Inequity in Writing Education

One problem in the field of writing education is racial inequity: students from different races performing differently on standard test exams. For example, on the Massachusetts Comprehensive Assessment System (MCAS) exams language arts section, white students show the highest performance, with Asians significantly below that, blacks below them, and Latinos even lower (Horn, 2003). With clear differences in performance between these groups, something needs to be done in order to ensure all students are getting an equal education and a fair chance. In order to determine if the difference between the scores of black and whites students on the MCAS exams are significant, we need to perform a t-test. One group of scores is as follows: For 10th grade black students ( % scored "needs improvement" or above - the score needed to graduate from High School) on the language arts portion of the exam four consecutive years (includes writing proficiency): 51, 43, 40, 60. For four 10th grade white students: 81, 73, 75, 88. For simplicity's sake I will treat these as four individual student scores.

We are going to perform a t-test for independent means on these numbers. Our research hypothesis will be that the white students outperform black students on the MCAS exams to a significance level of .05. The null hypothesis is that white students do not outperform black students on the MCAS exams to a .05 significance. We know that if the null hypothesis is true, the two populations will have equal means and the distribution of differences between the means also has a mean of zero. In a t-test for independent means we average the estimated variance of both populations (since these should be estimates at the same number). The variance is "the sum of squared deviation scores divided by the degrees of freedom" (Aron & Aron, 2003, p. 231). The mean for black students is 48.5 and the mean for white students is 79.25. Calculations are as follows:

6.25 + 30.25 + 72.25 + 132.25 = 241 / 3 (degrees of freedom for "4" students) = variance of 80.33

3.06 + 39.06 + 18.06 + 76.56 = 136.74 / 3 = 45.58

Averaged variance 80.33 + 45.88 / 2 = variance of 63

We don't need to do a weighted average because or number of students is the same in both groups. The variance of the distribution of means is s²pooled / N which in this case is 4 so 63 /4 = 15.75. S²difference = 15.75 + 15.75 = 31.5. Taking the square root to get the standard deviation of the distribution of differences between means gives us 5.61. For our result to be significant with total degrees of freedom of 6 (3 for the white students plus 3 for the black students) and a .05 significance level for a one-tailed test (since our hypothesis was clearly directional), we use a cutoff score of 1.943 standard deviations above the mean of 0. Our t-score is the difference between the two sample means 34.75 divided by the standard deviation of the distribution of differences between the means or 5.61, which equals 6.19. This means our t-score is above the 1.943 cutoff score, and our results are clearly significant. The null hypothesis is rejected and the research hypothesis that whites outperform blacks on the MCAS exams is supported by our results. This information could be used to support a research study on how to improve outcomes for African-American students on the MCAS exams, working towards the ultimate goal of giving all students an equal education both in writing and other subjects as well.

References

Aron, A. & Aron E. N. (2003). Measurement, Evaluation, and Ethics in Research.

Pearson Custom Publishing: Boston.

Horn, C. (2003). High-stakes testing ad students: stopping or perpetuating a cycle of

failure? Theory into Practice, 42(1), 30-41.