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After checking the assumptions for normality for students’ TAKS and TAAS reading scores and their math scores, it was determined that the datasets for all 16 years of data demonstrated evidence of non-normality. That is, the standardized skewness coefficients (i.e., the skewness value divided by its standard error) and the standardized kurtosis coefficients (i.e., the kurtosis value divided by its standard error) were almost all outside of the boundaries of +/- 3 (Onwuegbuzie&Daniel, 2002). The most likely reason for these students’ TAKS Reading and TAKS Math scores being non-normal is due to the content assessed on these tests being taught in Texas classrooms. Test items on the TAKS are designed to assess the information and skills taught in classroom settings. As such, 50% of the test scores would not be expected to be average or below, on content specifically taught to students. A final explanation is that in norm-referenced measures, student performance is compared to the performance of other peers. In the case of the two TAKS measures, student performance is compared to the number of items answered correctly. Each item receives a specific point value. Students, as noted above, who receive 40 points in Reading are rated as having passed the exam.
Because student achievement data were not normally distributed, nonparametric procedures were utilized to answer the research questions delineated above. Nonparametric procedures do not have as an assumption that test scores are normally distributed. As such, they are the optimal statistical procedure to use when the assumption of normality of data is violated.
In regard to the 2008-2009 academic year, the Wilcoxon signed-rank test revealed the presence of statistically significant differences in passing rates in reading between Hispanic students and White students, z = -26.18, p <.001, and in passing rates in math, z = -21.96, p <.001. Effect sizes were large, with a Cohen’s d of 0.93 for the reading pass rate difference, and moderate, with a Cohen’s d of 0.61 for the math pass rate difference (Cohen, 1988). Hispanic students averaged 8.89% points lower in their reading pass rates and 6.73% points lower in their math pass rates than White students.
Because of the space required to report in detail all of the statistical analyses conducted in this study, only the following information will be provided. Readers are requested to contact the authors directly for the detailed numeric phrases for each analysis. Statistically significant differences were yielded at the .001 level, using the Wilcoxon signed-rank test, in reading and in math between Hispanic and White students for the other 15 years of data analyzed. Effect sizes are depicted for each analysis in Tables 9 and 10, along with the mean difference in student passing rate.
2008-2009 School Year | n of schools | M | SD |
Reading Pass Rates | |||
Hispanic Students | 1,544 | 80.17 | 10.68 |
White Students | 1,544 | 89.06 | 8.30 |
Math Pass Rates | |||
Hispanic Students | 1,518 | 80.69 | 11.80 |
White Students | 1,518 | 87.42 | 10.32 |
2007-2008 School Year | |||
Reading Pass Rates | |||
Hispanic Students | 1,463 | 81.33 | 10.40 |
White Students | 1,463 | 89.79 | 7.66 |
Math Pass Rates | |||
Hispanic Students | 1,464 | 81.25 | 11.09 |
White Students | 1,464 | 88.48 | 9.14 |
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