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Chapter
12
Analysis of Variance
One-Way Analysis of Variance
We have already seen how to test for the equality of means between two different populations
with 2-SampZTest and 2-SampTTest. With the added assumption of common population
standard deviations, we can extend the tests to more than two populations with a technique
known as Analysis of Variance (ANOVA for short). The null hypothesis is that all of the
population means are equal; the alternative hypothesis is that at least two of the means differ.
The ANOVA function is on the STAT page in the TESTS list. To use it, first store the sample
data into lists, one per population. Then call ANOVA(L1, L2, . . . ) using whatever list names
are appropriate. The result contains the F test statistic, degrees of freedom, various sums of
squares, mean sums of squares, and most importantly the p-value for the test.
Example: Fourth Grade Arithmetic
Fifteen fourth-grade students were randomly assigned to three groups to experiment with three
different methods of teaching arithmetic. At the end of the semester, the same test was given to
all 15 students. The following table gives the scores of the students in the three groups.
Method I Method II Method III
48 55 84
73 85 68
51 70 95
65 69 74
87 90 67
Calculate the value of the test statistic F. (Assume that the three populations are normally
distributed with equal standard deviations. At the 1% significance level, can we reject the null
hypothesis that the mean arithmetic score of all fourth-grade students taught by each of these
three methods is the same?
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