Question

# Three professors are teaching large classes in introductory statistics. At the end of the semester, they...

Three professors are teaching large classes in introductory statistics. At the end of the semester, they compare grades to see if there are significant differences in their grading policies. Professor A B . C . D . F . WP . WF Smith . 12 45 . 49 . 6 . 13 . 18 . 2 Jones . 10 . 32 . 43 . 18 . 4 . 12 . 6 White . 15 . 19 . 32 . 20 . 6 . 9 . 7 Are these differences significant? Which test are you using? Are the grades assigned by Professors Jones and White significantly different? How would the results be interpreted?

Solution:

We use Analysis of Variance (ANOVA) test because it finds whether there is statistical difference between three or more independent groups.

 Using ANOVA in excel, we get the following output. Anova: Single Factor SUMMARY Groups Count Sum Average Variance Column 1 7 145 20.71429 349.9048 Column 2 7 125 17.85714 210.1429 Column 3 7 108 15.42857 84.95238 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 98 2 49 0.227907 0.798461 3.554557 Within Groups 3870 18 215 Total 3968 20

From the ANOVA output, the p-value is very large and hence the differences are not statistically significant.

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