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.