IPS - Day 56

Today we continued working on the hand-washing investigation. I had students go out and test their data collection procedures. I gave them approximately 15 minutes to try out their data collection methods. When the class returned, we discussed and issues or problems with the data collection.

It became apparent to the class that they were not going to be able to collect data during class-time. There were too many observers and not enough subjects to observe. I told students they would have to collect data outside of class. I asked that they have their data collected by the end of the day Monday. I will remind the class on Monday they need to have their data collected, as we will begin analyzing the data in the computer lab on Tuesday.

Next, I addressed my concern with their analysis. The class is not absorbing the idea that just because they see a difference in two means that the difference is necessarily meaningful. I am rethinking what I have covered during the semester and will make revisions to better emphasize random outcomes and the examination of how likely an event is in relation to random outcomes.

As it is, I decided that some manual manipulation of data may help the class better understand how resampling for redistribution works and how it is used to compare random outcomes to the specific outcome observed in real life.

I used the hand-washing data that was collected today. There were 10 males observed, 40% of whom did not wash hands. There were 6 females observed, 17% of whom did not wash hands.

I asked the class to consider an appropriate null and alternative hypothesis for this situation. A student provided the following:

     H₀: Males wash their hands at the same rate or higher than females.
     H_a: Females wash their hands at a higher rate than males.

I asked students to use a random number generator to reallocate the 16 observed individuals into two groups, one of size 10 and one of size 6. The random numbers 1-16 were used and each value between 1 and 16 could only be used once, since the same person could not be placed into more than one group. The values 7-10 corresponded specifically to the non-hand-washing males, and the value 16 corresponded to the non-hand-washing female.

Students generated their numbers. Some had to start over when I pointed out that the same random number could not be used twice. Once a group of 10 and a group of 6 were created, I asked that the percent of non-hand-washers be calculated.

The point of statistical analysis becomes is there anything different or special about the group of 10 and 6 individuals that was collected versus the random groups that were created?

We had eight random groupings created with percent of the group not washing hands:

     % Male     % Female
          30             34
          40             17
          10             60
          20             50
          30             34
          30             34
          30             34
          30             34

This is a small sample, but it shows that one of the eight random groupings had results as extreme as the one we observed. We need thousands of these random allocations to get a good fix on what random occurrences would look like. This is what software enables us to do. At least some of the students seemed to grasp this idea.

I closed by telling students that many times data differences are reported without considering if the differences might, in fact, just be random chance. This happens quite frequently. Without considering the random nature of outcomes, decisions could be made that are based on supposed fact but are actually no more informed than flipping a coin or rolling a die.

I will have students manually work through a bootstrapping example next class with the same purpose in mind. As the class completes the hand-washing investigation I'll be able to determine if there has been any movement in their ability to analyze data from a statistical perspective.

Visit the class summary for a student's perspective and to view the lesson slide.