How did students in my class perform in tests?

For the Lab-Based Statistics course in Semester 1 2014/15 academic session, there are two sections. Parts of the continuous assessments involve in-class tests. The tests are called Test 1, Test 1R (R=Resit), Test 2, Test 2R, and Test 3. The resit test covered the same materials as the original test. All students were given the opportunity to take the original and resit tests. The maximum marks for the tests are 24, except for Test 3 where the maximum mark is 22. The passing mark for each test is set at 50% of the maximum score; following the grading system of the university.

First, I would like to know if there are any differences of performance between students in the two sections. A ran an independent t-test for all the Tests. The results are as follow. Students in Section 1 tended to score lower than Section 2. In four tests, Section 2 had a higher means compared to Section 1. The only time Section 1 outperformed Section 2 is in Test 1R.  

Table 1. M and SD of test scores by section
	Section	N	M	SD
Test 1	1	40	9.74	4.58
	2	41	10.05	4.30
Test 1R	1	40	13.48	4.23
	2	41	12.39	4.93
Test 2	1	40	8.93	5.26
	2	40	9.55	4.94
Test 2R	1	40	14.78	5.33
	2	41	15.88	5.91
Test3	1	40	12.56	4.69
	2	41	15.37	3.88

The mean differences are presented in the Table 2 below together with the t-statistics. For all of the t-tests, there were equal variances between the groups; all the F values for the Levene’s test for equality are not significant.  

Table 2. Comparison of test performance between Section 1 and 2

		t		df		p		Mean Difference
Test 1	-.315		79		.753		-.3113
Test 1R	1.061		79		.292		1.0848
Test 2	-.548		78		.585		-.6250
Test 2R	-.881		79		.381		-1.1030
Test3	-2.935		79		.004		-2.8034

As Table 2 suggest, the test performance of students in Section 1 and 2 are similar, except for Test3. Students in Section 2 scored almost 3 points more than students in Section 1. Overall, there is no consistent evidence of bias in teaching and marking the tests. The test performances are similar except for the last test.

Secondly, the question that I would like to answer is whether students performed better when given a second chance. The resit tests covered the same materials as the original test. It would be interesting to look at the changes in performance when students took the resit test. Because the performances are similar between the two sections, the following analysis was performed using the combined scores. Table 2 summarises the results. There are marked improvements in the scores. Students performed significantly better in Test1R (M=12.93, SD=4.60) than in (Test1 M=9.90, SD=4.42), t(80)= -5.64, p<.001. The performance is also significantly better in Test2R (M=15.40, SD=5.63) than in Test2 (M=9.24, SD=5.08), t(79)=-8.90, p<.001.  The gain in the second resit is (6 points) double that of the gain in the first resit (3 points). Moreover, the improvements are also practically significant as the average marks went from the failure region to the pass region (more than 50% of the total mark). Therefore, we can conclude, on average, students were able to take advantage of the resit tests to improve their marks.