# The Measurement of Adolescents, II

## Some More Statistical Exercises

Your feedback is important to us!

After viewing our curriculum units, please take a few minutes to help us understand how the units, which were created by public school teachers, may be useful to others.

## Some Experiments

Another activity was suggested by an example in Samprit Chatterjee’s article “Estimating the Size of Wildlife Populations”, in
*
Statistics by Example:
*
*
Exploring Data
*
. The problem is to take a deck of cards select a number of them, record them, replace them in the deck, shuffle well, make another selection and record the number of repeats from the first selection. This simulates the technique used by ecologists to estimate the number of fish in a lake. A number of fish are captured and tagged (N1) they are then released. A short time later another fishing trip is made. The number in the second catch is N2 the number that have tags in the second catch is T. We now have a proportion. It is assumed that the ratio of tagged fish in the lake to the total number of fish in the lake is the same as the ratio of tagged fish in the second catch to the total number of fish in the second catch. So now do the same with your card data. Do you get the correct number?

Students are apt to just count the cards or tell you how many there are supposed to be in the deck if you ask the question. So give the directions first. In fact do not have any one student do both catches. Since we want data to plot have each student do only one selection of cards. Have each student make two copies of the selection they made. Having numbered each selection assign number pairs to each student to compare for repeats. With a class as small as 16 that is 120 comparisons. Do as many as you can stand. I started to do this experiment by hand. I had many questions. If you do it many times and record all the cards that you see eventually you see all the cards. It would have made more sense to count them in the first place if you repeat the draws. Should the two selections be the same number of cards? How many cards? I thought these questions would be answered by Chatteerjee’s second article “Estimating Wildlife populations by the Capture-Recapture Method” in
*
Statistics by Example:
*
*
Finding Models
*
. What the article did do was show the answer one gets by assuming a proportion is the maximum likelihood estimate. It is a feast of combinations, finding probabilities. I found doing 16 deals for 8 comparisons was tedious, so I wrote a computer program to make all the comparisons. The number of cards in a selection may be varied from 1 to 52, but the same number will be used in all selections, it was easier to program. Playing with the computer might give a hint to some of my questions. So there is another statistics problem for me to explore.