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Descriptive Statistics
Test subjects were 53.3% male and 46.7% female, as shown in the bar graph on the accompanying Excel spreadsheet. The test population has a mean age of 15.9 years (standard deviation=0.80). These descriptive statistics validate the randomized population of the research study, as the population is almost evenly split between males and females and the mean age is also very close to the median age (16) of the study's population (Healy, 2009). As ACT and SAT scores vary in their nominal values (a top score on the ACT test is 36, a top score on the SAT is 2400), scores were recorded as percentages of the total score to enable meaningful analysis of varying means (i.e. A score of 29 on the ACT and of 1920 on the SAT would both be recorded as 0.80) (Kaplan, 2004). Mean scores on the ACT were 0.47 (standard deviation=0.27), while mean scores on the SAT were 0.41 (standard deviation=0.31).
T-Test
A significance level of 0.05 was used for this test, which is in keeping with the data population size and the level of data collected (Healy, 2009). A t-test is commonly used to determine if two means differ significantly, and is well suited for the purpose of comparing academic scores given the ratio level of measurement (Healy, 2009). The t-test was conducted using the ACT score mean as the "control"...
A critical T. value for 0.05 significance and 29 (n-1) degrees of freedom is given by Excel's TINV function as 2.05; the standard error of the sample was calculated as 0.05. The t-value for the mean SAT score of 0.41 compared to the mean ACT score of 0.47 was calculated as 1.16, which is lower than the critical t value. This means that the null hypothesis is not rejected, and that the means do not differ significantly at a 95% confidence level (significance of 0.05) (Healy, 2009).
Interpretation
Based on this analysis, there does not appear to be any difference in ACT vs. SAT scores in low-income students. The alternative hypothesis that test construction would influence scores by mediating the impact of income is not upheld. It is not disproven, either, but this research does not support the conclusion.
References
Healy, J. (2009). Statistics. Mason, OH: Cengage.
Kaplan. (2004). SAT and ACT Score Comparison. Accessed 23 March 2009. http://phs.prs.k12.nj.us/guidance/sat_act_comparison.pdf
Kohn, A. (2000). The Case Against Standardized Testing. New York: Heinemann.
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