Question

In: Statistics and Probability

1. ANOVA stands for what words? 2. Suppose you read this statement: “The difference between the...

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

Solutions

Expert Solution

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.


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