STAT E-150 Summer 2022 Homework 4- Part 2 (1)

STAT E-150 Summer 2022 Homework 4-Part 2 6. To test whether different professors were harder or easier graders, a group of students submitted the same report to four different profs and recorded the mark given to each essay by each professor. The IV is professor, the DV is grade (as a percentage of 100). In the table below, has the assumption of sphericity been met? Please report your findings in APA format. Mauchly’s Test of Sphericity Measure: Measure_I Within Subjects Effect Mauchly’s W Approx. Chi-Square df Sig. Greenhouse -Geisser Huynh- Feldt Lower- bound Tutor .131 11.628 5 .043 .558 .712 .333 Mauchly’s test indicated that there is significant deviation from sphericity (χ2 = 11.628, p = . 043). 7. How did we arrive at the Lower-bound estimate of .333 in the table above? Please provide any necessary formula. The Lower-bound estimate was calculated using the formula 1/ k -1, where k= the number of groups. In this example, there are four professors, so the formula is 1/(4-1) 8. Based on your answer in Question 1, please provide an interpretation of the Test of Within- Subjects Effects Table below in APA format. Source Type III Sum of Squares df Mean Square F Sig. Partial Eta Squ. Tutor Sphericity Assumed Greenhouse-Geisser Huynh-Feldt Lower-Bound 554.125 554.125 554.125 554.125 3 1.673 2.137 1.000 184.708 331.245 259.329 554.125 3.700 3.700 3.700 3.700 .028 .063 .047 .096 .346 .346 .346 .346 Error (WL) Sphericity Assumed Greenhouse-Geisser Huynh-Feldt Lower-Bound 1048.375 1048.375 1048.375 1048.375 21 11.710 14.957 7.000 49.923 89.528 70.091 149.768 Because epsilon is less than .75, you must use the Greenhouse-Geisser estimates. Using G-G, there is no significant difference across tutors, F 1.673, 11.710 = 3.7, p = .063, partial h = .59 in terms of grades given.