Statistics Exericse 29
EXERCISE 29 t-TEST FOR INDEPENDENT GROUPS I
STATISTICAL TECHNIQUE IN REVIEW
The t-test is a parametric analysis technique used to determine significant differences between the scores obtained from two groups. The t-test uses the standard deviation to estimate the standard error of the sampling distribution and examines the differences between the means of the two groups. Since the t-test is considered fairly easy to calculate, researchers often use it in determining differences between two groups. When interpreting the results of t-tests, the larger the calculated t ratio, in absolute value, the greater the difference between the two groups. The significance of a t ratio can be determined by comparison with the critical values in a statistical table for the t distribution using the degrees of freedom (df) for the study. The formula for df for an independent t-test is: df = number of sobjects in sample 1 + number of subjects in sample 2 - 2
The t-test can only be used once to examine data from two study samples, otherwise the Type 1 error rate (alpha) may be inflated. A Type I error occurs when the researcher rejects the null hypothesis when it is in actuality true. Thus if researchers run multiple t-tests to evaluate differences of various aspects of a study 's data, this is considered a misuse of the t-test and often leads to an increased risk for a Type I error or finding two groups significantly different when they are not. To correct for the risk of a Type I error, the researcher can perform a Bonferroni procedure. The Bonferroni procedure is a simple calculation in which the alpha is divided by the number of t-tests run on different aspects of the study data. The resulting number is used as the alpha or level of significance for each of the t-tests conducted. For example, if a study 's alpha was set at 0.05 and the researcher planned on conducting 5 t-tests on the study data, the alpha would be divided by the 5 t-tests (0.05 ÷ 5 =
STATISTICAL TECHNIQUE IN REVIEW
The t-test is a parametric analysis technique used to determine significant differences between the scores obtained from two groups. The t-test uses the standard deviation to estimate the standard error of the sampling distribution and examines the differences between the means of the two groups. Since the t-test is considered fairly easy to calculate, researchers often use it in determining differences between two groups. When interpreting the results of t-tests, the larger the calculated t ratio, in absolute value, the greater the difference between the two groups. The significance of a t ratio can be determined by comparison with the critical values in a statistical table for the t distribution using the degrees of freedom (df) for the study. The formula for df for an independent t-test is: df = number of sobjects in sample 1 + number of subjects in sample 2 - 2
The t-test can only be used once to examine data from two study samples, otherwise the Type 1 error rate (alpha) may be inflated. A Type I error occurs when the researcher rejects the null hypothesis when it is in actuality true. Thus if researchers run multiple t-tests to evaluate differences of various aspects of a study 's data, this is considered a misuse of the t-test and often leads to an increased risk for a Type I error or finding two groups significantly different when they are not. To correct for the risk of a Type I error, the researcher can perform a Bonferroni procedure. The Bonferroni procedure is a simple calculation in which the alpha is divided by the number of t-tests run on different aspects of the study data. The resulting number is used as the alpha or level of significance for each of the t-tests conducted. For example, if a study 's alpha was set at 0.05 and the researcher planned on conducting 5 t-tests on the study data, the alpha would be divided by the 5 t-tests (0.05 ÷ 5 =