# Statistics Exericse 29

**Topics:**Statistics, Statistical hypothesis testing, Normal distribution

**Pages:**8 (2578 words)

**Published:**March 15, 2013

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 = 0.01), with a resulting alpha of 0.01 to be used to determine significant differences in the study. The Bonferroni procedure formula is: alpha (α) ÷ number of t - tests performed on study data = more stringent study α to determine the significance of study results . The t-test for independent 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. 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 observations within each group are independent.

The t-test is robust, meaning the results are reliable even if one of the assumptions has been violated. However, the t-test is not robust regarding between-samples or within-samples independence assumptions, or with respect to extreme violation of the assumption of normality. Sample 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. Thus, paired or matched groups are dependent, not independent; but a randomly selected sample with random assignment to groups does produce independent groups (Burns & Grove, 2005). RESEARCH ARTICLE

Source: Kristofferzon, M., Löfmark, R., & Carlsson, M. (2005). Perceived coping, social support, and quality of life 1 month after myocardial infarction: A comparison between Swedish women and men. Heart & Lung, 34 (1), 39–50. Introduction

Kristofferzon, Löfmark, and Carlsson (2005) conducted a comparative-descriptive study to determine if women and men differ in their perceived coping, social support, and quality of life one month post myocardial infarction (MI). The sample of convenience included 171 subjects, 74 women and 97 men. Each participant completed a study-specific questionnaire (demographics...

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