The student welfare office was interested in trying to enhance students’ exam pe

Question

The student welfare office was interested in trying to enhance students’ exam performance by investigating the effects of various interventions. They took five groups of students before their Research Methods II (RMII) exams and gave them one of five interventions: a control group just sat in a room contemplating the task ahead; the second group had a yoga class to relax them; the third was told they would get monetary rewards contingent upon the grade they received in the exam; the fourth was given betablockers to calm their nerves; and the fifth was encouraged to sit around winding each other up about how much revision they had/hadn’t done (a bit like what usually happens). The final percentage obtained in the exam was the dependent variable.

The student welfare office made four predictions: (1) all interventions should be different than the control; (2) yoga, bribery and betablockers should lead to higher exam scores than panic; (3) yoga and bribery should have different effects than the betablocker drugs; and (4) yoga and bribery should also differ. Please conduct the set of planned contrasts needed to test each of these hypotheses.

Explanation / Answer

Solution

Let us denote the various interventions as treatments as follows:

Treatment 1: No intervention

Treatment 2: yoga intervention

Treatment 3: intervention by way of promise of monetary rewards (bribery!!!);

Treatment 4: intervention by way of giving betablockers to calm the nerves; and

Treatment 5: intervention by way of encouraging students to sit around winding each other (Panic!!!)

A one-way ANOVA with equal or unequal number of responses per treatment would answer all questions scientifically.

So,

let xij be the score (%) of the jth student in the ith group, i.e., the group given treatment i.(I = 1 to 5, j = 1 to ni; where all nis could be same or different. i.e, number of students in each of the 5 groups can be same or different.)

Then, we assume xij = i + ij where i is the effect of treatment I and ij is the error factor.

Q1

Let the null hypothesis be H0: All is are equal vs H1 is false.

If ANOVA accepts H0, all questions are answered in one shot since this implies that the effect of all interventions are the same which is also not different from the control group.

If H0 is rejected, the interventions have some effect. So, further tests are necessary to answer questions (2), (3) and (4).

In all cases, a 2-sample t-test would do the trick. Details are explained below:

Q2

Test H01: 2 = 5 vs H11: 2 > 5;

         H02: 3 = 5 vs H12: 3 > 5;

         H03: 4 = 5 vs H13: 4 > 5.

And interpret the results.

Q3

Test H01: 2 = 4 vs H11: 2 4;

         H02: 3 = 4 vs H12: 3 4.

And interpret the results.

Q4

Test H0: 2 = 3 vs H1: 2 3.

And interpret the results.

[Note: in all cases, the test to be employed is 2-sample t-test. While Q2 will be one-sided(upper tail), Q3 and Q4 will be two-sided]

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.