Student T-tests are commonly used to compare the population means by testing their respective sample means. Therefore, performing sample t-tests helps a researcher determine whether there is a difference in population means and, if there is a difference, the follow-up question is, whether the difference is significant or it just happened by chance. Since sample t-tests are parametric, they can only be performed when the distribution of the data is known. Sample t-tests analysis includes; independent sample t-test, one sample t-test, and paired sample t-test. For each of the sample t-test to be performed, it depends on exactly which means you wish to compare, the nature of the data (i.e., the dependent and independent variables) and if the assumptions associated with the test are met (Picquelle & Mier, 2011).

Independent sample t-test

Independent samples t-test are performed when you have two data sets that are independent of each other and, you wish to compare their population means to investigate whether the two populations differ from one another. The dependent variable has to be a continuous variable. In our case, using the high school longitudinal data, we will run independent samples t-tests between masters an associate degree groups on X1SES as the dependent variable. We would like to determine whether the two groups differ in their means using a two-tailed hypothesis.

Masters population mean = associate degree population mean

Masters population mean ≠ associate degree population mean

Taking into consideration sampling distribution and homogeneity of variance assumptions, in this data, we assume that the sampling methods involved in the data collection were random. The test of homogeneity of variance is not violated since a p-value (sig) < 0.05 according to (Table 1) below for Levene’s test.

Table 1; Independent samples t-test table

From the independent samples t-test analysis, conducted, a p-value (sig) of .000 < .05 approves for rejection of our null hypothesis. The latter therefore means that there is a significant difference in the means of masters and associate degree groups.

One sample t-test

This test is conducted when your interest is to compare hypothesized mean based on a single sample with a continuous data set. Practically, to determine if the mean of the variable is equal to, greater or less than the specified value of interest (or a value that has been used in other research studies). Using the high school longitudinal data, we want to find out if the average X1SES level is equal to 1.00.

X1SES mean = 1

X1SES mean ≠ 1

Table 2; test for normality table

Table 3; One sample t-test table

Having considered the assumptions for continuous variable and test of normality (table 2), the one sample t-test was performed. The (table 2) indicates a p-value (sig) of 0.00 < .05. Therefore, the average X1SES level is not equal to 1.

Paired samples t-test

When a researcher wants to study the same sample at two different times, he /she can conduct a paired samples t-test. The test is often used to measure the difference in means of the same sample before and after a period of time (or after a particular intervention is implemented on the group). The sample data should be continuous, independent and normally distributed. Using the high school longitudinal, we will look at X1PAR1EDU and X2PAR1EDU whether they are different in mean. We aim to find out if the education level of the participants changes after a while.

X1PAR1EDU mean = X2PAR1EDU mean

X1PAR1EDU mean ≠ X2PAR1EDU mean

Table 4; paired samples t-test table

Table 4 shows a p-value (sig) of .00 which is less than .05 and, thus we ought to reject our null hypothesis. We then conclude that X1PAR1EDU mean is not equal to X1PAR1EDU mean and that there is a significant difference in their means. The latter further implies that after a period of time the sample experienced a change in participants’ education level. In the practical research, it means that after some time participants enroll for a higher level of education.

References

Picquelle, S. J., & Mier, K. L. (2011). A practical guide to statistical methods for comparing means from two-stage sampling. Fisheries Research, 107(1-3), 1-13.