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Proof
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Proof (Data Analysis) My student group consisted of 40 students, predominantly juniors, in Math Analysis Honors. During the trial period the students were given daily learning logs to complete and participated in guided practice sessions using the individual white boards. I calculated the average of each student's first 5 exams which were taken before implementing the learning log and white board use strategies. I also determined the average of the 3 test scores for chapters taught using the strategies. My sample data consisted of the 40 paired differences of these averages. Using a matched pair design on test score average differences, I received the following test results:
As indicated by the Fathom output, if it were true that the treatment had no effect on test scores, the probability of getting mean average in the paired differences of 11.25 or higher is less than 0.00001. In fact, the Student's t test statistic of 9.359, with 39 degrees of freedom, gives a probability of about 8 in one trillion. Use of a t-test is
conditional upon having a simple random sample, a roughly normal sample
distribution and a sample size less than 5 percent of the population.
Given the nature of my classes, it was not possible to randomize students to treatment
groups. To alleviate as many possible sources of bias as possible, I
conducted a matched pair design experiment. The test was run on the
difference of each student’s test scores using the strategies and his
pre-treatment test scores average. Shown below is the normal quantile plot of the difference data: its display
is roughly linear indicating that the difference data is roughly normal and a
t-test of size forty is appropriate. The data is quite clear that the strategies of learning logs and individual white board use had quite an impact on student achievement for my Math Analysis students. |
