Question: Overall standard deviation versus the pooled standard deviation. The last line of the summary table given in Exercise gives the mean and the standard deviation for all the data combined. Compare this standard deviation with the pooled standard deviation that you would use as an estimate of the model standard deviation. Explain why you would expect this standard deviation to be larger than the pooled standard deviation.
Exercise: E Exam accommodations and end-ofterm grades. The Americans with Disabilities Act (ADA) requires that students with learning disabilities (LD) and/or attention deficit 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.10 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 these digits 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 do you prefer? Give reasons for your answer.