# Independent Sample T-Test

Quantitative Results
Statistical Analysis

Independent sample t-test is a statistical technique that is used to analyze the mean comparison of two independent groups. In independent samples t-test, when we take two samples from the same population, then the mean of the two samples may be identical. But when samples are taken from two different populations, then the mean of the sample may differ. In this case, it is used to draw conclusions about the means of two populations, and used to tell whether or not they are similar.

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Assumptions in independent samples t-test:1. Assumes that the dependent variable is normally distributed.
2. Assumes that the variance of the two groups are the same as the dependent variable.
3. Assumes that the two samples are independent of each other.
4. Samples are drawn from the population at random.
5. In independent sample t-test, all observations must be independent of each other.
6. In independent sample t-test, dependent variables must be measured on an interval or ratio scale.Procedures for independent sample t-test:1. Set up the hypothesis.
a. Null Hypothesis: It is assumed when the means of the two groups are not significantly different.
b. Alternative Hypothesis: Assumes that the means of the two groups are significantly different.

2. Calculate the standard deviation for the independent sample t-test by using this formula:

3. Calculate the value of the independent sample t-test by using this formula:
4. Degree of freedom for independent sample t-test:
Where
V= degree of freedom
N1+N2= number of observations in both samples of the independent sample t-test.

5. Hypothesis testing: In hypothesis testing for the independent sample t-test, statistical decisions are made about whether or not the two population means are identical. Compare the calculated value of the independent sample t-test with the table value of the sample t-test. If the calculated value of the independent sample t-test is greater than the table value of the predetermined significance level, we will reject the null hypothesis and say that the means of the two groups are different. If the calculated value of the independent sample t-test is less than the table value, then we will say that the means of the two groups are the same.

Independent sample t-test and SPSS: Most statistical software has the option to perform the independent sample t-test. In SPSS, to perform the independent sample t-test we have to perform following procedure:

1. Click on the “SPSS 16” icon from the start menu.
2. Click on the “open data” icon and select the data for the independent sample t-test.
3. Click on the “analysis” option and select “compare mean” from the analysis option.
4. Select “independent sample t-test” from the compare mean option. As we click on the independent sample t-test, the following window will appear:
Select the grouping variable and insert them into the grouping variable box. Define the group in the independent samples t-test. Select the dependent variable and insert them into the test variable list. Click on “option” and select “% confidence interval.” As we click on the “ok” button, the result window for the independent sample t-test will appear in front of us.
Independent sample t-test group statistics table: This table will show the total number in each group, the mean, the standard deviation and the standard error for the independent sample t-test.

Independent sample t-test statistics table: In this table, the first test will be Levene’s test, which is used to test the assumptions of equal variance between all the groups in the independent sample t-test. Significance value of F is used to make the statistical decision about the assumptions of equal variance. The second test statistics will show the calculated value of the independent sample t-test, the degree of freedom, and the significance value of the independent sample t-test. This significance value is used to make the statistical decision about the mean of the two groups. If the calculated value is less than the predetermined significance level, then we can say that the means are significantly different.