Jun
24
I Know the Secret to Happiness
June 24, 2017  1 Comment
It may not be the secret to great joy but it is certainly the secret to avoiding unhappiness and it is simply this:
The absence of selfruminative thoughts.
I’d like to claim the idea was originally mine but the truth is I first heard this phrase over a decade ago in a talk by Albert Bandura (yes, THAT Albert Bandura) and he said one of the differences between people who are content with their lives and those who are unhappy is that the happy group have “an absence of selfruminative thoughts”.
There is a phrase I use a lot,
Not my circus, not my monkeys.
In other words, I don’t make everything about ME.
Here are tips to not ruminating too much.

What people think about you is none of your business (I stole this one from Darling Daughter Number Three)
I do the best I can. When I meet with employees or students, I tell them what I think needs to be said, listen to what they have to say and then I don’t worry about whether I was too harsh or too wishywashy, whether they respected my authority or thought I was incompetent. If random Joe on the Internet thinks I’m old and grey and should just shut up, well, as much as it pains me to have lost the good opinion of an anonymous person I have never met – oh, wait, no I don’t care.
2. Don’t take things personally
If I screw up, I try to learn from it. If I don’t get a grant, or a person decides not to invest in our company or a school decides not to buy our games, I listen to their reasons and if it is a reasonable suggestion for a change I can make, I try to do it. If not, I don’t worry about it. I still remember the astonishment I felt seeing a colleague throw a grant review in the trash without reading it.
What are you doing? Why didn’t you read the comments?
I asked. He responded,
Shit, why should I read it? They didn’t like me. They don’t think I’m a researcher.
It’s more than just not taking things personally, though. It’s also a matter of not making everything about how other people are not acting as YOU think they should behave.
3. Don’t make it about YOU when it’s not
Your adult children aren’t raising their kids the way you think they should? The neighbors don’t maintain their yard the way you think it should be ?
Not my circus, not my monkeys.
4. Look out instead of in
A few months ago, we had a really fascinating guest on the More Than Ordinary podcast, Jonathan Shaw. He’d just finished writing his autobiography, Scab Vendor, and he encouraged me to go away for a month and write my own autobiography. Jonathan’s book was interesting and his idea was intriguing. I randomly happened to be in an area known as a writer’s retreat in Lopinot, Trinidad and I tried for a bit. I have had a long strange trip around the world and back again, that’s for sure.
I just don’t get excited about the idea of looking back through all of the things that happened in my life. Jonathan said,
You’ll grow from the experience, but it will probably hurt – and I only saw ‘probably’ to be nice.
Maybe if I went back and hung out in the mountains I would find myself.
Jun
15
MANOVA, finally
June 15, 2017  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 Rsquared in ANOVA or regression is the square of the multiple R.
The multiple Rsquared 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 Rsquared 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 Ftests. If your F is significant, go on to post hoc tests.
ETAsquared 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 variancecovariance is in question. If two or more IVs are included in the analysis, factor interaction must be evaluated before main effects. “
Jun
15
MANOVA from beginning to end: Reliability
June 15, 2017  Leave a Comment
Where is the Multivariate Analysis of Variance ?
You promised there would be MANOVA ! Now we’re in the third post!
First there was recoding of variables.
Then, there was creating scales.
Now, we’re looking at reliability.
Patience is a virtue.
Before we get to doing a MANOVA we want to be sure that our dependent and independent variables are reliable and valid. Let’s move on to reliability.
I’m going to do a correlation matrix and a Cronbach alpha, which is a measure of internal consistency. The rationale is that if items all measure the same construct – say, knowledge of health practices, or autonomy or acceptance of wife beating – then those items should be related to one another. An alpha of 0 would indicate the covariance of items in the scale are zero, so, your scale sucks. An alpha of .95 would mean your scale is amazingly consistent.
So, I did three analysis for my three scales
Title "Health Variables " ;
proc corr data=example alpha ;
var hbs1 hbs3hbs7 ;
Title "Wife beating variables" ;
proc corr data=example alpha ;
var GR34  GR39 ;
Title "Decision Variables" ;
proc corr data=example alpha ;
VAR D_GR1A GR2A D_GR3A D_GR4A GR5a GR6A D_GR7A GR8A
D_GR9A GR9F D_GR10A D_GR12A GR10F GR12F ;
Let’s skip the simple statistics, mean, etc. you get from these analyses and go to the alpha
The alpha for the health scale is pretty bad. The value for the raw scores is .31, for standardized items, still really bad at .32. When we look at how deleting a variable would improve the alpha, if we dropped the first variable , the alpha would go up to .34 – but that is still awful.
For the wifebeating scale the raw value for alpha was .81 and also for the standardized value. So, that one was pretty good as far as reliability.
I put all of the decision variables together, the ones on whether the woman was involved in making decisions, could go places on her own, needed to ask permission to go places. The Cronbach alpha for the raw variables was .65, for standardized variables .81. Note that standardized variables are placed on the same metric, so my idea of some variables being much more important than others did not pan out.
So … I standardized the variables, then I read in that data set and created two scales, one that was a sum of the decision variables and the other that was the mean of the 6 wifebeating variables. There was no particular reason for using the mean of the six variables as opposed to just adding them up. I did both methods to show it was an option.
BEWARE THE SUM FUNCTION – Note, I did not use the sum function. If you add up the values, as shown below, and one of the variables has a missing value then the value of the sum is going to be missing. If you used the SUM function, the variables that have nonmissing values would be added up, so the missing value would be treated as a zero. There are times where that is acceptable. This is not one of those times.
While I’m at it, I want to check whether the scales have approximately normal distributions. A perfectly normal distribution would have skewness and kurtosis values of 0.
proc standard data=example mean=0 std=1 out=MAN_data;
Data create_manova ;
set man_data ;
* I could have used the mean function here, but I didn't ;
decision = D_GR1A + GR2A + D_GR3A + D_GR4A + GR5a + GR6A + D_GR7A + GR8A +
D_GR9A + GR9F + D_GR10A + D_GR12A + GR10F + GR12F ;
beating = mean(of gr34gr39);
proc univariate data=create_manova ;
var decision beating ;
The skewness values were relatively low: 1.3 and 0.2 for the two scales and kurtosis values were 2.0 and 1.2 . Since my scales aren’t a radical departure from normality, I’m now going on to MANOVA – finally!
Jun
14
MANOVA from beginning to end : Creating the scales
June 14, 2017  2 Comments
Last time, we saw how to recode variables to score answers correct or incorrect, on a rating scale and weighted by importance. Today, we’re going to look at creating some scales from those variables because for reasons I’m sure I have written about at some point in the past, single items are usually not very reliable. Whether you use SAS, SPSS, R or any other statistical package, you are still going to need to follow the steps of recoding your variables and creating and validating your scales before you get into MANOVA. Or, at least, you will if you are smart.
First, I want to check that there are no obvious errors or other problems in my data.
PROC MEANS DATA=example ;
VAR gr2A  gr39 hbs1 d_gr12a ;
You could type in the variable names but that is a lot of typing. The double dashes mean to include all variables in the data set in order from the first variable to the one that comes after the dashes. How do you know what order the variables are in? Click on the OUTPUT DATA tab at the top and look to the left under COLUMNS.
If you didn’t just run a program creating your data and hence don’t have an OUTPUT DATA tab, you can find your data file by clicking the MY LIBRARIES tab and then clicking on the library (directory) where your data are kept and clicking on the dataset to open it. You can also use the PROC CONTENTS procedure but today we are being all pointy and clicky with SAS Studio.
Sometimes you will see something like:
VAR item1 – item12 ;
The single dash is used for variables that end in a number and if you don’t have item1, item2 all the way through item12, it will give you an error and not run. Then you will be sad.
PROC MEANS will give you the N, mean, standard deviation, minimum and maximum.
Here are a few things to consider.
 Is the N substantially less than you had expected? If so, you have a lot of missing data and you should investigate that. The lowest N I have is 37, 814 out of 39, 430 people so not bad, but I might want to look at that one item, since most of the items have close to 39,000 for an N
 Is your standard deviation zero? STOP RIGHT THERE! On just what variable could 39,000 people give the same response? This likely shows a big problem with your data. I did not have that problem, so I continued.
 Are your minimum and maximum the minimum and maximum possible scores for the item? Now, this may not always be the case. On a scale of 1 to 10, say, with a sample of 50 people, maybe no one will say 1. However, I have over 39,000 people and the items are 0 or 1, o – 2 or 1 3, so I should have people from the minimum to the maximum or something is wrong. Nothing is wrong, and I continue.
 Are the means about what you expect? Well, I’m not really an expert on social structure and family relations in India, so I can’t say. About a third of the women said it was usual for a husband to beat his wife if her dowry was not what was expected. About threefourths said they would be allowed to visit a family or friend’s home alone.
Okay, so my results from the means procedure looks okay. Now what?
Next, I’m going to do a factor analysis to see if my supposition is supported of three scales related to health, beating your wife and autonomy.
Here is the code for my factor analysis.
PROC FACTOR DATA =example SCREE ROTARE= VARIMAX NFACTORS=5;
VAR gr2A  gr39 hbs1 d_gr12a ;
This is actually the second one I ran. In inspecting the results for the first, between the eigenvalues and scree plot, I decided that at most I should retain five factors. I’ve written a lot about factor analysis on this blog previously, so I’m not going to go into detail here. In short, the decisionmaking variables mostly loaded on the first factor with factor loadings of .70 and higher. The median communality estimate for those items was about .67. In short, considerable evidence for a decisionmaking factor. The wifebeating variables loaded on the second factor. All but one loaded above .67, and even that variable (Beating your wife if she had an extramarital affair – which 84% of the women said was accepted in their communities) loaded at .40. The variables regarding needing permission to go places loaded on the third factor and also had high communality estimates. The variables regarding going places by yourself loaded on the fourth factor and also had high communality estimates.
The health variables were a different story. Four out of six loaded between .47 and .67 on the fifth factor. The other two did not load on any factor.
It is starting to look like at this point that it is okay to retain the wifebeating items as a scale. The various measures of autonomy – decisionmaking, going places on your own and needing permission – seem to hang together within factors. I think it would be reasonable to put all three of these together in one scale. I talked about parceling in the past, and I could have done that as a step here, and then rerun the factor analysis to support (or not) my supposed autonomy factor. Since I have limited time and simply doing this analysis for educational and illustrative purposes, I skipped over this to the next procedure, which is reliability analysis.
Since this post is pretty long already, I’ll save that for the next post.
Jun
11
Other people want to go see the new Wonder Woman movie. I’ve been wanting to talk about MANOVA, but first, we need some decent dependent and independent measures.
I have the India Human Development Survey data on over 39,000 women and my hypothesis is that education is related to women’s rights’ issues, especially autonomy, health practices knowledge and domestic violence. I also think that mobility might be related, as women who get out of their native village might be exposed to new ideas.
Before I can test out my (supposedly) brilliant hypotheses, I need to create some variables because it turns out when they were collecting data in India in 2011 they were not thinking about my convenience. (Yes, I, too, am appalled by this lack of consideration.)
Independent Variables
First, I will need to create my independent variables from
EW11 Differences in family by mobility
1= same village/ town
2= another village
3 = another town
4 = metro (since only 1% fall in here, I’m going to delete this category)
and education (see below)
Items that will go into dependent variables (maybe)
HEALTH QUESTIONS
HB1 Milk harmful
HB3. 1st milk good for baby
Hb4 chulha smoke good
Hb5 child diarrhea drink more
Hb6 illness spread through water
Hb7 malaria spread
DECISIONS
The items below are scored 1 if the respondent decides, 0 if the respondent does not decide. (More than 1 person can decide, so if both husband and wife decide, the answer will be 1 for both. In this case, I just looked at if the wife had a say in the decision.)
 GR1a Cooking
 GR2A Expensive purchases.
 GR3A Decides number of children
 GR4A Decides what to do if sick
 GR5A Decides whether to buy land
 GR6A Decides wedding expense
 GR7A Decides if child is sick
 GR8A Decides who your children should marry
The items below are score 1 if the woman is allowed to do these things alone and 0 if she is not.
 GR9F Can visit health center alone
 GR10F Can visit relative/ friend alone
 GR12F. Can go short distance alone
These items relate to whether the woman needs to ask permission for activities, with 0 = no, 1 = must inform someone and 2 = yes
 GR9A Ask permission to visit health center
 GR10A Ask permission to visit relative
 GR12A. Ask permission to travel by bus/train
WIFE BEATING QUESTIONS
GR34 – GR39 – All of these relate to under what circumstances it is acceptable, coded yes = 1 or 0 = no.
As you can see, well, I hope you can see, each of these presents a different date recoding problem.
 Mobility and education needs to be coded into categories (there is a minor reason I will explain in a later post why this is not necessary but convenient), with the fourth category deleted,
 Health questions need to be scored as correct or incorrect.
 Decision questions are all scored equally – so deciding what food to cook and how many children you have are each scored a 1. I think that’s not right and I want to weight some decisions more than others.
 Independence questions need to be reverse coded, so not asking permission is a 2 and asking permission is a 0
 Wifebeating questions need no recoding
So … here we go. The first thing we’re going to do is create categories. Notice I don’t do anything with the category 4 for mobility, so those people will just have a missing value for MOBILITY and be dropped from the analysis.
Also, a note on ELSE as opposed to just IF statements.
I could just use all IF statements but that would be inefficient. It doesn’t really matter here with 39,000 records but if I had millions it would slow down processing. The ELSE statement is only processed if the preceding IF statement is false.
NOTE!!! In the second set of IF ELSE statements, I have
else if ew8 < 9 and ew8 ne . then education = “ELEM”;
This statement is only executed IF the preceding IF statement was false. Without the ELSE, everything less than 9, including those who had 0 years of education, would be set to ELEM. Without the and ew8 ne . in this statement, anyone that had missing data would be set to ELEM along with anyone who had 18 years of education.
data example ;
set mydata.india ;
If EW11 = 1 then Mobility = “None” ;
else if EW11 = 2 then mobility = “Vill” ;
else if EW11 = 3 then mobility = “TOWN”;
if ew8 = 0 then education = “NONE” ;
else if ew8 < 9 and ew8 ne . then education = “ELEM”;
else if ew8 > 8 then education = “HS +”;
*** The statements below recode the health items ;
*** For hb1 the correct answer is 0, so 1hb1 will score respondents who said 0 as correct (= 1) and those who said 1 as incorrect (=0);
*** For hb3 the correct answer is 1, so respondents who said 1 are scored as correct (= 1) and those who said any number higher than 1 as incorrect (=0);
*** For hb4 – hb7, the correct answer is scored as correct (=1) and any numbers in the incorrect set scored as incorrect (=0);
*** HEALTH QUESTIONS ;
hbs1 = 1 hb1 ;
If hb3 = 1 then hbs3 = 1 ;
Else if hb3 > 1 then hbs3 = 0 ;
If hb4 = 2 then hbs4 = 1 ;
Else if hb4 in (1,3) then hbs4 = 0 ;
If hb5 = 2 then hbs5 = 1 ;
Else if hb5 in (1,3,4) then hbs5 = 0 ;
If hb6 = 2 then hbs6 = 1 ;
Else if hb6 in (1,3,4) then hbs6 = 0 ;
If hb7 = 3 then hbs7 = 1 ;
Else if hb7 in (1,2,4) then hbs7 = 0 ;
/* DECISION QUESTIONS */
/* ALSO INCLUDES ADDITIONAL ITEMS NOT RECODED */
**** Here, I multiplied items by a factor based on my estimation of importance ;
D_GR1A = GR1A* 0.5 ;
D_GR3A = GR3A * 10 ; * BECAUSE I THINK IT’S IMPORTANT ;
D_GR4A = GR4A *2 ;
D_GR7A = GR7A *2 ;
**** These items are subtracted from 3 so doesn’t have to tell anyone = 2 ;
**** Needs to inform someone = 1 and needs to ask permission = 0 ;
D_GR9A = 3 – GR9A ;
D_GR10A = 3 – GR10A ;
D_GR12A = 3 – GR12A ;
**** KEEPS THE VARIABLES I PLAN TO USE ;
Keep EW8 EW5 Ew6 EW10 EW14a EW12a EW12b
HBS1 HBs3HBS7 D_GR1A GR2A D_GR3A D_GR4A GR5a GR6A D_GR7A GR8A
D_GR9A GR9F D_GR10A D_GR12A GR10F GR12F GR34 – GR39 mobility education;
So, there we go. You might think I would dive into a Multivariate Analysis of Variance now but you would be wrong. The next thing I am going to do is check the validity of my scales through a combination of factor analysis, univariate statistics and reliability analysis. Only after that step will I do the MANOVA.
Jun
8
An Introduction to Repeated Measures ANOVA
June 8, 2017  Leave a Comment
I’m teaching a course on multivariate statistics and for some of the students it’s been a minute since their last inferential statistics course.
So, I have been doing a few videos here and there to refresh, for example, what is a repeated measures ANOVA and why you might want to do it.
If you are interested in being a beta tester for our first bilingual game that teaches statistics, please email info@7generationgames.com
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 Andrew Gelman's statistics blog  is far more interesting than the name
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 Love Stats Blog  How can you not love a market research blog with a name like that?
 Me, twitter  Thoughts on stats
 SAS Blog for the rest of us  Not as funny as some, but twice as smart. If this is for the rest of us, who are those other people?
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