The Americans with Disabilities Act (ADA) requires that students with learning disabilities (LD) and/or attention de?cit disorder (ADD) be given certain accommodations when taking examinations. One study designed to assess the effects of these accommodations examined the relationship between end-of-term grades and the number of accommodations given.8 The researchers reported the mean grades with sample sizes and standard deviations versus the number of accommodations in a table similar to this:
(a) Plot the means versus the number of accommodations. Is there a pattern evident?
(b) A large number of digits are reported for the means and the standard deviations. Do you think that all of these are necessary? Give reasons for your answer and describe how you would report these results.
(c) Should we pool to obtain an estimate of an assumed standard deviation for these data? Explain your answer and give the pooled estimate if your answer is Yes.
(d) The small numbers of observations with 3 or 4 accommodations lead to estimates that are highly variable in these groups compared with the other groups. Inclusion of groups with relatively few observations in an ANOVA can also lead to low power. We could eliminate these two levels from the analysis or we could combine them with the 37 observations in the group above to form a new group with 2 or more accommodations. Which of these options would you prefer? Give reasons for your answer.
(e) The 245 grades reported in the table were from a sample of 61 students who completed three, four, or ?ve courses during a spring term at one college and who were quali?ed to receive accommodations. Students in the sample were self-identi?ed, in the sense that they had to request quali?cation. Even when quali?ed, some students choose not to request accommodations for some or all of their courses. Based on these facts, would you advise that ANOVA methods be used for these data? Explain your answer. (The authors did not present the results of an ANOVA in their publication.)
(f) To what extent do you think the results of this study can be generalized to other settings? Give reasons for your answer.
(g) Most reasonable approaches to the analysis of these data would conclude that the data fail to provide evidence that the number of accommodations is related to the mean grades. Does this imply that the accommodations are not needed or does it suggest that they are effective? Discuss your answer.