May
20
Parceling Items in Factor Analysis
Filed Under Software, statistics | 3 Comments
First of all, what are parcels? Not the little packages your grandma left on the table in the hall when she came back from shopping. Well, not only that.
In factor analysis, parcels are simply the sum of a small number of items. I prefer using parcels when possible because both basic psychometric theory and common sense tells me that a combination of items will have greater variance and, c.p., greater reliability than a single item.
Just so you know that I learned my share of useless things in graduate school, c.p. is Latin for ceteris paribus which translates to “other things being equal”. The word “etcetera” meaning other things, has the same root.
Know you know. But I digress. Even more than usual. Back to parcels.
As parcels can be expected to have greater variance and greater reliability, harking back to our deep knowledge of both correlation and test theory we can assume that parcels would tend to have higher correlations than individual items. As factor loadings are simply correlations of a variable (be it item or parcel) with the factor, we would assume that – there’s that c.p. again – factor loadings of parcels would be higher.
Jeremy Anglim, in a post written several years ago, talks a bit about parceling and concludes that it is less of a problem in a case, like today, where one is trying to determine the number of factors. Actually, he was talking about confirmatory factor analysis but I just wanted you to see that I read other people’s blogs.
The very best article on parceling was called To Parcel or Not to Parcel and I don’t say that just because I took several statistics courses from one of the authors.
To recap this post and the last one:
I have a small sample size and due to the unique nature of a very small population it is not feasible to increase it by much.I need to reduce the number of items to an acceptable subject to variables ratio. The communality estimates are quite high (over .6) for the parcels. My primary interest is in the number of factors in the measure and finding an interpretable factor.
So… here we go. The person who provided me the data set went in and helpfully renamed the items that were supposed to measure socializing with people of the same culture ‘social1’, ‘social2’ etc, and renamed the items on language, spirituality, etc. similarly. I also had the original measure that gave me the actual text of each item.
Step 1: Correlation analysis
This was super-simple. All you need is a LIBNAME statement that references the location of your data and then:
PROC CORR DATA = mydataset ;
VAR firstvar — lastvar ;
In my case, it looked like this
PROC CORR DATA = in.culture ;
VAR social1 — art ;
The double dashes are interpreted as ‘all of the variables in the data set located from var1 to var2 ‘ . This saves you typing if you know all of your variables of interest are in sequence. I could have just used a single dash if they were named the same, like item1 – item17 , and then it would have used all of the variables named that regardless of their location in the data set. The problem I run into there is knowing what exactly item12 is supposed to measure. We could discuss this, but we won’t. Back to parcels.
Since you want to put together items that are both conceptually related and empirically – that is, the things you think should correlate do- you first want to look at the correlations.
Step 2: Create parcels
The items that were expected to assess similar factors tended to correlate from .42 to .67 with one another. I put these together in a ver simple data step.
data parcels ;
set out.factors ;
socialp1 = social1 + social5 ;
socialp2 = social4 + social3 ;
socialp3 = social2 + social6 + social7 ;
languagep = language2 + language1 ;
spiritualp = spiritual1 + spiritual4 ;
culturep1 = social2 + dance + total;
culturep2 = language3 + art ;
There was one item that asked how often the respondent ate food from the culture, and that didn’t seem to have a justifiable reason for putting with any other item in the measure.
Step 3: Conduct factor analysis
This was also super-simple to code. It is simply
proc factor data= parcels rotate= varimax scree ;
Var socialp1 – socialp3 languagep spiritualp spiritual2 culturep1 culturep2 ;
I actually did this twice, once with and once without the food item. Since it loaded by itself on a separate factor, I did not include it in the second analysis. Both factor analyses yielded two factors that every item but the food item loaded on. It was a very nice simple structure.
Since I have to get back to work at my day job making video games, though, that will have to wait until the next post, probably on Monday.
—–
Be more than ordinary. Take a break. Play Forgotten Trail. I bet you have a computer!
May
2
What I learned from my favorite paper at SAS Global Forum
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At first, I was thinking it wasn’t right to have a favorite paper, but then I realized that was idiotic. It’s not like these papers (or their presenters) are my children.
My favorite paper was,
Statistical modeling for large complex data: Five new directions from SAS/STAT software
If you’re not a statistician, props to you for reading after that first sentence, especially since some of the lessons apply to any conference.
- You don’t always have to present or attend presentations on whatever is shiny and new. The techniques he presented, like GLMSELECT, a method for selecting the best model is not brand new. I remember when it was first added to SAS/STAT and thinking it was a way cool idea I should use – but, then, I didn’t. As you can see from the graph above, it can be pretty easy to select the best model. Looks a lot like a scree plot, doesn’t it? This also further supports my point that visual displays of data, like the one above, are everywhere and taking over. Now that I have been reminded of its existence, I’m looking for a use for it so I can really remember it. Unfortunately, this is a method for general linear models and what I am most interested in right now has a binomial outcome, whether a player finished a game or not.
- Don’t stop learning when you go home. I remembered that there was also an example in this paper that used HPGENSELECT for generalized linear models, including binomial distributions. So, I am going to try that out with this dataset. One of the areas where I am improving is actually reading all of those papers I mean to get around to when I get home. Whether it is a paper you attended, but is now jumbled around in your brain with the other 25 sessions, or one you could not attend because it conflicted with something else, when you get home, you should read it. Conferences can be expensive and you want to get the most out of that time and money you spent.
- Of course, I learned about sparse regression, quantile regression, classification and regression trees and more, which you can, too if you follow my advice from #2.
Okay, well there is a lot more to say about SAS Global Forum and my adventures with HPGENSELECT but we have a new game, Forgotten Trail, coming out for sale tomorrow, so back to work.
———-
Apr
22
Visual Analytics are EVERYWHERE: SAS Global Forum Continued
Filed Under Software, statistics, Technology | 1 Comment
The nice thing about going to SAS Global Forum is that it’s the gift that keeps on giving. Long after I have gone home, there are still points to ponder.
Visual analytics is big and not just in the sense of there is a product out called that which I have never used but that every presentation, no matter how ‘tech-y’ now makes very effective use of graphics. If I was the type of person to say I told you so, I would mention that I predicted this six years ago after I went to SAS Global Forum in 2010.
In my last post, I mentioned the propensity score graphic with mustaches.
Richard Culter’s presentation on PROC HPSPLIT, which was really excellent, made extensive use of graphics to illustrate fairly complex models.
You can create classification and regression trees (the model you can’t see in this tiny graphic on the left) and you can drill down into sub-trees for further analysis.
Sometimes your classification tree is very easily interpretable. For example, in this case here from the same presentation, each split represents a different type of vegetation/ land surface – water, two different species of tree, etc.
Speaking of classification, regression and PROC HPSPLIT ….
If you didn’t know, now you know
PROC HPSPLIT is a high performance procedure for fitting and classification now available in SAS/STAT which is useful for data sets where relationships are non-linear. It produces classification and regression trees, includes options for pruning trees and a whole lot more. It is now available on a single computer, not limited to high performance computing clusters. So, yay!
A regression tree is what you get when your dependent variable is continuous, and a classification tree when it is categorical, as in the vegetation example above.
On a semi-related note, graphics can even be used to show when a data set is not suited to a linear model as in the example below, also from Cutler’s presentation. You can see that all of the 1’s are in two quadrants and all of the 0’s in two other quadrants. Yes, you COULD use a regression line to fit this but that is not the best fit of the data.
Also, on a related topic that visualizing data, like all of statistics, really, is a process of iterations, I think this would be more obvious if the quadrants were color coded.
I have a lot more to say on this but I am in North Dakota speaking at the ND STEM conference this weekend and a kind soul gave me tickets to the hockey game in the president’s box, so, peace, I’m out.
Apr
19
SAS Global Forum Random Post 1: Statistics
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If you did not go to SAS Global Forum this week, here are some things you missed:
Me, rambling on about the 13 techniques all biostatisticians should know, including the answer to:
If McNemar and Kappa are both statistics for handling correlated, categorical data, how can they give you completely different results?
The answer is that the two test different hypotheses, apply different formula and are coded differently.
McNemar tests whether the marginal probabilities are the same. For example, when you switched your patients from drug one to drug two, was there a decrease in the number who experienced side effects? These are correlated data because they are the same people. Can’t get much more correlated than that.
Kappa tests whether the level of agreement of two raters is greater than would be expected by chance. I’ve rambled on it here before, using it to test the level of agreement that our 7 Generation Games raters have when scoring the pretest and post-test we use to assess whether kids are improving as a result of playing our games. Quick answer: Yes.
You also missed Lucy D’Agostino McGowan’s talk on propensity score matching integrating SAS and R.
Random notes from that presentation:
Why would you want to do this? Well, it would be lovely if you could do a randomized control trial and sending your subjects randomly off to treatment or control group.
However, what if your subjects tell you to drop dead they’re not going to be in your stupid treatment group?
In my experience, propensity scores have been commonly used when evaluating special programs that do not randomly receive patients. For example, patients sent to an Intensive Care Unit tend to be sicker than non-ICU patients. How then, do you decide if an ICU has any benefit when people in it are more likely to die?
Observational studies can use propensity scores to get a more unbiased estimate of treatment effects.
Propensity score matching assumes
- That there are no unmeasured confounders
- Every subject has a non-zero probability of receiving treatment.
Propensity scores are simply predicted values from a logistic regression predicting treatment
Useful rule of thumb:
Use caliper of .2 * pooled standard deviation
Only match people from treatment group to control group if their distance is within the caliper.
Also, I have slide envy because she thought to use mustaches and fedoras in illustrating propensity scores.
Also with really cool slides I was not quick enough to take a picture before he moved on …
Using Custom Tasks with In-memory statistics and SAS Studio by Steve Ludlow
I was able to find the slides from a related presentation he give in the UK last year. I linked to that one because it gave a little more detail on what SAS in-memory statistics is, how to use it and examples. If you had gone to his presentation, you probably would have wanted to learn more about this proc imstat and custom tasks of which he speaks.
Three points you might have come away with:
- Creating custom tasks is really easy
- Custom tasks could be really useful for teams sharing a large data base. Say, for example, you are on a longitudinal project study development of at-risk youth from age 12-25. You might have all kinds of people doing similar analyses, maybe looking at predictors of high school dropout, say. You could save your task and re-run it with next year’s data, only for females or in a hundred other ways.
- Custom tasks could be super-useful for teaching. Have the students run and inspect tasks you create and then modify these for their own analyses.
Okay, off to more sessions. Just a reminder, if you are here and feeling guilt that you left your children/ grandchildren at home, you can buy Fish Lake or Spirit Lake for them to play while you are gone. They’ll get smarter and you will get brownie points from their mom / dad / teacher .
Apr
2
Statistics Guru Predicts Republican Sweep! With Proc GMAP
Filed Under Software, statistics | Leave a Comment
Esteemed statistics guru, Dr. Nathaniel Golden has some sobering news for Democrats. His latest models predict a Republican blow out. As can be seen by the map below, the Republican front-runner has tapped into the mood of resentment in the country’s non-elites. When the dust has settled, only the two highest earning states in the country will remain in the blue column, Maryland and New Jersey (seriously, New Jersey). Code used in creating this map and the statistics behind it can be found below.
Step 1: Create a data set
Oh, and April Fool’s ! I just made up these data. If you really do need a data set with state data aligned to SAS maps, though, you can do what I did and pull it from the UCLA Stats Site. If you had real data, say percent of people who use methamphetamine, or whatever, you could just replace the last column there with your data. Since I did not have actual data, I just created a variable that was 40,000 for everything less than 51,000, and 51,000 for everything over. I’m going to use that in the PROC FORMAT below.
Also, even though my data are not nicely aligned here, note that the statename variable has a width of 20 so make sure you align your data like that so that state comes in column 22 or after.
DATA income2000;
INPUT statename $20. state income ;
IF income < 51000 THEN vote = 40000 ;
ELSE vote = 51000 ;
DATALINES ;
Maryland 24 51695
Alaska 2 50746
New Jersey 34 51032
Connecticut 9 50360
— a bunch more data
;
Here’s how you set up a PROC FORMAT for the two categories.
PROC FORMAT
VALUE votfmt low-50000="Republican"
50001-high="Democrat";
*** Making the patterns red and blue ;
pattern1 value=msolid color=red;
pattern2 value=msolid color=blue;
*** Making the map ;
proc gmap data = income2000 map=maps.us;
id state;
choro vote;
format vote votfmt.;
The important thing to keep in mind is if you want a U.S. map with the states that maps.us is in a SAS library named maps. Like the sashelp library, it’s already there, you don’t need to create it or assign it in the LIBNAME statement, you can just reference it. Go look under your libraries. See, I was right.
And don’t forget to vote. I don’t care how busy you are. You don’t want this, do you?
Mar
20
Plots of Relative Risk: A picture says 1,000 words
Filed Under Software, statistics, Technology | 1 Comment
I can’t believe I haven’t written about this before – I’m going to tell you an easy (yes, easy) way to find and communicate to a non-technical audience standardized mortality rates and relative risk by strata.
It all starts with PROC STDRATE . No, I take that back. It starts with this post I wrote on age-adjusted mortality rates which many cohorts of students have found to be – and this is a technical term here – “really hard”.
Here is the idea in a nutshell – you want to compare two populations, in my case, smokers and non-smokers, and see if one of them experiences an “event”, in my case, death from cancer, at a higher rate than the other. However, there is a problem. Your populations are not the same in age and – news flash from Captain Obvious here – old people are more likely to die of just about anything, including cancer, than are younger people. I say “just about anything” because I am pretty sure that there are more skydiving deaths and extreme sports-related deaths among younger people.
So, you compute the risk stratified by age. I happened to have this exact situation here, and if you want to follow along at home, tomorrow I will post how to create the data using the sashelp library’s heart data set.
The code is a piece of cake
PROC STDRATE DATA=std4
REFDATA=std4
METHOD=indirect(af)
STAT=RISK
PLOTS(STRATUM=HORIZONTAL);
POPULATION EVENT=event_e TOTAL=count_e;
REFERENCE EVENT=event_ne TOTAL=count_ne;
STRATA agegroup / STATS;
The first statement gives the data set name that holds your exposed sample data, e.g., the smokers, your reference data set of non-exposed records, in this example, the non-smokers. You don’t need these data to be in two different data sets, and, this example, they happen to be in the same one. The method used for standardization is indirect. If you’re interested in the different types of standardization, check out this 2013 SAS Global Forum paper by Yang Yuan.
STAT = RISK will actually produce many statistics, including both crude risk estimates and estimates by strata for the exposed and non-exposed groups, as well as standardized mortality rate – just, a bunch of stuff. Run it yourself and see. The PLOTS option is what is of interest to me right now. I want plots of the risk by stratum.
The POPULATION statement gives the variable that holds the value for the number of people in the exposed group who had the event, in this case, death by cancer, and the count is the total in the exposed group.
The REFERENCE statement names the variable that holds the value of the number in the non-exposed group who had the event, and the total count in the non-exposed group (both those who died and those who didn’t).
The STRATA statement gives the variable by which to stratify. If you don’t need your data set stratified because there are no confounding variables – lucky you – then just leave this statement out.
Below is the graph
The PLOTS statement produces plots of the crude estimate of the risk by strata, with the reference group risk as a single line. If you look at the graph above you can see several useful measures. First, the blue circles are the risk estimate for the exposed group at each age group and the vertical blue bars represent the 95% confidence limits for that risk. The red crosses are the risk for the reference group at each age group. The horizontal, solid blue line is the crude estimate for the study group, i.e., smokers, and the dashed, red line is the crude estimate of risk for the reference group, in this case, the non-smokers.
Several observations can be made at a glance.
- The crude risk for non-smokers is lower than for smokers.
- As expected, the younger age groups are below the overall risk of mortality from cancer.
- At every age group, the risk is lower for the non-exposed group.
- The differences between exposed and non-exposed are significantly different for the two younger age groups only, for the other two groups, the non-smokers, although having a lower risk, do fall within the 95% confidence limits for the exposed group.
There are also a lot more statistics produced in tables but I have to get back to work so maybe more about that later.
I live in opposite world
Speaking of work — my day job is that I make games for 7 Generation Games and for fun I write a blog on statistics and teach courses in things like epidemiology. Actually, though, I really like making adventure games that teach math and since you are reading this, I assume you like math or at least find it useful.
Share the love! Get your child, grandchild, niece or nephew a game from 7 Generation Games.
One of my favorite emails was from the woman who said that after playing the games several times while visiting her house, her grandson asked her suspiciously,
Grandma, are these games on your computer a really sneaky way to teach me math?
You can check out the games here and if you have no children to visit you or to send one as a gift, you can give one to a school – good karma. (But, hey, what’s with the lack of children in your life? What’s going on?)
Mar
10
SENSITIVITY, SPECIFICITY AND SAS USAGE NOTES
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SENSITIVITY AND SPECIFICITY – TWO ANSWERS TO “DO YOU HAVE A DISEASE?”
Both sensitivity and specificity address the same question – how accurate is a test for disease – but from opposite perspectives. Sensitivity is defined as the proportion of those who have the disease that are correctly identified as positive. Specificity is the proportion of those who do not have the disease who are correctly identified as negative.
Students and others new to biostatistics often confuse the two, perhaps because the names are somewhat similar. If I was in charge of naming things, I would have named one ‘sensitivity’ and the other something completely different like ‘unfabuloso’. Why I am never consulted on these issues is a mystery to me, too.
Specificity and sensitivity can be computed simultaneously, as shown in the example below using a hypothetical Disease Test. The results are in and the following table has been obtained:
Disease | No Disease | |
Test Positive | 240 | 40 |
Test Negative | 60 | 160 |
Results from Hypothetical Screening Test
COMPUTING SENSITIVITY AND SPECIFICITY USING SAS
Step 1 (optional): Reading the data into SAS. If you already have the data in a SAS data set, this step is unnecessary.
The example below demonstrates several SAS statements in reading data into a SAS dataset when only aggregate results are available. The ATTRIB statement sets the length of the result variable to be 10, rather than accepting the SAS default of 8 characters. The INPUT statement uses list input, with a $ signifying character variables.
DATALINES;
a statement on a line by itself, precedes the data. (Trivial pursuit fact : CARDS; will also work, dating back to the days when this statement was followed by cards with the data punched on them.) A semi-colon on a line by itself denotes the end of the data.
DATA diseasetest ;
ATTRIB result LENGTH= $10 ;
INPUT result $ disease $ weight ;
DATALINES ;
positive present 240
positive absent 40
negative present 60
negative absent 160
;
Step 2: PROC FREQ
PROC FREQ DATA= diseasetest ORDER=FREQ ;
TABLES result* disease;
WEIGHT weight ;
Yes, plain old boring PROC FREQ. The ORDER = FREQ option is not required but it makes the data more readable, in my opinion, because with these data the first column will now be those who had a positive result and did, in fact, have the disease. This is the numerator for the formula for sensitivity, which is:
Sensitivity = (Number tested positive)/ (Total with disease).
TABLES variable1*variable2 will produce a cross-tabulation with variable1 as the row variable and variable2 as the column variable.
Weight weightvariable will weight each record by the value of the weight variable. The variable was named ‘weight’ in the example above but any valid SAS name is acceptable. Leaving off this statement will result in a table that only has 4 subjects, 1 subject for each combination of result and disease, corresponding to the data lines above.
Results of the PROC FREQ are shown below. The bottom value in each box is the column percent.
Because the first category happens to be the “tested positive” and the first column is “disease present”, the column percent for the first box in the cross-tabulation – positive test result, disease is present – is the sensitivity, 80%. This is the proportion of those who have the disease (the disease present column) who had a positive test result.
Table of result by disease | |||
result | disease | ||
Frequency Percent Row Pct Col Pct |
present | absent | Total |
positive | 240 48.00 85.71 80.00 |
40 8.00 14.29 20.00 |
280 56.00 |
negative | 60 12.00 27.27 20.00 |
160 32.00 72.73 80.00 |
220 44.00 |
Total | 300 60.00 |
200 40.00 |
500 100.00 |
Output from PROC FREQ for Sensitivity and Specificity
The column percentage for the box corresponding to a negative test result and absence of disease is the value for specificity. In this example, the two values, coincidentally, are both 80%.
Three points are worthy of emphasis here:
- While the location of specificity and sensitivity in the table may vary based on how the data and PROC FREQ are coded, the values for sensitivity and specificity will always be diagonal to one another.
- This exact table produces four additional values of interest in evaluating screening and diagnostic tests; positive predictive value, negative predictive value, false positive probability and false negative probability. Further details on each of these, along with how to compute the confidence intervals for each can be found in Usage Note 24170 (SAS Institute, 2015).
- The same exact procedure produces six different statistics used in evaluating the usefulness of a test. Yes, that is pretty much the same as point number 2, but it bears repeating.
Speaking of that SAS Usage Note, you should really check it out.
Feb
24
SAS Studio: Finding prevalence with pointing and clicking
Filed Under Software, statistics | 3 Comments
Policy makers have very good reason for wanting to know how common a condition or disease is. It allows them to plan and budget for treatment facilities, supplies of medication, rehabilitation personnel. There are two broad answers to the question, “How common is condition X?” and, interestingly, both of these use the exact same SAS procedures. Prevalence is the number of persons with a condition divided by the number in the population. It’s often given as per thousand, or per 100,000, depending on how common the condition is. Prevalence is often referred to as a snapshot. It’s how many people have a condition at any given time.
Just for fun, let’s take a look at how to compute prevalence with SAS Studio.
Step 1: Access your data set
First, assign a libname so that you can access your data. To do that, you create a new SAS program by clicking on the first tab in the top menu and selecting SAS Program.
libname mydata "/courses/number/number/" access=readonly;
(Students only have readonly access to data sets in the course directory. This prevents them from accidentally deleting files shared by the whole class. As a professor with many years of experience, let me just tell you that this is a GREAT idea.)
Click on the little running guy at the top of your screen and, voila, your LIBNAME is assigned and the directory is now available for access.
(Didn’t believe me there is a little running guy that means “run”? Ha!)
Next, in the left window pane, click on Tasks and in the window to the right, click on the icon next to the data field.
From the drop down menu of directories, select the one with your data and then click on the file you need to analyze.
Step 2: Select the statistic that you want and then select the variable. In this case, I selected one-way frequencies, and one cool thing is that SAS will automatically show you ONLY the roles you need for a specific test. If you were doing a two-sample t-test, for example, it would ask for you groups variable and your analysis variable. Since I am doing a one-way frequency, there is only an analysis variable.
When you click on the plus next to Analysis Variables, all of the variables in your data set pop up and you can select which you want to use. Then, click on your little running guy again, and voila again, results.
So … the prevalence of diabetes is about 11% of the ADULT population in California, or about 110 per 1,000.
You can also code it very simply if you would like:
libname mydata “/courses/number/number/” access=readonly;
PROC FREQ DATA = mydata.datasetname ;
TABLE variable ;
Of course, all of this assumes that your data is cleaned and you have a binary variable with has disease/ doesn’t have disease, which is a pretty large assumption.
Now, curiously, the code above is the exact SAME code we used to compute incidence of Down syndrome a few weeks ago. What’s up with that and how can you use the exact same code to compute two different statistics?
Patience, my dear. That is a post for another day.
Feb
16
Urban vs Rural Barriers to Ed Tech: An example of Fisher’s Exact Test
Filed Under computer games, Software, statistics, Technology | Leave a Comment
Who was it that said asking a statistician about sample size is like asking a jeweler about price. If you have to ask, you can’t afford it.
We all know that the validity of a chi-square test is questionable if the expected sample size of the cells is less than five. Well, what do you do when, as happened to me recently, ALL of your cells have a sample size less than five?
The standard answer might be to collect more data, and we are in the process of that, but having the patience of the average toddler, I wanted that data analyzed NOW because it was very interesting.
It was our hypothesis that rural schools were less likely to face obstacles in installing software than urban schools, due to the extra layers of administrative approval required in the latter (some might call it bureaucracy). On the other hand, we could be wrong (horrors!). Maybe rural schools had more problems because they had more difficulty finding qualified personnel to fill information technology positions. We had data from 17 schools, 9 from urban school districts and 8 from rural districts. To participate in our study, schools had to have a contact person who was willing to attempt to get the software installed on the school computers. This was not a survey asking them whether it would be difficult or how long it would take. We actually wanted them to get software ( 7 Generation Games ) not currently on their school computers installed. To make sure that cost was not an issue, all 17 schools received donated licenses.
You can see the full results here.
In short, 8 of the 9 urban schools had barriers to installation of the games which delayed their use in the classroom by a median of three months. I say median instead of mean because four of the schools STILL have not been able to get the games installed. The director of one after-school program that wanted to use the games decided it was easier for his program to go out and buy their own computers than to get through all of the layers of district approval to use the school computer labs, so that is what they did.
For the rural schools, 7 out of 8 reported no policy or administrative barriers to installation. The median length of time from when they received the software to installation was two weeks. In two of the schools, the software was installed the day it was received.
Here is a typical comment from an urban school staff member,
“I needed to get it approved by the math coach, and she was all on board. Then I got it approved at the building level. We had new administration this year so it took them a few weeks to get around to it, and then they were all for it. Then it got sent to the district level. Since your games had already been approved by the district, that was just a rubber stamp but it took a few weeks until it got back to us, then we had all of the approvals so we needed to get it installed but the person who had the administrator password had been laid off. Fortunately, I had his phone number and I got it from him. Then, we just needed to find someone who had the spare time to put the game on all of the computers. All told, it took us about three months, which was sad because that was a whole semester lost that the kids could have been playing the games. “
And here is a typical comment from a rural staff member.
“It took me, like, two minutes to get approval. I called the IT guy and he came over and installed it.”
The differences sound pretty dramatic, but are they different from what one would expect by chance, given the small sample size? Since we can’t use a chi-square, we’ll use Fisher’s exact test. Here is the SAS code to do just that:
PROC FREQ DATA = install ;
TABLES rural*install / CHISQ ;
Wait a minute! Isn’t that just a PROC FREQ and a chi-square? How the heck did I get a Fisher’s exact test from that?
Well, it turns out that if you have a 2 x 2 table, SAS automatically computes the Fisher exact test, as well as several others. I told you that you could see the full results here but you didn’t look, now, did you?
You can see the full results here.
In case you still didn’t look, the probability of obtaining this table under the null hypothesis that there is no difference in administrative barriers in urban versus rural districts is .0034.
If you think these data suggest it is easier to adopt educational technology in rural districts than in urban ones, well, not exactly. Rural districts have their own set of challenges, but that is a post for another day.
Feb
9
Watch me work: Finishing the test scoring with more SAS character functions
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Recall that in the last post we were using SAS functions to score a test that had been completed by middle school and upper elementary students. Since we wanted to make it as easy as possible for students to enter their answers, we accepted just about any format.
Picking up where we left off …
SUBSTR FUNCTION – READING ONLY PART OF AN ANSWER
In one question, the correct answer is 1/8 . Students entered 1/8, 1/8 cup, 1/8 cup of beans, and so on. To score these, we use the substr function to read the first 3 characters and score the problem correct if those are “1/8”
If substr(q22,1,3) = “1/8” then q22 = 1 ;
else q22 = 0 ;
MISSING FUNCTION – TO CHECK FOR MISSING DATA
For q27, students clicked on which of the equations are correct. If they clicked the correct equation, the variable was set to 1.
When they didn’t click on anything, it was missing. I wanted that to be changed to a zero, so I used the missing function, like this:
if missing(q27) then q27 = 0 ;
ARRAY, DO-LOOP and INPUT FUNCTION
Now, SAS is not the newest kid on the block
and I can relate, because neither am I, not even if I’m on a relatively old block
The problem with being an older language is that you have static types and you cannot have mixed arrays. What does that mean? It means that if you have defined q1 as a character variable because it might have a $ in it then by God it is going to stay a character variable and you can’t be doing any funny stuff like finding the mean and standard deviation of it. Also, if you are going to have an array, everything in it better be either all character variables or all numeric variables.
Well, fine, then, here is how I change all those now scored questions to numeric. First, I created a new numeric array of 32 items. You can tell it is numeric because there is no $.
Second, I used a DO loop and the INPUT function. The input function will read in a variable and and read it out in a different format, in this case, a numeric variable with a length of 8 and 0 decimal places.
I dropped the index variables j and i , which I mentioned in a previous post.
Now that I have my variables all nicely numeric, I can use the SUM function and add up all of the scored items into a total score.
array items {32} item1 – item32 ;
do j = 1 to 32 ;
items{j} = input(qs{j},8.0);
end;
drop i j ;
total = sum(of item1-item32);
Now that I have my data, the fun stuff begins, but that’s for another post because I need to get back to making games.
This is my day job. Check it out. Buy a game. Maturity is over-rated!
Or donate a game to a school for good karma.