As described in Chapter 2, assumptions need to be checked to ensure that the p- value for each ANOVA F- test is reliable:
• The observations within each group (each factor-level combination) are independent and identically distributed.
• Each group has equal variances.
• The residual values follow a normal distribution with a mean of zero.
a. Examine the individual value plot in Figure 4.1 and comment on the assumptions for these hypothesis tests. Is there evidence of any skewness or outliers that may cause us to doubt the normal assumption for the PopRate within each factor- level combination of Brand and Time?
b. Does Figure 4.1 indicate that the spread of each group appears roughly similar, so the equal variance assumption seems reasonable? Another informal check of the equal variance assumption can be done by calculating the ratio of the maximum sample standard deviation to the minimum sample standard deviation. If this ratio is less than two, we can generally assume that there is not strong evidence against the equal variance assumption. Compare the standard deviations of the four treatment level combinations to determine if
max(sij)/min(sij) < 2
c. Create a normal probability plot or histogram of the residuals from Question 13. Does it appear that the residuals follow a normal distribution?