Independent Sample t-test Using SPSS - Coursework Example

Independent Sample t-test Using SPSS Independent t-test compares the means between two sets of unrelated values based on the same dependent variable. For our particular case, 150 students were selected randomly from those taking level 1 business management to participate in an Entrepreneurship Project. The participants were marked on scale of 0-100 and asked to indicate whether they took Business at A-level or any other similar standard before joining university. The primary expectation is that those who had taken Business previously had an advantage in the project. a. The independent t-test determines whether unknown means of two populations are different based on independent samples drawn from each population. Generally, the term ‘population’ (N) in statistics refers to the entire pool from which an investigator obtains a statistical sample. For this particular case, the samples were collected from the population (total number) of students studying Level 1Business Management at the University, and who took part in an Entrepreneurship Project. Therefore, one would say that the inclusion criterion was for students taking Business at level 1 and undertaking the project. Consequently, two different samples of unknown means were obtained randomly from this population: those who had studied Business previously (At A-level or equivalent), and those who had not. Generally, samples for t-test can be selected from a single population that is divided into two subgroups like our case. In descriptive research, we can define study population based on geographic location or sex, with additional variables and attributes such as our case where we used previous Business study as an attribute to categorize the group. b. The common statistical procedure is to assume that populations were samples are drawn have equal variances. However, it is important to test this assumption because certain statistical tests require equal variances of populations. Levene’s Test, an inferential statistic helps to assess whether variances are equal for two groups. That is, it tests the homoscedasticity or null hypothesis of equal population variances, also called the homogeneity of variance. Consequently, there are three possible instances where testing variance equality is a major concern. The first instance is when drawing inferences about population variances due to scientific interests. The second is when suspecting heterogeneity of variances in a t-test (or ANOVA), and the third is when we have concerns about heterogeneity of variances in t-test where the number of observations are widely disparate in the group. For our particular case, the inclusion of Levene’s Test can help determine whether the two sub-samples (those who had taken Business at A-level and those who had not), had equal variances or different variances. This is especially important because our analysis assumes they are of equal variances hence the need to test that hypothesis. Therefore, inclusion of Levene’s Test in our independent t-test allows making conclusions about their variances, an essential precondition of t-test analysis. c. The Null Hypothesis for Levene’s Test is that the variances are equal or the same. For our particular case, the Null Hypothesis is that the variances between the group that had taken Business at A-level and that had not are the same. Generally, the dominant approach for making valid inferences in science questions is to frame the question in terms of two contrasting statistical hypothesis: 1 represents no difference between population parameters of interest either bidirectional and unidirectional (alternative hypothesis). When comparing two groups of interest, the assumption is that they have zero difference between their true means. d. In Levene’s Test, we reject null hypothesis of same (equal) variances if the Levene’s p value is less than the selected significance level (0.05), and therefore accept the alternate hypothesis. However, if the Levene’s p is greater than the selected significance level, then we do not reject (or accept) the Null Hypothesis, thus we conclude the variances are the same. For our particular case, p = 0.857 is greater than α (0.05). Therefore, we do not reject the null hypothesis of equal variances. We conclude that the variances of the two groups are equal, and hence confirm the precondition for independent samples t-test. e. SPSS provides two assumptions ‘Equal variances assumed’ and ‘Equal variances not assumed”. For the particular case, we should use the t-test labeled Equal Variance Assumed because it is consistent with the underlying assumption of the independent t-test. That is, independent –t-test requires equal variances of test variables. f. The assumptions of independent t-test also focus on population distribution and sampling besides population variance. T-test of considered robust because its assumption of equal violence can be violated without serious introduction of test error for normal distribution. Therefore, the assumption is that errors are independent (random) such that the difference between values and group mean affects only one value. g. The Null Hypothesis for t-test states that two population means from unrelated groups are the same (equal). Four our case, the Null Hypothesis is the means of the two groups are equal. That is, H0: u0 = u1 h. For this particular case, p value (Equal Variances Assumed) is 0.001. Since this value (0.001) is less than 0.05, then we reject the Null Hypothesis that there is no significant difference in means, which indicates that there is statistically significant difference in the means of the two groups, which cannot be attributed to sampling error. i. For this particular case, it is suitable to use a two-tailed test. Since we used significance level 0.05, the 2-tailed test allotted half of the alpha to testing significance in one direction and the other half of the alpha to testing significance in the other direction. That is, 0.025 in each distribution tail. This suits our case because we tested the possibility of the relationship of the two samples in both directions. The one-tail test of the tail distribution tests the possibility of relationship in one direction, with complete disregard for any in the other direction. Therefore, one-tailed t test is not appropriate for our case because our sole purpose in the case is to attain significance. j. From the case, we make the following overall conclusions: From the Group Statistics, we find that the mean for condition ‘0’ (Business at A-Level) is 41.95 while the mean for condition ‘1’ is 52.45. The standard deviation for ‘0’ is 18.296 while for ‘1’ is 18.535. The Number of participants (n) in each condition differs with condition 79 for condition ‘0’ and 71 for condition ‘1’. In summary of the Group Statistics, we conclude that 79 students out of the 150 selected for the survey did Business at A-level (or equivalent) while 71 did not take Business at A-Level. The mean score of those who took business in previous level was 41.95 while the mean score for those who did not was 52.45. Looking at the independent samples test, the Levene’s Test finds no significant difference between the variances (p = 0.857). Further analysis of t-test for Equity of means shows significant difference between the two means (p = 0.001). Therefore, we conclude that students who had not taken Business in A-level (mean = 52.45) performed significantly better (p = 0.001) than those who did Business in A-level (Mean = 41.95). Read More