (

Image Credit: Doug Buckley (

[IMPORTANT NOTE! As of April 20, 2015 I now have a NEW FAVORITE introductory statistics textbook… the one I’ve always dreamed of having, but it just never existed before. But today it does!! <3]

Not too long ago, Darrah Turman from New Jersey contacted me for some additional insight into preparing for the ASQ Certified Six Sigma Black Belt (CSSBB) exam. He’s taking it in March, and like many prospective Black Belts, he’s most concerned about the statistics parts of the exam… it’s been many years since he’s had a statistics course.

As a result, I’m going to start a series of blog posts over the next two weeks that you can follow along with if you’re busily getting ready for your exam. Today, we’ll start with one of Darrah’s questions: How do I focus on the right statistics? I’ve decided to post my “Top 10 Statistics Topics” that seem to be featured heavily in Six Sigma. 

Here are My Top 10 Six Sigma Statistics Topics!

  1. Central Limit Theorem – This is the magic that serves as the foundation for so much of what quality professionals practice. In short, whenever you take many samples for which you have a sum or an average value that you’ve computed over that sample, the distribution of the whole collection of sums or means is going to be normal!! This is why when we’re spot checking parts or products in quality control, we take batch averages and know they’re going to be distributed normally. Find out more here!
  2. Know Your Distributions! – Distributions come in many shapes and sizes, and you should be familiar with how to describe and characterize them (also, be able to recognize their equations). Continuous, discrete, normal, Poisson, binomial, hypergeometric, exponential, Weibull, uniform, symmetric, unimodal, bimodal… you should be familiar with all the words that describe distributions.
  3. Know Your Inference Tests! – It’s helpful to have a general sense of which inference test is appropriate for which kind of problem. For example, if you’re trying to figure out whether two categorical variables are independent, that’s a Chi square test of independence. If you’re trying to figure out whether a mean matches a particular standard, target, or recommended value, that’s a one-sample t-test. As part of knowing your inference tests, you should know what the form of the null hypothesis is for each test, as well as the form for each incarnation of the alternative hypothesis (there will be between one and three of them for each test).
  4. Type I, Type II, and Power Analysis[Book Chapter + PPT] – If you’re planning a statistical inference test, it’s important to know how big a sample size you need so that your results will be statistically significant, and you’ll also need to balance the trade-offs between the different types of errors you can encounter. This chapter will help you do all that.
  5. Computing Confidence Intervals – Just by knowing the average and standard deviation of a small sample size, you can use the Student’s t distribution to quickly and easily compute a confidence interval, because all confidence intervals come in the form Estimate +/- Margin of Error. The most complex part is learning how to look up the t value for the appropriate confidence interval size, and degrees of freedom. (Confused as to whether you should use the normal distribution or the t distribution? Don’t be… always use the t distribution. As your sample size gets bigger and bigger, the shape of the t distribution will get more and more like the shape of the corresponding normal distribution, until they are exactly the same.)
  6. Using the Normal Model to Find Areas Under the Curve[Book Chapter + PPT] – It’s really good to be familiar with z-score problems. In addition to making you more comfortable with the normal model, it’s a useful technique for finding the probability of observing values in a particular range.
  7. Understanding Scatterplots, Correlation Coefficient (r), and Coefficient of Determination (R2) – Scatterplots help us see the relationship between values of two quantitative variables. Correlation tells us how much scatter is in the data, and the coefficient of determination tells us what proportion of the variability in the data is explained by a (typically linear) model.
  8. Process Capability Problems – You should be able to tell the difference between your Cp’s and Cpk’s, and perform basic calculations. Also know that if your data is not normal, you’re going to have to use some kind of data transformation before you determine process capability.
  9. Know Your Control Charts! – There are many different incarnations of control charts. You should be able to distinguish your variables from your attributes, and understand when to apply the various kinds of control chart (along with basic calculations).
  10. Logit-Probit & Odds Ratios – These models help you deal with situations where there is a binary response variable. Basic familiarity with what the regression models do, and how to calculate odds, should be a part of your study plan.

Enjoy! Check back for more chapters throughout February 2015.

Top Books Every Quality Professional Should Read

jones-qmIn January 2015, Julia McIntosh shared what the ASQ staff believe are the “Top 8” books every quality professional should have on their shelf. Before I read her blog post, I thought about what would constitute my own personal favorites… and I was happy to see that her list and my list were well aligned! However, there are two other books that I’d add to ASQ’s “Top 8” — rounding it out to a “Top 10”. Here they are:

Out of the Crisis, by W. Edwards Deming: I’m including this book as a result of my 2013 research, published in ASQ’s Quality Management Journal (QMJ), that examined all of the research articles in the first 15 years of the QMJ to see what resources and references were the most central to the citation network. This classic 1986 book topped the list — it informs the most research articles that have been published by QMJ to date. As a result, everyone should read it! Keep in mind that this was written 30 years ago… and as a result, you have to read it with the zeitgeist of the 1980’s in mind. It’s a unique look into the quality transformation that many organizations were experiencing during the time, and provides fascinating insights into the core philosophy of quality improvement that many of us still honor and promote. (Let me know if you’d like me to send you a copy of my 2013 article, which also provides a research agenda for the future.)

Quality Management for Organizations Using Lean Six Sigma Techniques, by Erick C. Jones:  This book is, in my opinion, the best overview of quality management available… integrating basic principles, Lean, and Six Sigma in such an articulate and elegant way that it has encouraged me to design an entire college course around it. Here is the book review I wrote that appeared in the July 2014 QMJ:

                This book aims to “establish the concepts and principles by which students… practitioners, and quality managers will learn about Lean Six Sigma and its origins… and how it can be integrated into manufacturing, logistics, and health care operations.” Despite its broad goal, in 29 chapters, this book delivers. Section I provides an overview of quality management, quality awards, and key standards. The highlight is Chapters 4 through 6, which describe Lean and Six Sigma separately, followed by a very nice and concise articulation of the “real difference” that characterizes Lean Six Sigma, and encourages practitioners to find the appropriate balance for each project, given its particular context.

Section II examines Lean Six Sigma from the level of the organization as a whole. Chapters within this section explain how to qualitatively and economically justify a Lean Six Sigma project, data-driven approaches for how an organization can decide which projects to resource, how to assess the relationship between LSS efforts and firm performance, benchmarking at the organizational level, and considerations for human resources policies to ensure that the right people are recruited to perform key LSS activities. Section III starts by covering basic concepts of statistics, but then moves on to describe each phase of the Define, Measure, Analyze, Improve, and Control (DMAIC) methodology in detail. There is enough information provided in each of these areas to easily navigate a Six Sigma project in practice.

Section IV is unique and powerful, focused entirely on comprehensive case studies, many of which include using radio frequency identification (RFID). Section V covers roles and responsibilities of Six Sigma professionals, descriptions of certifications and belt levels, and how these individuals typically interact as a project is chartered and executed. Limited case studies are provided throughout the text that effectively supplement the material. Although the case studies do not provide extensive technical detail, they are still instructive and very useful. There are also appendices scattered throughout the book which vary in content and quality. For example, Appendix 3B starts out by stating that its purpose is to compare quality management practices in the U.S. and Mexico. However, even though testable hypotheses are presented along with data, there is no connection made between analysis of the data and what insights it provides regarding the hypotheses. Against the backdrop of the rest of the book, though, such minor issues should not be a concern.

In this reviewer’s opinion, this is the most comprehensive book to date covering Lean Six Sigma in a completely integrated fashion, with material that will be equally valuable to managers, practitioners, and instructors who teach quality management or quality engineering. This is a fantastic guidebook for certification as well, comparable to Kubiak and Benbow’s (2009) book, The Certified Six Sigma Black Belt Handbook. It is sure to have lasting value on many bookshelves.

A High-Quality Academic Book Review

qmj-coverexampleI’ve recently been assigned the role of Book Review Editor for ASQ’s Quality Management Journal starting with the second issue in 2013, under the guidance of new Editor, Larry Fredendall of Clemson University. As we are preparing our book reviews for this issue, Matthias Thurer (who will also be preparing regular reviews with me) asked me for guidelines and what constitutes a “good” review. Here is my message for Matthias, as well as for any of you who are interested in preparing a book review for an academic journal.

In my opinion, the book review should be 500 to 900 words and discuss some or all of the following, as appropriate. These questions, which have been adapted from, are consistent with the excellent structure adhered to by the late James Kohnen who served as the QMJ Book Review Editor for many years:

  • What are the 1-3 main messages of the book?
  • Does the book achieve its stated goals?
  • Is the book a contribution to the field or discipline, and if so, what is that primary contribution? 
  • Does the book relate to a current debate or trend in the field and if so, how? 
  • Is the book well-written? What is the writing style and who would it appeal to?
  • How accurate is the information (e.g., the footnotes, bibliography, dates)? Who would benefit from reading this book? 
  • How does the book compare to other books in the field? 
  • If it is a textbook, what courses can it be used in and how clear is the book’s structure and examples?

If you know of a recently released (or pre-release) book that is relevant to academics and practitioners in quality management, or would like to prepare a book review for our pipeline into the QMJ, please let me know by email (at myfirstname dot mylastname at gmail)! We will be including 3-5 book reviews in each issue of the QMJ.

I invite you to add to this discussion – as a reader or writer, what are your criteria for a high-quality book review? Please share in the comments.

Cramming for Your Six Sigma Black Belt Exam?

Nervous about your Six Sigma exam?

Are you making last minute preparations for your ASQ Certified Six Sigma Black Belt (CSSBB) exam? If so, you’re probably reviewing your notes, hoping that you’re bringing all the right stuff in with you. When I passed my CSSBB on the first attempt, I found that I had GREAT notes with me, and I’d like to share them with you!!



The attached PDFs contain PRECISELY what I carried with me into the exam, along with a few books and a handful of good habits and good luck charms.

[IMPORTANT NOTE! As of April 20, 2015 I now have a NEW FAVORITE introductory statistics textbook… the one I’ve always dreamed of having, but it just never existed before. But today it does!! <3]

[Note: On February 9, 2015 I also added my Top 10 Statistics Topics for the CSSBB Exam to this blog]


An Easy Trick to Reduce Your Resistance to Losing Weight

(Image Credit: Doug Buckley of

Measurement is an important aspect of assuring and improving quality(*). As a result, I think about it often, especially in the context of maintaining and losing weight. My BMI is not bad (23.5) but I don’t like to exercise, so I try to eat without reckless abandon. But I have one little tiny problem.

“Weigh Yourself Often” is a commonly reported success strategy for losing weight. But what if you’re too scared to step on the scale???  That kind of gets in the way of being able to weigh yourself a lot.

I hadn’t stepped on the scale to weigh myself in about… well… a year. I admit, I’m scared of it. In fact, every time I go to the doctor I specifically tell them NOT to tell me what I weigh – unless it’s REALLY GOOD. (Usually they say nothing, which I’ve never been able to interpret. I’m hoping that they just don’t want to speculate what I would consider “good”.) I don’t want to hop on the scale and see a number that makes me feel lousy about myself all day (and maybe the next day… and the next).

I just know that it’s an invitation to disaster to see those HUGE numbers upon which I’ll allow an entire coral reef of self-loathing to grow uninhibited, attracting the slithery fish of dismay.

But a few days ago, I put on a pair of dress pants that I hadn’t worn in a while, and they almost fell off. I had to make sure I didn’t stand up too straight or accidentally suck in my gut while I was wearing them, otherwise they would have fallen off. (I have to wear them again next Friday and I’m going to safety pin them together to be safe.) As you can imagine, this made me feel pretty good, and stirred belligerence in the face of the bathroom scale!! So I climbed on the scale this morning in optimistic defiance and saw a number that was pretty darn good. If I lose 10 lbs, I will weigh the same as I did in junior high. So I think I’m pretty motivated to bump off those extra 10 just to say “I did it”.

I did have a contingency plan, though. I realized that the thing holding me back from actively monitoring and reducing my weight was the NEGATIVE EMOTION associated with getting on the scale.

The key is to MEASURE in a way that doesn’t stimulate those negative emotions. So if you live in the US and want to lose POUNDS, set your scale to KILOGRAMS. Start weighing yourself using a measurement scale that you have no psychological or emotional attachment (or resistance) to. The first number you see will mean nothing to you, and as you actively work to reduce your weight, that number will go down. You will not be scared of the scale any more. After you start feeling good, then feel free to convert your new weight back into the measurement scale you’re more familiar with. The new number you weigh might not be your target weight, but at least you will know it’s a weight at which you feel good.

And isn’t that the point?

(*) “Measurements provide critical data and information about key processes, outputs, and results. When supported by sound analytical approaches that project trends and infer cause-and-effect relationships, measurement provide an objective foundation for learning, leading to better customer, operational, and financial performance.” – Evans & Dean, “Total Quality: 3rd Ed.”

How to Pass Your ASQ Certified Six Sigma Black Belt (CSSBB) Exam

[IMPORTANT NOTE! As of April 20, 2015 I now have a NEW FAVORITE introductory statistics textbook… the one I’ve always dreamed of having, but it just never existed before. But today it does!! <3]

[Note: On February 9, 2015 I added my Top 10 Statistics Topics for the CSSBB Exam]

[Note: On October 4, 2012 I posted the notes I brought into the exam. You might want to check them out.]

* * * * * * * *

(Or more appropriately maybe… how I did it, and what I wish someone had blogged about before I sat for the exam! This is the chronicle of my CSSBB experience.)

I just took my ASQ Six Sigma Black Belt (CSSBB) exam… and PASSED! On the FIRST TRY!! (My reaction upon hearing the news was… “I am a statistics NINJA!!!” A very academic friend corrected me, and said no – not quite – the CSSBB is more like a learner’s permit for a PhD in statistics. OK, that’s cool too.)

My intent in this post is to share with you what I believe helped me get through this very daunting 150-question, 4-hour, heavy-on-the-math multiple choice exam. (Relevant superstitions and helpful snacks are described elsewhere.) This was a particular achievement for me, because although I had been doing small scale Six Sigma projects for several years, I originally intended to take the exam in the fall of 2008… and just didn’t get around to it. I had, at that time, recently completed a couple of doctoral level statistics courses and so I felt super powerfully capable at the time. But what inevitably happens is that as the days go by, and you don’t use the knowledge for practical problem solving, you get rusty and you forget.

Fast forward three years, to the fall of 2011.

When I took the plunge and signed up for one of the most recent offerings of the exam, I knew I had a lot of ground to re-cover before sitting to take the test. I knew I’d have to order some books or flashcards and spend a lot of quality time with them. I knew I’d have to refresh my memory on the nooks and crannies of all those statistical tests, especially the ones that are most frequently used in manufacturing situations. So my first step was to search Google to see if anyone had posted their personal experiences studying for – and hopefully succeeding with – the ASQ CSSBB exam.

I wanted to know: What resources helped? What resources didn’t help? What books were the most useful references to you as you were studying? Are the flashcards useful? I searched and searched all over the web, but couldn’t find any useful advice. I used search terms like “cssbb advice,” “how I passed my Six Sigma Black Belt exam,” “best resources for the Six Sigma Black Belt exam” and “best study guides for the Six Sigma Black Belt exam.” No luck. Everything led me back to companies trying to sell their training sessions. I didn’t want a training session… I wanted practical, free advice from someone who had been in my shoes not too much earlier than me.

So here it is! Feel free to post some comments if any of this advice is helpful, or if you want to add information about what you found useful when you were studying. (Remember, personal experiences with CSSBB prep are hard to find on the web, so anything you contribute is bound to be helpful to people who are actively preparing to be certified.)

#1 CSSBB Primer from the Quality Council of Indiana

BEST. Book. Ever. I ordered the CSSBB Primer as well as the CD with the practice exam questions, and although I was daunted by the sheer heft of the book, the large fonts make this reference a pleasure to get to know. It feels like someone is giving you all the essential knowledge you need for the exam, along with a cookie, a glass of milk, a hug, and a heartfelt “you can do it!!”

I read through the entire book, underlined definitions or phrases that I thought were important, and used post-it notes to tab topics that I thought I’d want easy access to during the exam.

Do ALL the questions in the blue part of the CSSBB Primer. It will take time… for me, it took about 3 weeks, working on about 10 to 20 questions a day. Understand not only what the right answer is for each question, but also WHY THE OTHER OPTIONS ARE WRONG. You won’t be able to take any of the blue pages into the exam with you, so make sure you take notes about the key facts, formulas, or techniques when you have “a-ha” moments doing the practice problems. YOU WILL NOT REGRET IT.

The real ASQ CSSBB exam is actually EASIER than the questions in the CSSBB Primer, but the question styles and formats are very similar. The reason that the real exam is easier is that there are a lot of questions in the Primer where at least two of the multiple choice options will tempt you into believing that they are both correct. The multiple choice options on the real exam seem to be much more distinct – that is, you’ll have an easier time distinguishing why the wrong ones are wrong.

I think the number one reason that I passed the exam was because of the time I spent on the practice exam questions in the CSSBB Primer. The practice questions on the CD were useful too, but I think the ones in the book were the most useful.

#2 (NEW) Statistics (The Easier Way) With R by Me (Nicole)

SECOND BEST BOOK EVER. Disclaimer: I am biased.

In 2014, I wrote the book that I wish had been written previously… to help people understand the fundamental statistical concepts that you NEED to know before the more advanced Six Sigma concepts. Although I did not take this book with me into my CSSBB exam in 2012, I did take the NOTES that became this book 🙂

#2 (OLD)  The Certified Six Sigma Black Belt Handbook, Second Edition by Kubiak & Benbow

This is the second book I took with me into the CSSBB exam.

This book has mixed reviews on Amazon because apparently the book made it into print with a bunch of calculation errors in it. I didn’t lean on the calculations in this book, though, because I had the CSSBB Primer for that – and as a result, I thought this book was a great reference. Some of the concepts aren’t covered in enough depth, e.g. TPM, but there were several problems on the real exam that I wanted to double check in the references before I shaded that scantron circle with my #2… and this was the book that helped out the most in that regard.

#3  An Introduction to Statistical Methods and Data Analysis by Ott & Longnecker

This was the third book I took with me into the CSSBB exam, and I think I needed it for 3 questions, 2 of which had to do with arcane aspects of DOE. However, it’s also the book that helped me get all my hypothesis testing straight, AND understand the assumptions for all of those tests.

I also LOVE LOVE LOVE this book, and think it should be a required book on the bookshelf of every Six Sigma aficionado out there.  I was first introduced to this awesome, awesome book as a student in STAT 451 at Penn State… an upper level applied stats class (which I believe is now STAT 460). In addition to providing great explanations of the concepts, Ott presents every statistical test as a recipe… what assumptions to check, how to set up the null and alternative hypotheses, how to calculate the test statistic, and how to interpret the calculated and critical values of the test statistic depending upon what alternative hypothesis you selected.

I have a hard time trying to remember whether your calculated test statistic has to be greater than or less than the critical value that you look up in a table… and this is the reference that helped me keep all those important details straight.

This book is expensive, but it’s worth it. If you can find an earlier version, these are usually much more affordable and JUST AS GOOD. Thank you, R. Lyman Ott, for making me love statistics, want to use statistical tests all the time, and want to teach college students how to do it too. You have been one of the most influential people in my life.

#4 Six Sigma for the Next Millennium: A CSSBB Guidebook by Kim Pries

I really tried to like this book, but it’s big, heavy, and there is a lot of whitespace on many of the pages (very unlike the CSSBB Primer). The amount of information per pound is relatively low. HOWEVER, I like the way it consolidates notes by topic with one topic per page. For example, there is one page with Deming’s 14 points. There’s one great page on Project Scope and another great page on Scope Containment Ideas. I’m definitely going to use some of the one-sheeters for teaching my statistics and quality classes.

Unfortunately, the book just didn’t help me as I was studying for the certification exam.

#5 The Six Sigma Handbook, Third Edition by Pyzdek & Keller

Great book but HARD TO FIND STUFF QUICKLY. I’d say read this before your exam instead of bedtime stories, take it with you when you lay on the beach, bring it to the coffee shop while you’re gently relaxing over synthesizing your Six Sigma knowledge into your blood and muscles. This is an excellent book for getting a deeper, more thoughtful understanding of Six Sigma related topics, but was not one I chose to bring into the exam with me.

#6 Statistics for Six Sigma Made Easy by Warren Brussee

This was the LEAST useful book to me for my exam prep (but it might just be as result of how my brain is wired). I find that whenever an author writes very conversationally, trying to simplify the concepts by writing long explanations of the topics (as if he or she were sitting there with you trying to explain them to you), it just confuses me. I need recipes, like what Ott provides in his book.

I can definitely see how this book might help you if you’re totally new to statistics, or if you’re starting off on the path to becoming a Six Sigma Green Belt, or if you just need someone to explain to you what in the world the meaning is behind these statistical tests.

However, IF YOU’RE CLOSE TO BECOMING A BLACK BELT, you should have a lot of this material under yours already. As a studying resource, Brussee’s book won’t be as useful to you.

Hope this helps! If you have any questions, please post them as comments below, and I will try to respond to all.

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