Independent t Test (Comparing Two Means)


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1 Independent t Test (Comparing Two Means) The objectives of this lesson are to learn: the definition/purpose of independent ttest when to use the independent ttest the use of SPSS to complete an independent ttest the interpretations of results Definition Independent ttest involves examination of the significant differences on one factor or dimension (dependent variable) between means of two independent groups (e.g., male vs. female, with disability vs. without disability) or two experimental groups (control group vs. treatment group). For example, you might want to know whether there is a significant difference on the level of social activity between individuals with disabilities and individuals without disabilities. When to Use Independent ttest Any analysis where: There is only one dimension or factor (dependent variable) There are three or more groups of the factor (independent variable) One is interested in looking at mean differences across two independent groups Steps for Independent ttest Using SPSS We will use a stepbystep approach to go through the steps for an Independent ttest using SPSS statistical analysis package. Here is the background information of the sample data we are using here. Number of subjects: 60 Independent variable (Factor): Gender (male = 1, female = 2). Dependent variable: Vocational rehabilitation service cost (VRS cost)
2 Data: Table 1 Table 1 M a le F e m a le Steps for Independent ttest: Step 1 : A statement of statistical hypothesis H : µ = µ or means for two groups are equal There is no significant difference between genders in receiving vocational rehabilitation service cost H a : µ 1 µ 2( µ 1 f µ 2or µ 1 p µ 2) Step 2 : Setting the α level of risk associated with the null hypothesis (or Type I error) The level of Type I error is.05. Step 3 & 4: Test statistic using SPSS/ interpreting results Figure 2 Analyze Compare Means Independent ttest (Figure 2)
3
4 Group 1 = Male = 1 Group 2 = Female = 2 Alpha level =.05
5 SPSS Output and Interpretation TTest Group Statistics VR Cost Gender Males Females Std. Error N Mean Std. Deviation Mean Interpretation: This table displays the number of subjects, mean value of VRS cost, standard deviation, and standard error for the test variable(s) within categories defined by the grouping variable (Males and Females). Since the Independent t Test procedure compares the two group means, it is useful to know what the mean values are (Male mean = , Female Mean = ). Independent Samples Test VR Cost Equal variances assumed Equal variances not assumed Levene's Test for Equality of Variances F Sig. t df Sig. (2tailed) ttest for Equality of Means Mean Difference 95% Confidence Interval of the Std. Error Difference Difference Lower Upper
6 Interpretation: The Independent t Test procedure compares means for two groups of subjects. If the significance value for the Levene test is high (greater that 0.05), use the results that assume equal variances for both groups. Otherwise, Use the results that do not assume equal variances for both groups. In our case, the equal variances are assumed (p =.404 >.05). A significance value of.743 (greater than.05) indicates that there is no significant difference between the two group means. Furthermore, the confidence interval for the mean difference contains zero within its range. This also indicates that the difference is not significant. If the significance value is high (typically greater than.05) and the confidence interval for the mean difference contains zero, then you cannot conclude that there is a significant difference between the two group means. Step 5: Conclusion Based on the results of independent ttest (p =.743 >.05), we failed to reject the null hypothesis (Ho). Therefore, we concluded that there was no significant difference between male and female in VRS cost.
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