Understanding Independent Samplest-Test

Exercise 16
Understanding Independent Samplest-Test

Statistical Technique in Review
Theindependent samplest-testis a parametric statistical technique used to determine significant differences between the scores obtained from two samples or groups. Since thet-test is considered fairly easy to calculate, researchers often use it in determining differences between two groups. Thet-test examines the differences between the means of the two groups in a study and adjusts that difference for the variability (computed by the standard error) among the data. When interpreting the results oft-tests, the larger the calculatedtratio, in absolute value, the greater the difference between the two groups. The significance of atratio can be determined by comparison with the critical values in a statistical table for thetdistribution using the degrees of freedom (df) for the study (seeCritical Values for Student’stDistribution at the back of this text). The formula fordffor an independentt-test is as follows:
df=(numberofsubjectsinsample1 numberofsubjectsinsample2)2

Exampledf=(65insample1 67insample2)2=1322=130

Thet-test should be conducted only once to examine differences between two groups in a study, because conducting multiplet-tests on study data can result in an inflated Type 1 error rate. A Type I error occurs when the researcher rejects the null hypothesis when it is in actuality true. Researchers need to consider other statistical analysis options for their study data rather than conducting multiplet-tests. However, if multiplet-tests are conducted, researchers can perform a Bonferroni procedure or more conservative post hoc tests like Tukey’s honestly significant difference (HSD), Student-Newman-Keuls, or Scheff test to reduce the risk of a Type I error. Only the Bonferroni procedure is covered in this text; details about the other, more stringent post hoc tests can be found inand.
The Bonferroni procedure is a simple calculation in which the alpha is divided by the number oft-tests conducted on different aspects of the study data. The resulting number is used as the alpha or level of significance for each of thet-tests conducted. The Bonferroni procedure formula is as follows: alpha () number oft-tests performed on study data = more stringent study to determine the significance of study results. For example, if a study’s was set at 0.05 and the researcher planned on conducting fivet-tests on the study data, the would be divided by the fivet-tests (0.05 5 = 0.01), with a resulting of 0.01 to be used to determine significant differences in the study.
Thet-test for independent samples or groups includes the following assumptions:

1.The raw scores in the population are normally distributed.
2.The dependent variable(s) is(are) measured at the interval or ratio levels.
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3.The two groups examined for differences have equal variance, which is best achieved by a random sample and random assignment to groups.
4.All scores or observations collected within each group are independent or not related to other study scores or observations.

Thet-test is robust, meaning the results are reliable even if one of the assumptions has been violated. However, thet-test is not robust regarding between-samples or within-samples independence assumptions or with respect to extreme violation of the assumption of normality. Groups do not need to be of equal sizes but rather of equal variance. Groups are independent if the two sets of data were not taken from the same subjects and if the scores are not related (;). This exercise focuses on interpreting and critically appraising thet-tests results presented in research reports.provides a step-by-step process for calculating the independent samplest-test.

Research Article
Source
Canbulat, N., Ayhan, F.,