A study by Holder, Plikaytis, and Carlone (1996) compared two laboratory protocols designed to measure antibody levels in an enzyme-linked immunosorbent assay (ELISA) for Streptococcus pneumoniae. One protocol incorporates a "blocking step that is thought to increase the specificity of the assay, maximizing the yield of the specific antibody; the other protocol does not use the blocking step. The data shown below provide the ELISA results on six specimens (i.e., samples), each with Streptococcus pneumoniae Serogroup 4. This is a balanced repeated measures ANOVA design with six measurements on each sample, three of which use the protocol with the blocking step and three of which do not use the blocking step.
a. Should the factor Blocking Step be considered a fixed or random factor? Explain.
b. State the subject-specific scalar regression model for this analysis. (For these data, the subjects are the samples.)
c. State the subject-specific matrix model for this analysis.
d. State the null hypothesis that there is no significant effect of Blocking Step in terms of a statement about the parameters in the regression model given in part (b).
e. Based on a comparison of sample means, does there appear to be a meaningful effect of the Blocking Step factor? Explain.
f. Below are given computer results for a repeated measures analysis of these data. Based on these results, is there a significant effect of the Blocking Step factor? Explain by specifying the F statistic, its degrees of freedom, and its P-value appropriate for these data.
Antibody yields for two protocols measuring
Streptococcus pneumoniae serogroup 4
Specimen (or Sample) Number

g. Use the computer output to test whether there is a significant interaction effect between Specimen (or Samples) and Blocking Step. If such a test is nonsignificant, why might you be concerned about the model that has been fit, and how might you redo the analysis?

2 3 Sample Mean 7.3 Yes 9.3 2.3 3.2 2.8 3.7 3.6 3.6 28.4 29.2 35.9 0.4 0.4 0.6 0.8 1.0 1.0 1.0 2.8 3.1 2.8 7.66 Blocking 6.4 Sep No 91 27.2 25.5 28.3 3.6 7.67 9.1 9.3 1.4 2.0 4.5