The Test Statistic sample essay

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The Test Statistic sample essay

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The decreasing scores of students in standardized tests in math and science have been a cause for concern for most education reformers; hence, intensive remediation had been designed for those who have been found to perform poorly at these tests. In order to test whether the intervention programs are effective, scores in the previous tests before the remediation was given will be compared to test scores after the remediation.

Statement of the problem:

Is there a significant difference in the test scores of students before and after the remediation program?

Independent variable:

Remediation program

Dependent variable:

Test scores (before and after remediation)


Null hypothesis: There is no significant difference in the test scores of students before and after the remediation program.

Alternative hypothesis: There is a significant difference in the test scores of students before and after the remediation program.

Effect size

The effect size would indicate the magnitude of the difference of the scores, using Cohen’s (1988) conventional system, an effect size of .02 is small, .05 is moderate and .08 is large. The probability value would only tell us whether to reject of accept the null hypothesis but in no way tells us whether the difference is small or large.


t = 5.192

df = 214

n = 216

Effect size: .05


The answered research question is “Is there a significant difference between the test scores of students in science and math before and after the remediation program?” The hypothesis tested is as follows:

Ho: p = 0

Ha: p ≠ 0

The result of the t-test on student scores in the science and math test (t=5.192 at .05) which is larger than the t-critical value (p> 4.33), with a sample size of 216 and a degrees of freedom of 214. Therefore the null hypothesis is rejected and the alternative hypothesis is accepted, thus, the remediation programs have indeed statistically increased the test scores of the students in science and math.

The effect size is at .05 which is moderate (Cohen, 1988), this would indicate that the difference in the before and after test scores is moderate in value and hence is not really that large as expected. This would mean that the present remediation program has done its work but much is desired before it could be said that it has really reached its objective.


Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences. New York: Academic


Cohen, B. (2001). Explaining Psychological Statistics. New York: Wiley.

Moore, D.S. (2000). The Basic Practice of Statistics 2nd ed. New York: W.H. Freeman.

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