Question

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?

Answer #1

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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