Biostatistics Homework 2

The data below come from Carnegie Mellon StatLib, a repository for statistical data sets. I copied the data and the basic story behind the data from:

The story behind the data is as follows: The data are the results of an experiment to test whether directed reading activities in the classroom help elementary school students improve aspects of their reading ability. A treatment class of 21 third-grade students participated in these activities for eight weeks, and a control class of 23 third-graders followed the same curriculum without the activities. After the eight-week period, students in both classes took a Degree of Reading Power (DRP) test which measures the aspects of reading ability that the treatment is designed to improve. Original source: Schmitt, Maribeth C., The Effects on an Elaborated Directed Reading Activity on the Metacomprehension Skills of Third Graders, Ph.D. dissertaion, Purdue University, 1987.

  1. When you conducted your two-sample t-test in Homework 1, you had not looked at the data to see whether it was normal or if the sample size was large enough that some deviation from normality was all right. Do that now. Typically such analyses are not reported in detail in a scientific paper and should not typically be included in any project for this course. You simply do it before you decide what statistical test to employ to test your hypotheses. However, include your normal probability plots (quantile-quantile plots) in your report for this homework assignment.
  2. For the fun of it, also test whether the variances are equal between the treated and control groups. Since you most likely used a Welch's t-test, this is likely an unnecessary step in validating your previous analysis.
Hints: (1) You have to be sure to analyze the treated and control groups separately since they may not come from a common nomral distribution.

(2) There is no requirement to use R and the analysis will probabably be easier for most of you in Minitab. If you use R, good commands to look up include qqnorm and qqline. Note that R puts the sample on the y-axis and the normal distribution on the x-axis so that it flips what Minitab does unless you force R to flip it back. There is no need to flip it one way or the other, but you have to assess deviations from normality appropriately for the way you plot the data.

(3) The test of normality in R has command: shapiro.test. Look it up using the help command as described in Lab 1.

(4) Levene's test is not in base R. You have to first install and then load the "lawstat" package. Then, following Lab 1, the command would be:

 levene.test(data[,2], data[,1])

Treatment	Response
Treated	24
Treated	43
Treated	58
Treated	71
Treated	43
Treated	49
Treated	61
Treated	44
Treated	67
Treated	49
Treated	53
Treated	56
Treated	59
Treated	52
Treated	62
Treated	54
Treated	57
Treated	33
Treated	46
Treated	43
Treated	57
Control	42
Control	43
Control	55
Control	26
Control	62
Control	37
Control	33
Control	41
Control	19
Control	54
Control	20
Control	85
Control	46
Control	10
Control	17
Control	60
Control	53
Control	42
Control	37
Control	42
Control	55
Control	28
Control	48