ANOVA is a technique that permits the comparison of the equality of means for multiple populations. Thus, 3 means could be compared and a determination of whether or not one of the means is significantly different from others can be made. This technique is extremely useful, but, as is always the case, the application requires a firm understanding of models assumptions. Consider the following scenario. A meticulously determined random sample of 200 observations is taken from a very large population. This data divides into 4 groups or factor levels, and a numerical measure for each observation is recorded. The population distribution of the measure appears to be slightly skewed positive. The 4 groups have the following number of observations 30, 100, 15 and 55. Which of the following statements leads to the greatest concern in using ANOVA as an analytical technique. a. Unequal sample sizes among groups can seriously affect the power of the test.
b. Slightly skewed positive distribution of population measures seriously affect the power of the test.
c. In this scenario, I should be concerned about whether the data has been gathered in a biased fashion.
d. Four is not a sufficient number of groups into which to divide the data.