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.
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?
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.