Independent samples t-test

• Types of two-sample design include independent groups/samples, where two sets of data are provided by different groups of participants, and repeated measures, where both sets of data are provided by the same participants.
• Between Subjects Design is a type of design where intrinsic variables are present, such as sex, and the choice becomes a necessity.
• Dart-throwing ability of “trained” versus “non-trained” could be done as a repeated measures design or as independent samples design.
• The term “independent samples” is also referred to as “independent groups”, “between groups”, and “between subjects”.
• An example of an independent samples design is Does aerobic training increase fitness? with two groups matched on the basis of age, weight, height, etc. (however, motivation as a factor cannot be controlled) and assessed by a trainer after 4 weeks.
• The independent samples t-test is used to test if there is a significant difference between the groups.
• The assumptions and conditions for independent samples t-test include: the design is a two-group, independent samples design, the data type is interval/ratio, both samples are normally distributed, and there is homogeneity of variances in both samples.
• If the data does not meet some of these assumptions, the independent samples t-test cannot be used and a “non-parametric equivalent” to the independent samples t-test, called the Mann-Whitney test, must be used instead.
• The independent samples t-test can be performed in SPSS by hypothesis formulation, entering the data into SPSS, generating descriptive statistics, running the test in SPSS, making a decision about the hypothesis, and reporting the results APA style and in Plain English.
• The null hypothesis for the independent samples t-test is “there will be no significant difference in BMI scores of the aerobic training group, and the control group”.
• The two-tailed Experimental hypothesis is “there will be a significant difference in BMI scores of the aerobic training group, and the control group”.
• A one-tailed hypothesis is also possible, for example: “The aerobic training group will obtain significantly better BMI scores, than the free-training group”.
• If Levene’s test is NOT significant (i.e “sig” under Levene’s is > 0.05), the variances between two groups are equal – use TOP row of the t-test results.
• If the p-value (sig value) is < 0.05 (smaller), the test is statistically significant (accept exp hypothesis).
• In SPSS, the output table shows two rows of statistics, depending on the significance of Levene’s Test for Homogeneity of Variance.
• To get descriptive data for each group separately in SPSS, use the option “Pop-up window options: Select OPTIONS for a range of other statistics (e.g Variance).
• To code a categorical variable in SPSS, go to Variable view and assign 1 for Aerobic and 2 for Control.
• SPSS gives the significance values as two-tailed, if performing the hypothesis/test as a one-tailed test simply divide the SPSS two-tailed sig value by 2, to get the one-tailed sig value.
• In our example, sig (2-tailed) for the t-test was 0.039, so the sig (1 tailed) can be calculated as 0.039/2 = 0.0195.
• If the p-value (sig value) is >0.05, the test is not statistically significant (reject exp hypothesis).
• If the words do not appear, ensure “value labels” option is ticked in View (On top menu).
• Each row in SPSS Table is one participant.
• If the one-tailed test is significant, the p-value (sig value) is compared with 0.05 to determine whether or not the test is significant.
• To select the test in SPSS: Analyze, Compare means, Independent-samples t-test.
• In our case, p=0.039 which is < 0.05, thus, the t-test is significant (accept exp hypothesis).
• In SPSS, the p-value (sig value) of the test statistic in the output table is used to determine if the test is statistically significant.
• If Levene’s test is significant (i.e the “sig” value listed under Levene’s equality of Variance <0.05), the variances between two groups are not equal – use BOTTOM row of the t-test results.