This homework is due at the time that you take quiz four. A researcher looks at
ID: 3224442 • Letter: T
Question
This homework is due at the time that you take quiz four. A researcher looks at the effectiveness of four different teaching methods. Each method is used in a different class of high school students. Each of the four classes has 20 students. a. In this situation what does the between group variance represent? b. What does the within group variance represent? c. What is K and n for this situation? The summary F table is partially filled in below. Using information that you know about the relationships between parts of the table and rules of df, complete the rest of the table and evaluate the F value for statistical significance.Explanation / Answer
1) a) The between group variance of an F-Test (Anova) represents how different is each group's average value from the overall average value. In this case, it represents how different are the average of the four groups from the average of all the 80 students put together.
b) The within group variance represents how different is each element in a group different from that group's average. In this case, it represents how different are each of the elements from the average of the groups they belong to.
c) K is the number of groups in an Anova. Here it is 4. n is the number of elements in each group. Here it is 20.
2) Total SS = Between SS + Within SS. So, 1336 = 633 + Within SS. So Within SS = 1336 - 633 = 703
Total df = Between df + Within df. So, 39 = 3 + Within df. So Within df = 39 - 3 = 36
MS Between = Between SS/Between df = 633/3 = 211
MS Within = Within SS/Within df = 703/36 = 19.52
F = MS Between/MS Within = 211/19.52 = 10.80
F Statistic for (Within df, Total df) at 0.05 significance = 1.9 (from F table). Observed F (10.8) is greater than F statistc from the table, so the null hypothesis that there is no difference among the different groups is rejected. There is atleast one group that is different from the others (out of the 4 groups available), at a 5% significance level.
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