Other research examining the effects of preschool childcare has found that children who spent time in day care, especially high-quality day care, perform better on math and language tests than children who stay home with their mothers (Broberg, Wessels, Lamb, & Hwang, 1997). Typical results, for example, show that a sample of n = 25 children who attended day care before starting school had an average score of M = 87 with SS = 1536 on a standardized math test for which the population mean is μ = 81.
a. Is this sample sufficient to conclude that the children with a history of preschool day care are significantly different from the general population? Use a two-tailed test with α = .01.
b. Compute Cohen’s d to measure the size of the preschool effect.
c. Write a sentence showing how the outcome of the hypothesis test and the measure of effect size would appear in a research report.
20. A random sample is obtained from a population with a mean of μ = 70. A treatment is administered to the individuals in the sample and, after treatment, the sample mean is M = 78 with a standard deviation of s = 20.
a. Assuming that the sample consists of n = 25 scores, compute r2 and the estimated Cohen’s d to measure the size of treatment effect.
b. Assuming that the sample consists of n = 16 scores, compute r2 and the estimated Cohen’s d to measure the size of treatment effect.
c. Comparing your answers from parts a and b, how does the number of scores in the sample influence the measures of effect size?