In: Statistics and Probability
1. ANOVA stands for what words?
2. Suppose you read this statement: “The difference between the
means was not statistically significant at the .05 level (F =
2.293, df = 12, 18).” Should you conclude that the null hypothesis
was rejected?
3. Why would ANOVA be better for comparing the mean of four
independent groups than doing t-tests between each of the
pairs?
4. To find a significant difference with an analysis of variance,
you would hope to maximize which of the following: between groups
mean square or within groups mean square?
5. What are at least three assumptions of the ANOVA test?
1. ANOVA Please calculate the following by hand, showing all
your work. 1. An anthropologist is interested in studying dietary
habits in a community divided into three ethnic groups. The
researcher wishes to determine if the groups consume different
quantities of rice, a prized food source in two of the groups. The
anthropologist records the number of cups of uncooked rice prepared
and consumed per week in random samples from the three groups. The
households have been matched for the number of persons in the
household. The null hypothesis is H0:
I have already calculated the mean and standard deviation for you,
but I have also included the original data set for comparison.
Please estimate the within groups Mean Square (Variability), the
between groups Mean Square (Variability), and the F-ratio. Please
explain how you interpret this F-ratio. What does this test
indicate?
Data Set:
Group A
4 7 8 3 6
Group B
6 10 8 9 7
Group C
2 5 2 7 3
Group A:
N= 5
Mean = 5.60
Standard deviation = 2.07
Group B:
N= 5
Mean = 8.00
Standard deviation = 1.58
Group C:
N= 5
Mean = 3.80
Standard deviation = 2.17
1. ANOVA stands for Analysis of variance.
2. “The difference between the means was not statistically significant at the .05 level (F = 2.293, df = 12, 18).” So we should conclude that the null hypothesis was failed to reject.
3. t-test is used whether two populations are statistically different from each other, whereas ANOVA is used whether more two populations are statistically different from each other. Hence ANOVA is the equivalent of running multiple t-tests.
4. To find a significant difference with an analysis of
variance, we would hope to maximize between groups mean
square.
5. Three assumptions of the ANOVA test are:
i. Each group is drawn from a normal population.
ii. Population variances of all groupsd are constant.
iii. Observations are independent.
6.