STA 210B/ENV 251
Statistics and Data Analysis for the Biological Sciences

Objective: Determine whether an experimental treatment has an effect where the response is measured before and after treatment.

Material: Use drug.jmp.

Background: Read relevant portions of Chapters 7 and 8 of  JMP Start Statistics. In this data set, LBI is a bacteria count before treatment, and LBS is the count after treatment. The 30 subject were randomly allocated to three groups. Drug indicates the treatment group. Two groups received drugs, and the third, a placebo. We are interested in whether either drug reduces bacteria.

Note that this exercise calls for ANOVA, which we will cover Thursday. Do the computations now, and write up the analysis later. You will have until Tuesday to turn it in.

Main Questions: Does either drug reduce bacteria with more effect than the placebo?

Steps:
1. Compare the means of the LBS by Drug group. Are there any significant pairwise differences?

2. Examine a scatterplot of LBS by LBI. Test whether the regression slope is equal to 1. How might the relationship between LBS and Drug be confounded by LBI?

3. Random allocation, independent of LBI, should assure that the three treatment groups have the same mean for the pre-treatment measurements. Perform oneway ANOVA of LBI by Drug to verify that this equivalence of means. How strong is the evidence against proper randomization?

4. The results of steps 2 and 3 raise doubts about the validity of the analysis in step 1. Even without these doubts, we may wish to analysis the pre-post difference, LBS - LBI, as this measures the individual effect of treatment. Open a new column Diff for this difference. Test whether the treatment effects of Diff by Drug are all equal.

5. Does the treatment effect, Diff,  for placebo differ significantly from 0? Is this a mere coincidence or does pre-post measurement eliminate the need for a placebo or other control group?

Note that the result of step 2 implies that the slope of Diff by LBI is not significantly distinct from 0.

Report:
Write up the steps. Plots are not necessary, but include them if it clarifies discussion. Explain, finally, whether either drug significantly reduces bacteria as compared with placebo. This involves the nontrivial choice of LBS or Diff as the appropriate response variable.

Due: Following Tuesday lecture.