This is a hypothetical question, but it could easily happen. Let me give you a real example.

Using a mobile phone game, we administered a standard depression screening measure (CESD-C) to 18 children living on or near an American Indian reservation. All children had a family member who was an alcoholic or addicted to drugs.  I decide to do a one-sample t-test of the hypothesis that the mean for this population = 15, which is the cutoff value for symptoms of depression .  Here is the code but I didn’t code it (more about that later).

PROC TTEST DATA=cesd_score SIDES=2 H0=15 plots(showh0);

var CESDTotal;

The results are shown below, with  a mean of 21 and a range from 3 to 38.

ttest results

You can see that the t-value of 2.34 is significant at p < .05, that is the mean for this sample is significantly different than the cutoff score of 15. You can see more results here.  What if it hadn’t been, though? What if, instead of .0317 the probability was .0517?

What if dropping out this one person with a score of 3 changed the result? In fact, it did change the mean to 22, and the p-value to .0115 . You can see all of those results here.

So, let’s say that hypothetically dropping out this outlier WOULD change your results. Would you do it? Would you report it?

Think about it. In a couple of days, I will give you my answer and my justification.

As to not having coded it – I used the tasks in SAS Studio which I found to be pretty fun, but more on that in my next post.

Play Aztech: Meet the Maya – for your iPad in the app store, in Spanish and English.  The second in our series of bilingual games teaching basic statistics and Latin American history. Only $1.99 

girl in jungle

P.S. There is a third possibility here, which is changing the test from a two-tailed test to one-tailed test. Surely, an argument can be made that we don’t expect children with a family member who is addicted to alcohol or drugs to be less depressed than the cut-off score? They would either be equal or more depressed. Personally, I don’t buy that argument. I could accept that the sample might be more depressed than the average but I’m not sure one could justify that the mean necessarily MUST be more than the cut-off for depressive symptoms. 




Let me say right off the bat that the number of contracts I’ve had where people wanted me to tell them what to do I can count on one hand – and I’ve been in business 30 years. Generally, whether it is an executive in an organization where I’m an employee or a client for my consulting services, people don’t want me to tell them what to do,

Hey, you should do a repeated measures ANOVA.

Nope, they want me to DO it. It’s funny how often I find myself doing the same procedures for vastly different organizations, everywhere from the middle of Missouri to downtown Los Angeles to American Indian reservations in North Dakota to (soon) Santiago, Chile.

view over the top of my ipad

There are also those procedures I only use once in a great while, but that’s the topic of another post. Here are a couple of my go-to procedures.

Fisher’s Exact Test

Earlier this year I wrote about the Fisher’s Exact Test and how I had used this teeny bit of code

PROC FREQ DATA = install ;
TABLES rural*install / CHISQ ;

is an example of how you do it in SAS for everything from testing whether urban school districts have significantly more bureaucratic barriers to using educational technology than rural districts (they do) to whether mortality rates are lower in a specialized unit in a hospital than for patients with the same diagnosis in a standard unit.

Confidence Limits for the Mean

Working with small samples in rural communities, I often don’t have the luxury of a control group. I know this makes me sound like a terrible researcher and that I never read a quantitative methods or experimental design textbook. However, let me give you an example of the types of conversations I have all of the time.

Me:  I’d like to use your program as a control group. I’ll come in and test all of your students and then two months later, I’ll test them all again.

Principal/ Superintendent/ Program Director:  You mean you want me to take up two periods of class / counseling time for your tests?

Me: Yes.

Them: You wouldn’t actually be giving our students any services or educational program, you’d just be taking two hours from all of our students.

Me: Yes, and then I’ll compare their results to those of the students who do get services.

Them: What do our students get out of it?

You can see where this conversation is going. One solution might be to pay all of the students some amount to stay after school or come in for an extra counseling period or whatever is being compared, so they aren’t missing out on services to take the test. However, Institutional Review Boards are cautious about having substantial incentives because then they feel very low income might be coerced into participating – for some of the people on our research, $10 is a lot of money.

The result is that I don’t always have a control group, but all is not lost. Being smarter than I look (yes, really),  I often use standardized measures for which there is a lot of research documenting the mean and I can do a one-sample test.

proc means data=cesd_score alpha=.05 clm mean std ;
var cesdtotal ;

This will give me the 95% confidence interval for the mean and I can see if my sample is significantly different from the mean .  For example, with a sample of 18 children from an American Indian reservation, the mean score on the CESD – C, a measure of depression, the mean score was 21. The cutoff for considering the respondent as showing depressive symptoms is 15. With a confidence interval from 15.6 to 26.4  I can say that there is a greater than 95% probability that the population mean fits the cutoff for depressive symptoms. Notice that the lower confidence limit still is above the screening cutoff point of 15.

There is an interesting question related to this specific study, but it will have to wait for tomorrow since I have to head to the airport in a few hours. This week, I’m heading to Missouri. If you want to meet up and talk statistics, video games or just drink beer, let me know.

Play Aztech: The Story Begins – free for your iPad in the app store, in Spanish and English.  The first in our series of bilingual games teaching math and history.

girl in jungle


Almost always when I get asked to teach anything my answer is:


I don’t even think about it . Just, no. I’m too busy.  Usually, I’ll teach one graduate class a year and that’s it. However, recently I had the opportunity to teach an introduction to statistics course and design the whole course from the ground up, which sounded like my idea of fun. The college is predominantly an arts school, with students majoring in screenwriting, dance, drama and a smattering of entertainment business majors.

Normally, when I teach graduate statistics courses I use SAS, I require students to learn at least a minimal amount of programming and be able to do things like partition the sums of squares.

Julia in Trinidad

The Spoiled One NOT computing the area under the curve

It just so happens that The Spoiled One, who is a Creative Writing major (what does she want to be when she graduates? Unemployed, apparently) took statistics last year, which resulted in many 11 pm (2 am Eastern time where she attends school) phone calls to me on things like how to compute the area under the curve between two z-scores.

Despite my best efforts, I believe she left the class with zero conviction that she would ever use statistics, and I really don’t blame her. There is not a lot of call in one’s daily life for looking up values in a z table, it being the 21st century and all and us having computers.

Here is my honest appraisal of my soon-to-be students – nearly 100% of them will be able to use skills such as creating graphs with Excel, computing averages, understanding the difference between the median and the mean and when which measure is appropriate. I can tell them truly how they could use this information in deciding which contract to accept, in which film to invest and whether a particular dance studio is preferable to another in terms of business viability. There is less than a 10% chance that as juniors and seniors in an arts college they are going to change their minds and decide they want to go into a research career. If they do make that choice, everything they learn in this course will apply.  What I did not do was include a lot of proofs and matrix algebra or computation.

I gave some thought to using JMP because of the graphics, and to SAS Studio, because it is available free and we could use the tasks menu, which is pretty cool, but the fact is these students are most likely familiar with Excel and the campus already has a license. It’s installed on every computer in the lab. Installing the analysis toolpak is super-easy, whether you are using Office 365 or the regular Office (I hear some people calling that the productivity suite).

So, if I am not having students use SAS or calculate the area under a curve, what am I doing?

One thing I am requiring is that every student create their own livebinder. You’re welcome to take a look at it in the livebinder I’m preparing for my own purposes for the course. Just look under the livebinder assignment tab.

I have a lot more to write about this later. Right now,  I have guests on the way so I’ll try to post more tomorrow.

Want to learn statistics in a game?  Play Aztech: The Story Begins – free for your iPad in the app store, in Spanish and English.  The first in our series of bilingual games teaching math and history.