- Description

*t ***-Test for Independent Groups**** **** **

**This Weeks Statistical Technique for Review – t-test for Independent Groups**

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 (dj) for the study. The formula for *df *for an independent *t-*test is:

* df *= number of subjects 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 divided by the number of *t*-tests performed on study data = more stringent study ex to determine the significance of study results.

The *t*-test for independent groups includes the following assumptions:

- The raw scores in the population are normally distributed.
- The dependent variable(s) is (are) measured at the interval or ratio levels.
- The two groups examined for differences have equal variance, which is best achieved by a random sample and random assignment to groups.
- 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).

#### Introduction** **

Kristofferzon, Lofmark, 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 and risk factors), the ]CS-60 (measured use of coping strategies), the social network and social support questionnaire (measured social participation and emotional support), the SF-36 Health Survey (measured perceived health-related quality of life), and the QLI (measured perceived quality of life). In addition, the researchers conducted a chart review of each participant’s medical record. In this study the results showed that “compared with men, women used more evasive and supportive coping and rated psychologic aspects of the heart disease as more problematic to manage. More women perceived available support from friends and grandchildren, and more men perceived available support from their partner. Women rated lower levels in physical and psychologic dimensions of quality of life” (Kristofferzon et al., 2005, p. 39).

#### Relevant Study Results

** **“A consecutive series of patients was selected from the medical records in 1 hospital between August 1999 and July 2001 for women and between August 1999 and August 2000 for men. With regard to a lower incidence rate of MI in women, a longer selection period was needed for them We decided to include 100 women and 100 men to have a comfortable margin for dropouts.

“An introductory letter, informed consent form, and questionnaires were mailed to eligible subjects 1 month after an acute MI. After 1 week, the first author phoned the patients. Those interested in participating returned the signed consent form and the completed questionnaires to the investigator within 1 to 2 weeks. The same questionnaires were mailed to the subjects on 3 occasions, 1, 4, and 12 months after MI. Data from 1 month are presented in this article” (Kristofferzon et al., 2005, p. 41).

“Of the target population of 338 women, 20% died before inclusion, 35% did not meet the inclusion criteria, and 23% declined participation; of the target population of 317 men, the corresponding numbers were 17%,27%, and 26%, respectively………….. The final sample consisted of 74 women and 97 men” (Kristofferzon et al., 2005, p. 41).

In Table VI, are the quality of life measures reported by Kristofferzon et al. (2005) in their study of women and men following an MI. The level of significance or alpha for this study was set at 0.05.

#### Case Study Homework Questions** **

*t*= -1.99 describes the difference between women and men post myocardial infarction (MI) for what variable?- Consider t= -2.74 and t= -2.31. Which calculated
*t*ratio has the smaller p value? Provide a rationale for your - Examine the results in Table VI. Which
*t*ratio listed in the table had the largest*p*value? What was the focus of this*t*-test, and were the results significant? Provide a rationale for your - What is
*df*? Why is it important to know the*df*for a t ratio? How would you calculate the*df*for a*t*-test, and what is the*df*for this study?

- What is the cause of an increased risk for Type I errors when
*t-tests*are conducted? How might researchers eliminate the increased risk for a Type I error in a study? - Given the information presented in Table VI, calculate a Bonferroni procedure for this
- Does this study meet the assumptions for the t-test? Provide a rationale for your
- What sampling method did the researchers use in this study? Provide a rationale for your
- What level of data is analyzed by means and standard deviations? Is this level of data compatible with the assumptions for the
*t-test?*Provide a rationale for your - Is the sample size adequate to detect significant differences between the two groups in this study?

**Source**: Kristofferzon, M., l.ofrnark, 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.