### Jan

#### 28

# Maybe you *can* use SAS to teach art majors

Filed Under Software, statistics, Technology | Leave a Comment

I was supposed to be teaching statistics to undergraduate Fine Arts majors this semester but I’m going to Santiago to open a Latin American office for 7 Generation Games instead.

I’m a bit disappointed because even though when I was younger and got asked at cocktail parties what I did for a living, I would say,

I teach statistics to people who don’t want to learn it.

teaching Fine Arts majors would probably be a new experience.

I was planning on using Excel to teach that course. However, as I take a closer look at SAS Studio I think it might be feasible to use SAS.

First of all, it’s free for academics and you can use it on any device, including an iPad. I know because I’ve tested it.

Second, and more important for this group, you can use the tasks and do some real-life analyses with almost no coding.

For example, I want to know if the sample of students we tested on American Indian reservations who had a family member addicted to methamphetamine were, on the average, over the cutoff for depressive symptoms. On the scale we used, the CESD-C , the cutoff score is 15.

Step 1: Run the code to assign the directory with the data I made available for the course, for example,

libname in “/home/annmaria.demars/data_analysis_examples”;

run;

Step 2: Under the TASKS menu on the left select STATISTICS and then t TESTS

3. Next to the DATA field you’ll see a thing that looks kind of like a spreadsheet. It’s supposed to symbolize a data file. Click on that and a box will come up that lets you pick the directory (library) and the file within it. In my case, it is the CESD_score file.

4. Now that I have my dataset selected, from the ROLES menu I select one-sample t-test.

5. Click the + next to Analysis Variable and select the dependent variable, in my case, this is CESDTotal

6. Now click on the OPTIONS tab. Two-tailed test is selected as the default. That’s good, leave it. The alternative hypothesis tested is usually that the mean is equal to 0, but I want to change that to 15. Just click the little running guy at the top to get results.

I showed the results in a previous post, the mean for my sample of 18 youth was 21 (p <.05).

What if we did an UPPER one-tailed t-test? Then my p-value is .015 instead of .03.

What if we did a LOWER one-tailed test? Then my p-value is 1.0.

To get these latter 2 tests takes about 5 seconds. All I need to do is change the option for tails and click on the running man again.

Now, in just a few minutes, I have data under three different assumptions, from an actual study. My students and I can start discussing what that means.

Bottom line, check out SAS Studio. It may be more of an option for your students than you think.

### Jan

#### 13

In a previous post, I asked what you would do if one person’s score changed your results?

- Would you throw them out?
- Leave them in?
- Does it depend on whether they support your hypothesis or not?

A few people suggested collecting more data and I completely agree with their very valid points that if one person can change your results from significant to non-significant, you probably have a small sample size, which we did, and that is a problem for a number of reasons that warrant their own posts. It’s not always possible to collect more data, due to time, money or other constraints (only so many people are considerate enough to die from rabies bites in a given year). In our case, we have a grant under review to follow up on this pilot study with a much larger sample so if you are on the review committee let me just take this opportunity to say that you are good-looking and your mother doesn’t dress you funny **at all**.

A couple of other people commented on not getting tied up with significance vs non-significance too much, especially since a confidence interval with a sample size this small tends to be awfully wide. I agree with that also, but that, too, is a post in itself.

## So, what would I do?

First of all, I would check if there were any problems in data entry. You’d laugh if you knew how often I have heard people trying to explain results due to an outlier and that outlier turns out to be a data entry person who typed 00 instead of 20 or a student who just went down the column circling everything “Always”.

For example, on this particular screening measure for depression, some of the items are reverse coded. If you did not pay attention to that and you just answered “A lot” for every item you would get an artificially depressed score (no pun intended). That was not the case here. I looked at the individual responses and, for example, the subject answered “Not at all” to “I felt down and unhappy” and “A lot” to “I felt happy”.

I checked to see that the measure was scored properly. Yes, there answers were consistent, with “Not at all” to all of the depressed items and “A lot” to all of the reverse coded items. This was just a happy kid.

So, that wasn’t it.

Second, I checked to see if there was a problem with the subject. Occasionally, we will get a perfect score on the pre or post-tests for our math games and upon closer examination, it turns out that prodigy is actually a teacher who wanted to see what our test was like for him/herself. Either that, or it was a really dumb kid whose failed fifth-grade 37 times.

That wasn’t it, either. This student was in the same target age group from one of the same two American Indian reservations as the rest of the students.

After ruling out both non-sampling error and sampling error, I then went and did what most people recommended. I analyzed the data both ways. Now, in my case, the one student did not change the results, so when I reported the results to staff from the cooperating reservations, I mentioned that there was one outlier but 2/3 of the youth tested were above the screening cut off for symptoms of depression and the cut-off score is 15 while the mean for the young people assessed on their reservation was 21. I should note that this was not a random sample but rather a sample of young people who had a family member addicted to alcohol or drugs, mostly methamphetamine.

Since in this case the results did not change substantively, I just reported the results including the outlier.

If there HAD been a major difference, I would have reported both results, starting with the results without the outlier and state that this was without one subject included and that with that outlier, the results were X.

I think the results without the outlier are more reliable because if you finding significance (or not) depends on that one person it’s not a very robust finding.

Here is my general philosophy of statistics and it has served me well in terms of preventing retracted results and looking like an idiot.

**Look for convergence.**

What I mean by that is to analyze your data multiple ways, and, if possible, over multiple years with multiple samples.That’s one reason I’m really grateful we’ve received USDA Small Business Innovation Research funding over multiple years. Where university tenure committees are fond of seeing people crank out articles, the truth is, at least with education, psychology and most fields dealing with actual humans, it often takes quite some time for an intervention to see a response. Not only that, but there is a lot of variation in the human population. So, you are going to have a lot more confidence in your results if you have been able to replicate those with different samples, in different places, at different times.

If your significant finding only occurs with a specific group of 19 people tested on January 2, 2018 in De Soto, Missouri, and only when you don’t include the responses from Betty Ann McAfferty, then it’s probably not that significant, now is it?

### What I do when I’m not blogging — make educational video games.

Please check our latest series in the app store for your iPad, Aztech Games, which teaches Latin American history and (what else) statistics. The first game in the series is free.

### Dec

#### 30

# What would you do if one person changed your results?

Filed Under Software, statistics | Leave a Comment

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.

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

*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. *

### Dec

#### 27

# DO statistics and you can go almost anywhere

Filed Under Software, statistics, Technology | 2 Comments

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.

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.

### Dec

#### 5

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

No.

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.

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.

### Nov

#### 20

# The statistical knowledge you need the most – almost everywhere

Filed Under Dr. De Mars General Life Ramblings, statistics | 3 Comments

## What do a herd of deer and a sea lion have to do with statistics?

Friday, I was on the Spirit Lake Dakota Nation in North Dakota. Most of the time while I was there, I spent at the Spirit Lake Vocational Rehabilitation Project, an impressively effective group of people who help tribal members with disabilities get and keep jobs. A few years back, I wrote a system to track their data using PHP and MySQL. It is deliberately simple because they wanted a basic database that would give reports on the number of people served, how many had jobs, and some demographic information. A research project used SAS to analyze the data to try to identify predictors of employment.

Due to a delayed flight, I spent the night with my friend in Minot, discussing, among other things, the decline in native speakers of Cree, and not the herd of deer in her backyard, which was common place enough to pass without comment.

Saturday, I was back home in California, on a dinner cruise in Marina del Rey. We were discussing how to analyze the data on persistence in our games to show that the re-design, with a longer lead-in story line and a higher proportion of game play early on was effective. I suggested maybe we could use survival analysis. Really, it’s the same scenario as how many people are alive after 2, 3 or 4 months or how many people kept playing the game after the 2nd, 3rd or 4th problem.

The deer, the large loud sea lion on the dock and I spent the exact same amount of time discussing the probability mass function for a Poisson distribution and proving the Central Limit Theorem.

My point is, that everywhere I go, and that is a REALLY broad range of places, people are interested in the application of statistics, but SO much of school is focused on teaching how to compute the area under the normal curve or how to prove some theorem or computing coefficients using a calculator and plugging numbers into a formula, inverting matrices. I’m not sure how helpful that was to a student and I can guarantee you that the last time I computed the sums of squares without using a computer was about 35 years ago.

Whether you are are using SAS, SPSS, Excel, R, JMP or any one of a dozen other statistical packages, it lets you focus on what’s really important. Does age actually predict whether or not someone is employed (in this case, no)? Do rural school districts have fewer bureaucratic barriers ? Is this a reliable test? Did students who played these games improve their math scores?

When I was young, and many of the current statistical packages were either very new and limited or didn’t yet exist, someone asked me if I was worried that I would be out of a job. I laughed and said no, because what computers were replacing was the computational part of statistics, and except for that tiny proportion of people who were going to be developing new statistics, the jobs were all going to be in applying formula, not proving them and sure as hell not computing them with a pencil and a piece of paper. A computer allows you to focus on what’s important.

What IS important? That’s a good question and another post.

### Having trouble teaching basic statistics to students? Start with Aztech: The Story Begins — free from the app store (and it’s bilingual)

### Nov

#### 5

# Forget your dream, kid. Follow statistics

Filed Under Dr. De Mars General Life Ramblings, statistics | Leave a Comment

I saw this poster in a high school, supposedly said by a basketball coach:

## People say, “Follow your dreams. ” I say, “Forget your dreams, kid, follow math.”

He goes on to give the percentage of high school athletes who compete in college – 3.4% for men’s basketball, by the way, 1% of high school athletes make it in Division I. Even if you make it to the college level, your odds of becoming a professional athlete are dismal – 1.1% of college basketball players make it to the major professional teams, yes, that is 1% of 1%, so you have a .01% chance of making it into the Lakers even if you are playing in high school.

If you are that 1 in 10,000 who makes it on the roster, your median salary will be $3.7 million and you will play for around 4.8 years, giving you a career salary of around $18.5 million.

Let’s say you are a statistician with a Ph.D. With 5-9 years of experience, your median salary is around $130,000. In my experience, it is going to be considerably less your first year but go up fairly rapidly. Let’s say you have the sense to get some scholarship and grant funds to pay for your tuition – my total student loan debt was $900 – and that you graduate in your 30s – I was 31 and that was with taking a few years out to work as an engineer. There isn’t any particular reason you have to retire before 65 or 70. It’s not like your knees go out and they fire you from your statistician job. I’m going to give a ballpark figure of $150,000 a year average over those 36 years, which is turns out to be about the median salary for a statistician who doesn’t work in academia, according to the American Statistical Association. You’re at $5.4 million. That’s not counting 36 years of health insurance, 401 K and other benefits like not having a boss who is referred to as your “owner” , which I personally find kind of creepy weird, but you also have to consider you don’t get all the $5.4 million at once, either.

So, let’s present this to you:

- You have a 1 in 10,000 chance of making $18.5 million
- You have a 55 out of 100 chance of making $5.4 million.

### You can only buy one ticket. Which lottery ticket do you buy?

Oh, by the way, did I mention you have a 90 out of 100 chance of making over $3 million ?

The coach’s point was that you may be dreaming about a spot in the NBA but you have a much greater chance of success in life if you spend your time in the math class instead of on the court. As a good friend of mine often says, “Too many people confuse wishes with plans.”

So, you may dream of slam dunks in the NBA but you would be a lot better off planning to take Calculus, several statistics courses and study a field like business, psychology, political science or epidemiology where you can apply those statistics.

You might think I don’t have any heart, that I have no idea what it means to dream of being a successful athlete. Actually, you’d be wrong. I ran track in college. I won the world championships in judo. Then, the next year, I went into a Ph.D. program and specialized in statistics because, well, I’m good enough at math to see what had the better probability of paying off in the future.

There are SO many ways to learn and use statistics. That’s another post, though. I’d best toddle off to bed since I need to catch a plane tomorrow after I go do a charity walk in the morning.

Early morning and snow, two things I hate the most. Well, life can’t be perfect all the time. I think I can prove that statistically.

### Sep

#### 13

# It only seems like this has nothing to do with statistics

Filed Under Dr. De Mars General Life Ramblings, statistics | 2 Comments

Last post, I talked about bricolage, the fine art of throwing random stuff together to make something useful. This is something of a philosophy of life for me.

## Seems rambling but it’s not …

Over 30 years ago, I was the first American to win the world judo championships. A few years ago, I co-authored a book on judo, called Winning on the Ground.

When it came to judo, although I was better than the average person, I was not the best at the fancy throws – not by a long shot. I didn’t invent any new judo techniques. I wanted to call our book The Lego Theory of Judo but my co-author said, “That’s stupid” and the editor, more tactfully, said, “Nobody will know what you are talking about unless they read the book and you want a title that will get them to buy the book”. So, I lost that argument.

What I was really good at was putting techniques together. I could go from a throw to a pin to an armbar and voila – world champion! Well, it took a long time and a lot of work, too.

## How does this apply to statistics?

Let’s start with Fisher’s exact test. Last year, I wrote about using this test to compare the bureaucratic barriers to new educational technology in rural versus urban school districts. Just in case you have not memorized my blog posts, Fisher’s exact test can be used when you have a 2 x 2 matrix that fails to meet the chi-square minimum of five observations per cell. In that instance, with only 17 districts, chi-square would not be appropriate. If you have a 2 x 2 table, SAS automatically computes the Fisher exact test, as well as several others. Here is the code:

`PROC FREQ DATA = install ;`

TABLES rural*install / CHISQ ;

Ten years ago, I was using this exact test in a very different context, as a statistical consultant working with a group of physicians who wanted to compare the mortality rates between a department that had staff with a specific training program and a similar department where physicians were equally qualified except for participation in the specialized program. Fortunately for the patients but unfortunately for statistical analysis purposes, people didn’t die that often in either department. Exact same problem. Exact same code except for changing the variable names and data set name.

In 35 years, I have gone from using SAS to predict which missiles will fail at launch to which families will place their child with a disability in a residential facility to which patient in a hospital will die to which person in vocational program will get employed to which student will quit playing an educational game. ALL of these applications have used statistics and in some cases, like the examples above, the identical statistics applied in very diverse fields.

## Where do the Legos come in?

In pretty much every field, you need four building blocks; statistics, foundational programming concepts, an understanding of data management and subject specific knowledge. SAS can help you with three of these and if you acquire the fourth, you can build just about anything.

**More on those building blocks next post.**

For random advice from me and my lovely children, subscribe to our youtube channel 7GenGames TV

### Jul

#### 9

Once every year, I teach an actual course, not a workshop or professional development, but a class with 20 – 40 students. One where I need to write a syllabus, have lectures, papers to grade, homework and exams.

Now, I’m not comparing teaching masters or doctoral students 3- 6 hours a week to my friends who teach middle school six hours a day. In fact, when I go for a day or two, as a guest speaker for six classes a day, and I need to stand on my feet and keep 40 teenagers’ attention for all of that time, I think yet again that teachers don’t get paid nearly enough.

There are several reasons that it is important to me to teach a course every year, and one is that I think it is super-important as someone who makes educational technology that I be in an actual classroom with students. It’s easy to forget how unbelievably BUSY teachers are if you are not in that situation day after day.

It’s also easy to overestimate the amount of time teachers have to investigate new technology. For example, for the course I am just finishing, I considered just two possible types of statistical software – SAS and SPSS. The university had a license for one and it was available free (through SAS Studio) for the other. I knew R existed, of course, but I did not consider it as an option for these students (long story I will skip). I had a short time to decide and someone suggested to me another option – JMP – that I had not considered, but by then I didn’t have time to research it, find a possible textbook and integrate it in my syllabus and lectures. If I’d had more time to look into it, that might have been a good choice.

I know there are other options out there- I had looked at Statistica at one point and it looked pretty cool. However, now that I have my syllabus done, lectures written, textbooks selected, model assignments and my students are generally doing pretty well, it is hard to see myself spending a lot of time researching new software applications for my engineering students. (Social Science and Education might be a different issue).

My point is that one evident challenge for anyone who makes educational technology is the “good enough” problem. That is, if things are going good enough, teachers are not highly motivated to look for something better.

One of the things that drives me crazy, is those teachers who think it’s “good enough” when the vast majority of their students are below grade level or not proficient – but that’s a rant for another day.

### Jun

#### 15

# MANOVA, finally

Filed Under statistics | Leave a Comment

So, after three posts of

we have arrived at MANOVA. If you skipped those three posts, feel shame at trying to take shortcuts, go back and read them.

Before we dive into coding, let’s take a look at some basic background on MANOVA.

The difference between ANOVA and MANOVA is simple

- With ANOVA you have one dependent variable

With MANOVA you have multiple dependent variables

How does that work? Think back to what you know about multiple correlation

In correlation, you are looking at the relationship between two variables, X and Y. You predict changes in X from changes in Y

Y = bX

In multiple correlation you are looking at the relationship between Y and MULTIPLE X variables.

You have an equation something like

Predicted Y = b0X0 + b1X1 + b2X2 + b3X3

And you are looking at how the Y variable changes in relation to the PREDICTED Y. Notice that predicted Y is a sum of all of your variables, each of which is multiplied by a regression coefficient.

The correlation between these predicted Ys and the actual Y is your multiple R and the multiple R-squared in ANOVA or regression is the square of the multiple R.

The multiple R-squared answers the question – how much of the variance in the dependent variable can be explained by variance in the independent variable (s) ?

In the case of ANOVA, this variance is in group membership, so we are testing the null hypothesis that the mean of group1 = the mean of group 2 all the way to group N

With MANOVA, you have multiple variables on the Y side of the equation

The variable you are predicting/ explaining in this case is also a weighted sum

Dependent = w1Y1 + w2Y2 + w3Y3

Our null hypothesis is that the mean of this weighted combination is equal for groups 1, 2 and all the way up to group N

Instead of looking at a multiple R-squared in this case, we look at two other statistics, Wilk’s lambda and Pillai’s trace

- Assumptions of MANOVA
- Independent, randomly sampled observations
- Variables follow a multivariate normal distribution
- Homoscedasticity – population covariances for the dependent groups are equal
- Relationship of dependent variables is linear (because notice you made the dependent into a linear equation)

Also note that in the case of a repeated measures ANOVA certainly assumption 1 and possibly assumption 3 are violated

When you have conducted your MANOVA the first thing you should look at is the Multivariate tests – Wilk’s lambda, Pillai’s trace . Rejecting the null hypothesis that the model does not explain the difference in the VECTOR of means then leads you to examine the second logical question, which of these dependent variables differs ? So , if you don’ t have a significant, lambda, trace, etc. STOP. If you do, move on and check out the univariate F-tests. If your F is significant, go on to post hoc tests.

ETA-squared is the variance accounted for IN THE LINEAR COMBINATION OF THE DEPENDENT VARIABLES by the model.

Mertler and Vannata said it well.

“When the IV has only two categories, the F test for Pillai’s Trace, Wilks’ Lambda, and Hotelling’s Trace will be identical. When the IV has three or more categories, the F test for these three statistics will differ slightly but will maintain consistent significance or nonsignificance. Although these test statistics may vary only slightly, Wilks’ Lambda is the most commonly reported MANOVA statistic. Pillai’s Trace is used when homogeneity of variance-covariance is in question. If two or more IVs are included in the analysis, factor interaction must be evaluated before main effects. “