Do two graders score the same essays differently?

Question

Two graders independently score the same 20 essays on a 100-point scale. For each essay, compute the difference (grader 1 minus grader 2). The differences have a mean of 2.2 points and a sample standard deviation of 4.0 points.

Run a paired t-test at the 5% level (two-sided): do the graders differ systematically? Report the t-statistic.

Accepted Answer

Each essay is scored by both graders, so the scores are paired. Use the differences di with a one-sample t-test on 20 - 1 = 19 degrees of freedom. Hypotheses: H0: \mud = 0 (no systematic difference) versus H1: \mud 
eq 0. Standard error: 	ext{SE} = \frac{sd}{\sqrt{n}} = \frac{4.0}{\sqrt{20}} = \frac{4.0}{4.472} = 0.8944 	ext{ points}. Test statistic: t = \frac{2.2}{0.8944} = 2.46. The two-sided 5% critical value for 19 degrees of freedom is t{0.025,\,19} = 2.093. Since 2.46 2.093, reject H0. The p-value is about 0.024. Conclusion: grader 1 scores systematically higher, by about 2.2 points …

Do two graders score the same essays differently?

Your answer

More Statistics questions