### Mar

#### 25

# How to compute a standard deviation and control chart when you don’t have raw data

Filed Under Software, statistics, Technology | 1 Comment

- I created two data sets, named q4disc and q4disc3, keeping the month of discharge and the number dissatisfied at discharge and dissatisfied 3 months later, respectively.
- I read in the 3 values I was given, month of sample, number unsatisfied at discharge and number unsatisfied 3 months later.
- Now, I am going to create a data set of raw data based on the numbers I have. First, in a do loop, for as many as people said they were unsatisfied, I set the value of undisc (unsatisfied at discharge) to to 1 and output a record to the q4disc dataset.
- Next, in a do loop for 500- the number dissatisfied, I set undisc = 0 and output a record to the same dataset.
- Now, repeat steps 3 & 4 to create a data set of the values of people unhappy 3 months after discharge.
- Following the programming statements are the original data.

So, now, I have created two data sets of 6,000 records each with three variables. Doesn’t seem that efficient of a way to do it but now I have the data I need and it didn’t take long and doesn’t take up much space.

“The XSCHART statement creates and charts for subgroup means and standard deviations, which are used to analyze the central tendency and variability of a process.”

For the three months after discharge variable, just do another PROC SHEWHART with q4disc3 as the dataset and undisc3 as the measurement variable.

OR , once you have the dataset created, you can get the chart using SAS Studio by selecting the CONTROL CHARTS task

Either way will give you this result:

### Mar

#### 12

Perhaps you have watched the Socrata videos on how to do data visualization with government data sets and it is still not working for you. Here is a step by step example of answering a simple question.

### Is the prevalence of alcohol use among youth higher in rural states than urban ones?

You can click on a link below to go directly to that step.

First, I went to this Chronic Disease and Health Promotion Data & Indicators site.

Second, I selected Chronic Disease Indicators for my health area of interest.

Third, I selected ALCOHOL – which brought me to the screen showing all the columns of data and a bunch of choices.

Fourth, I clicked on FILTER on the right of the screen and then select a column to filter by.

Chrome did not give me a scroll bar so the furthest option I could get was Topic. I switched over to Firefox and was able to get this menu where I selected Question and Alcohol use among youth. You have to type in the value that you want. Make sure it is spelled exactly the same as in the data set.

Fifth, since I wanted to compare urban and rural states, I clicked Add a New Filter Condition and then selected California, New York, North Dakota and Wyoming with LocationDesc as the filter condition. Make sure the box next to each condition you want is clicked on.

Sixth, I looked at my data, saw there was no data for California and I was sad. Not every state participates in every data set.

7. So, I decided to compare urban, eastern states wth rural midwest/west and I selected New York, New Jersey, Massachusetts, Wyoming, North Dakota and Montana All had data so I was good to go.

In case you were wondering, I based my choice on the listing of states by urbanization , New Jersey is #2, MA 5 and NY 13

On the other extreme, Wyoming is 39, North Dakota is 42, and Montana 47 so I thought this was a pretty good split.

8. I clicked on visualize on the right, selected Column as the type of chart, Location Desc as the label data, DataValueAlt as the data value, and there was my chart

Note: I could not select DataValue. My guess is that was a string variable. I had to select DataValuealt, which was the exact same value

9.Just to make it more obvious, I went in and sorted on data value, which caused the chart to be recreated automatically.

You can see below the chart it created. It’s pretty clear that in these data there is no relationship between urbanization and alcohol use among youth.

New York and New Jersey where the lowest and highest prevalence, respectively. I was hoping to see a pattern with more rural states higher, but it seemed to be pretty unrelated.

HOW TO DOWNLOAD THE DATA SETS FOR ANALYSIS

Perhaps you would prefer to download the data set for import into some other tool, say, Excel or SAS. The first three steps are the same, into you find the data set you want.

This next step is not required , but the data sets can be pretty big, so I’d suggest filtering on at least one major variable first. For example, you can click the three rows next to any column, say, Question, and then select the question that interests you, say Binge Drinking.

Next, click the EXPORT button at the top right of the screen. Select the format in which you want your file to be downloaded. That’s it!

### Mar

#### 2

# Excel for regression analysis: What a surprise!

Filed Under Software, statistics, Technology | Leave a Comment

I wouldn’t normally consider Excel for analysis, but there are four reasons I’ll be using it sometimes for the next class I’m teaching. First of all, we start out with some pretty basic statistics, I’m not even sure I’d call them statistics, and Excel is good for that kind of stuff. Second, Excel now has data analysis tools available for the Mac – years ago, that was not the case. Since my students may have Mac or Windows, I need something that works on both. Third, many of the assignments in the course I will be teaching use small data sets – and this is real life. If you are at a clinic, you don’t have 300,000,000 records.Four, the number of functions and ease of use of functions in Excel has increased over the years.

**For example,**

**TRANSPOSE AN ARRAY IN EXCEL**

Select all of the data you want and select COPY

Click on the cell where you want the data copied and select PASTE SPECIAL from the edit menu. Click the bottom right button next to TRANSPOSE and click OK. Voila. Data transposed.

**PERFORMING A REGRESSION ANALYSIS**

Once you have your data in columns (and if it isn’t, see TRANSPOSE above), you just need to

- Add the Analysis Pack. You only need to do this once and it should be available with Excel forever more. To do that, go to TOOLS and select EXCEL ADD-INS. Then click the box next to Analysis ToolPak and click OK.
- Now, go to TOOLS, select DATA ANALYSIS and then pick REGRESSION ANALYSIS

You just need to select the range for the Y variables, probably one column, select the range for the X variables, probably a column adjacent to it, and click OK. You may also select confidence limits, fit plots, residuals and more.

So, yeah, for simple analyses, Excel can be super-simple.

Believe it or not, this is what I do for fun. In my day job, I make video games that teach math and social studies.

You can check out the games we make here.

### Dec

#### 9

# Standardized testing: Solving your reliability problem

Filed Under computer games, statistics | Leave a Comment

One person, whose picture I have replaced with the mother from our game, Spirit Lake, so she can remain anonymous, said to me:

But there is nothing we can do about it, right?I mean, how can you stop kids from guessing?

This was the wrong question. What we know about the measure could be summarized as this:

- Students in many low-performing schools were even further below grade level than we or the staff in their districts had anticipated. This is known as new and useful knowledge, because it helps to develop appropriate educational technology for these students. (Thanks to USDA Small Business Innovation Research funds for enabling this research.)
- Because students did not know many of the answers, they often guessed at the correct answer.
- Because the questions were multiple choice, usually A-D, the students had a 25% probability of getting the correct answer just by chance, interjecting a significant amount of error when nearly all of the students were just guessing on the more difficult items.
- Three-fourths of the test items were below the fifth-grade level. In other words, if you had only gotten correct the answers three years below your grade level, the average seventh-grader should have scored 75% – generally, a C.

There are actually two ways to address this and we did both of them. The first is to give the test to students who are more likely to know the answers so less guessing occurs. We did this, administering the test to an additional 376 students in low-performing schools in grades four through eight. While the test scores were significantly higher (Mean of 53% as opposed to mean of 37% for the younger students) they were still low. The larger sample had a much higher reliability of 87. Hopefully, you remember from your basic statistics that restriction of range attenuates the correlation. By increasing the range of scores, we increased our reliability.

The second thing we did was remove the probability of guessing correctly by changing almost all of the multiple choice questions into open-ended ones. There were a few where this was not possible, such as which of four graphs shows students liked eggs more than bacon . We administered this test to 140 seventh-graders. The reliability, again was much higher: .86

However, did we really solve the problem? After all, these students also were more likely to know (or at least, think they knew, but that’s another blog) the answer. The mean went up from 37% to 46%.

To see whether the change in item type was effective for lower performing students, we selected out a sub-sample of third and fourth-graders from the second wave of testing. With this sample, we were able to see that reliability did improve substantially from .57 to. 71 . However, when we removed four outliers (students who received a score of 0), reliability dropped back down to .47.

What does this tell us? Depressingly, and this is a subject for a whole bunch of posts, that a test at or near their stated ‘grade level’ is going to have a floor effect for the average student in a low-performing school. That is, most of the students are going to score near the bottom.

It also tells us that curriculum needs to start AT LEAST two or three years below the students’ ostensible grade level so that they can be taught the prerequisite math skills they don’t know. This, too, is the subject for a lot of blog posts.

—-

*For schools who use our games, we provide automated scoring and data analysis. If you are one of those schools and you’d like a report generated for your school, just let us know. There is no additional charge.*

### Nov

#### 20

Last post I wrote a little about local norms versus national norms and gave the example of how the best-performing student in the area can still be below grade level.

Today, I want to talk a little about tests. As I mentioned previously, when we conducted the pretest prior to student playing our game, Spirit Lake, the average student scored 37% on a test of mathematics standards for grades 2-5. These were questions that required them to say, subtract one three-digit number from another or multiply two one-digit numbers.

Originally, we had written our tests to model the state standardized tests which, at the time, were multiple choice. This ended up presenting quite a problem. Here is a bit of test theory for you. A test score is made up two parts – true score variance and error variance.

True score variance exists when Bob gets an answer right and Fred gets it wrong because Bob really knows more math (and the correct answer) compared to Fred.

Error variance occurs when, for some reason, Bob gets the answer right and Fred gets it wrong even though there really is no difference between the two. That is, the variance between Fred and Bob is an error. (If you want to be picky about it, you would say it was actually the variance from the mean was an error, but just hush.)

How could this happen? Well, the most likely explanation is that Bob guessed and happened to get lucky. (It could happen for other reasons – Fred really knew the answer but misread the question, etc.)

If very little guessing occurs on a test, or if guesses have very little chance of being correct, then you don’t have to worry too much.

However, the test we used initially had four multiple-choice items for each question. The odds of guessing correctly were 1 in 4, that is, 25%. Because students turned out to be substantially further below grade level than we had anticipated, they did a LOT of guessing. In fact, for several of the items, the percentage of correct responses was close to the 25% students would get from randomly guessing.

When we computed the internal consistency reliability coefficient (Cronbach alpha) which measures the degree to which items in a test correlate with one another, it was a measly .57. In case you are wondering, no, this is not good. It shows a relatively high degree of error variance. So, we were sad.

**SAS CODE FOR COMPUTING ALPHA**

`PROC CORR DATA = mydataset NOCORR ALPHA ;`

VAR item1 – item24 ;

The very simple code above will give you coefficient alpha as well as the descriptive statistics for each item. Since we very wisely scored our items 0 = wrong, 1= right a mean of say, .22 would indicate that only 22% of students answered an item correctly.

To find out how we fixed this, read the next post.

### Nov

#### 19

# Standardized Testing In Plain Words

Filed Under computer games, statistics | 1 Comment

I hate the concept of those books with titles like “something or other for dummies” or “idiot’s guide to whatever” because of the implication that if you don’t know microbiology or how to create a bonsai tree of take out your own appendix you must be a moron. I once had a student ask me if there was a structural equation modeling for dummies book. I told her that if you are doing structural equation modeling you’re no dummy. I’m assuming you’re no dummy and I felt like doing some posts on standardized testing without the jargon.

I haven’t been blogging about data analysis and programming lately because I have been doing so much of it. One project I completed recently was analysis of data from a multi-year pilot of our game, Spirit Lake.

Before playing the game, students took a test to assess their mathematics achievement. Initially, we created a test that modeled the state standardized tests administered during the previous year, which were multiple choice. We knew that students in the schools were performing below grade level but how far below surprised both us and the school personnel. A sample of 93 students in grades 4 and 5 took a test that measured math standard for grades 2 through 5. The mean score was 37%. The highest score was 63%.

Think about this for a minute in terms of local and national norms. The student , let’s call him Bob, who received a 63% was the highest among students from two different schools across multiple classes. (These were small, rural schools.) So, Bob would be the ‘smartest’ kid in the area. With a standard deviation of 13%, Bob scored two standard deviations above the mean.

Let’s look at it from a different perspective, though. Bob, a fifth-grader, took a test where three-fourths of the questions were at least a year, if not, two or three, below his current grade level, and barely achieved a passing score. Compared to his local norm, Bob is a frigging genius. Compared to national norms, he’s none too bright. I actually met Bob and he is a very intelligent boy, but when most of his class still doesn’t know their multiplication tables, it’s hard for the teacher to get time to teach Bob decimals, and really, why should she worry, he’s acing every test. Of course, the class tests are a year below what should be his grade level.

One advantage of standardized testing, is that if every student in your school or district is performing below grade level it allows you to recognize the severity of the problem and not think “Oh, Bob is doing great.”

He wouldn’t be the first student I knew who went from a ‘gifted’ program in one community to a remedial program when he moved to a new, more affluent school.

—

### Oct

#### 24

# Statistics Answers the Most Important Social Question

Filed Under computer games, statistics | Leave a Comment

Occasionally, when I am teaching about a topic like repeated measures Analysis of Variance, a brave student will raise a hand and ask,

Seriously, professor, WHEN will I ever use this?

The aspiring director of a library, clinic, afterschool program, etc. does not see how statistics apply to conducting an outreach campaign or HIV screening or running a recreational program for youth – or whatever one of hundreds of other good causes that students intend to pursue with their graduate degrees. Honestly, they often look at the required research methods and statistics courses is a waste of time mandated for some unknown reason by the University, probably to keep professors employed. Often, they will find a way to do a dissertation using only qualitative analysis and never think about statistics again.

This is a huge mistake.

For all of those people who say, “I never used statistics in my career”, I would answer, “well, I never used French in my career either and you know why – because I never learned it very well.”

Now, those people who don’t see a real use for French probably aren’t convinced. However, to me, it’s pretty evident that if I could speak French I could be making games in both French and English.

Actually, statistics can answer the very most important question in any social program – does it work?

So, I had written a couple of blogs about the presentation I gave at SACNAS (Society for the Advancement of Chicanos and Native Americans in Science) where I discussed using statistics to identify need for intervention and mathematics for students prior to middle school. I also gave examples of teaching statistics concepts in games.

The question is, did these games work for increasing student scores?

For this – surprise! Surprise! Drumroll – – – we used repeated measures Analysis of Variance. If you look at the graph below you can see that the students who played the games improved substantially more from pretest to posttest than the students in the control group.

This was a relatively small sample, because it was our first pilot study, and conducted in two small rural schools, that also happen to have very high rates of mobility and absenteeism, so we were only able to obtain complete data from 58 students.

Now, the results look impressive but where these differences higher than one would expect by chance with four groups (two grades from each school) of a fairly small size?

Well, when we look at the ANOVA results we see that the time by school interaction, which tests if one school changed more overtime than the other is quite significant (F = 7.13, P = .01). Yes, the P value equaled exactly .0100.

The time by school by grade 3 – way interaction was not significant. It’s worth noting that the fifth grade at the intervention school had less time playing the game due to logistical reasons – they had to schedule the computer lab as opposed to playing in their classroom, and sometimes, their class being scheduled later in the day, they missed playing the game altogether when school was let out early due to weather.

One way that I could reanalyze these data – and I will – would be to look at it not by grade but by time spent playing. So, instead of four groups, I would have three – those who played the game not at all, in other words, the control group, those who played at less than recommended and those who played it the recommended amount.

My point is that repeated measures ANOVA is just one of the many statistical techniques that can answer the most important questions in social programs – whether something works and under what conditions it works best. There’s also the question of who it works best for – and statistics can answer that too.

**So, my answer to the student who questions if he or she will ever use this is, “if you’re smart you will.”**

For all of those who have asked us if these data are going to be published, the answer is yes, we have two articles in press that should come out in 2017.

We are working on more in our copious spare time that we do not have, but right now we are focusing on game updates.

and on our new, free iPad game, Making Camp

### Oct

#### 14

# Statistics save the world

Filed Under statistics | 1 Comment

I will be the first to admit that I’m not the warm fuzzy type. Maybe you’re like me, you’d like to do good for your community but you just can’t see yourself as a physician.

Maybe your bedside manner is to snap at someone to quit being a whiner.

Or maybe you really are a sweet kind person but you are not very extroverted. You just can’t see yourself looking someone in the eye and asking them to tell you about their problems at home. Perhaps you really genuinely care about children in your community and really would like to help them succeed in school but the thought of speaking in front of the 30 people makes you break out into a cold sweat – even if the 30 people are all under 13 years old.

Maybe, like me, you really like math. To be specific, maybe you really like analyzing data, looking for correlations, inspecting distributions. Maybe, you really like programming. Or that’s what we called it in my day – now all the cool kids call it coding.

Does that mean that we are condemned to be a bunch of Silicon Valley dwelling, Soylent swigging, soulless drones with nothing to keep us warm at night but our stock options? In fact, quite the opposite! These last few years I have been having a lot of fun working with statistics in two very different ways.

First of all, I’ve been working with our team at 7 Generation Games to make adventure games that teach statistical concepts.

Let me give you an example. Some items are more valuable than others. Why? Try to figure it out by looking at this distribution.

Players can click on this interactive graph for help reading it. They have a sentence written with blanks to fill in to model academic language.

Once a student answers one or two questions in the game correctly, the reward is being able to play a related game – in this case, collecting items in the jungle. As you might guess, the more common items are worth less in the game.

Here is a second example. Below, we have a section of our 3D game where the player is building a pyramid.

To build your pyramid fast enough that the Emperor doesn’t decide to chop off your head, you want to get stronger than average workers. What is an easy way to determine if you have stronger than average workers? Find the median!

Players can also click a button to switch the page to an explanation in Spanish.

Just because we were all out last night at the Latino Tech meet-up to celebrate Hispanic Heritage Month, don’t assume everything we make it is focused on Latinos.

Here is yet another example of teaching statistics in a game, this one re-tracing the Ojibwe migration.

In this case, the player computes an average to figure how many miles need to be walked per day to get to the end of the trail in eight days.

Get this question right and you can play the next level, where you canoe down the river to meet up with your old uncle who will – surprise – pose another statistics problem before you can move on to the next level.

So, there you have it! You can apply your knowledge of statistics to create adventure video games that teach students. As you can see, you also can apply knowledge of programming to meet the special needs of students whether it is to have a page read to them (did you notice the read it to me button in the page above?) Or to have it translated into a second language.

I’ll bet that you thought I was going to talk about using statistics to evaluate whether the games worked. That, is a post for another day.

_______

### Oct

#### 13

# Statistics as social justice

Filed Under statistics | Leave a Comment

To be honest, when I first began studying statistics social justice never entered the equation. Like most people in America, I think, I was concerned about problems like crime, poverty, low educational attainment of minority groups. Like most people, my concern didn’t translate into much actual effort on my part.

No, I took my first statistics course because it seemed really interesting. I made a C+ in it because it was Monday, Wednesday and Friday afternoons and the fraternity parties started on Friday afternoon, so I missed every third class. When later research of mine showed a negative correlation between absenteeism and grades I was not surprised. I had personal experience. I mentioned this too, because I have seen too many women and minority students discouraged from science and technical fields when they were not at the top of the class right away.

It’s a very long journey for my first statistics class in 1978 to now. Although I started learning statistics because I was just very interested in what I would call “messing around with data” and I like programming a lot, along the way I learned something interesting.

A lot of money is allocated based on statistics. Maybe not directly so, not very often does someone say to you,

“That’s a very interesting statistic. Have $9 million!”

Statistics do come into play. About 1/4 of a century ago, I realized that grant money often did not go to the program where the funds were needed most or the staff were most effective. No, they went to the programs that would best at writing grant proposals. These proposals included statistics on needs assessment and evaluation of prior efforts. Often, people who were really good at helping low income students raise their academic achievement or getting people with substance abuse disorders off of drugs were nowhere near as good at writing grant proposals.

For all of those proposals, statistics were required. What proportion of students in the target schools are achieving below grade level? What was the distribution of test scores of students in the previous three years and how does that compare to the state or national average? What evidence is there that the proposed program for academic enrichment will have any impact on the students at all?

Often, my very well meaning colleagues disagreed with the necessity for this type of analysis, even while they appreciated me doing it and made good use of the grant funds. Their point of view was that they knew what worked in their classrooms or clinics.

Personally, I feel that if all I had done in my career was bring tens of millions of dollars in grant money to programs that apply those funds to do good in their communities that would have been a satisfactory accomplishment. However, I’d like to argue that I did a little bit more good than that because I disagree with some of my esteemed colleagues that, “*I know it when I see it*“, is adequate for determining program effectiveness.

I can give you many many reasons why statistics are essential. First of all, something I have seen over and over in my career is that what gets measured gets done. If you are measuring the number of tutoring sessions or the number of times students play your games or the duration of those sessions, that allows you to correlate the “dose” of treatment your students received with the “response” in terms of increased achievement.

Many times, I have seen programs that were initially judged ineffective because everyone who came through the door was lumped together whether they were seen 10 times, once or not at all, having left before they ever saw a tutor counselor or whatever. Tracking your interaction with people allows you to determine whether you are effective for people who spend some substantial amount of time with your program. It also lets you tell what percentage of the people fall through the cracks that is who come in, fill out a form to be part of your program and then drop out almost immediately.

In brief, effective application of statistics cannot only help you obtain money but also see that money from federal agencies, foundations, etc. is intelligently applied.

If you are interested, I will be speaking at the Society For the Advancement Of Chicanos And Native Americans In Science annual conference in Long Beach on Saturday , Discovery and Societal Impact with Statistical Science. You can come to hear much more on this topic (or just read my next blog post).

———

### Jul

#### 20

# Mom! That Evaluator Keeps Looking at Me!

Filed Under computer games, Software, statistics, Technology | Leave a Comment

If I were to give one piece of advice to a would-be program evaluator, it would be to get to know your data so intimately it’s almost immoral.

Generally, program evaluation is an activity undertaken by someone with a degree of expertise in research methods and statistics (hopefully!) using data gathered and entered by people’s whose interest is something completely different, from providing mental health services to educating students.

Because their interest in providing data is minimal, your interest in checking that data better be maximal. Let’s head on with the data from the last post. We have now created two data sets that have the same variable formats so we are good to go with concatenating them.

DATA answers hmph;

SET fl_answers ansfix1 ;

IF username IN(“UNDEFINED”,”UNKNOWN”) or INDEX(username,”TEST”) > 0 THEN OUTPUT hmph;

ELSE OUTPUT answers;

*PRO TIP : I learned from a wise man years ago that one should not just gleefully delete data without looking at it. That is, instead of having a dataset where you put the data you expect and deleting the rest, send the unwanted data to a data set. If it turns out to be what you expected, you can always delete the data after you look at it.*

There should be very few people with a username of ‘UNDEFINED’ or ‘UNKNOWN’. The only way to get that is to be one of our developers who are entering the data in forms as they create and test them, not by logging in and playing the game. The INDEX function checks in the variable in the first argument for the string given in the second and returns the starting position of the string, if found. So, INDEX(username, “TEST”) > 0 looks for the word TEST anywhere in the username.

Since we ask our software testers to put that word in the username they pick, it should delete all of the tester records. I looked at the hmph data set and the distribution of usernames was just as I expected and most of the usernames were in the answers data set with valid usernames.

**Did you remember that we had concatenated the data set from the old server and the new server?**

I hope you did because if you didn’t you will end up with a whole lot of the same answers in their twice.

*Getting rid of the duplicates*

PROC SORT DATA = answers OUT=in.all_fl_answers NODUP ;

by username date_entered ;

The difference between NODUP and NODUPKEY is relevant here. It is possible we could have a student with the same username and date_entered because different schools could have assigned students the same username. (We do our lookups by username + school). Some other student with the same username might have been entering data at the same time in a completely different part of the country. The NODUP option only removes records if every value of every variable is the same. The NODUPKEY removes them if the variables in the BY statement are duplicates.

All righty then, we have the cleaned up answers data, now we go back and create a summary data set as explained in this post. You don’t have to do it with SAS Enterprise Guide as I did there, I just did it for the same reason I do most things, the hell of it.

**MERGING THE DATA**

PROC SORT DATA = in.answers_summary ;

BY username ;

PROC SORT DATA = in.all_fl_students ;

BY username ;

DATA in.answers_studunc odd;

MERGE in.answers_summary (IN=a) in.all_fl_students (IN=b) ;

IF a AND b THEN OUTPUT in.answers_studunc ;

IF a AND NOT b THEN OUTPUT odd ;

The PROC SORT steps sort. The MERGE statement merges. The IN= option creates a temporary variable with the name ‘a’ or ‘b’. You can use any name so I use short ones. If there is a record in both the student record file and the answers summary file then the data is output to a data set of all students with summary of answers.

There should not be any cases where there are answers but no record in the student file. If you recall, that is what set me off on finding that some were still being written to the old server.

**LOOK AT YOUR LOG FILE!**

*There is a sad corner of statistical purgatory for people who don’t look at their log files because they don’t know what they are looking for. ‘Nuff said.*

This looks exactly as it should. A consistent finding in the pilot studies of assessment of educational games has found a disconcertingly low level of persistence. So, it is expected that many players quit when they come to the first math questions. The fact that of the 875 players slightly less than 600 had answered any questions was somewhat expected. As expected, there were no records where

NOTE: There were 596 observations read from the data set IN.ANSWERS_SUMMARY.

NOTE: There were 875 observations read from the data set IN.ALL_FL_STUDENTS.

NOTE: The data set IN.ANSWERS_STUDUNC has 596 observations and 11 variables.

NOTE: The data set WORK.ODD has 0 observations and 11 variables.

So, now, after several blog posts, we have a data set ready for analysis ….. almost.

Want to see these data at the source?

You can also donate a copy of the game to a school or give as a gift.

**Further Reading**

For more on SAS character functions check out Ron Cody’s paper An Introduction to Character Functions, an oldie but goodie from WUSS back in 2003.

Or you could read my last post!