T-Test

The following general procedure is used for both the Independent-Samples T-Test and the Paired-Samples T-Test.

1. Express what we are looking to identify in terms of a null and research hypothesis.

• The null hypothesis is that the statistical difference between the averages (means) is the same.
• The research hypothesis is that there is a difference between the averages (means) is different.

2. Identify the level of risk or significance we are willing to accept.

• We will go with 0.05 as it is often considered standard. One may determine the level of risk associated with their study by looking at literature in the field.

3. Determine which statistical analysis. For:

• Independent-Samples T-Test: measuring the differences between variables for two groups with one measurement.
• Paired-Samples T-Test: measuring the differences between a variable for two groups that are being tested more than once.

4. Calculate the test statistic.

• Utilize a software package such as SPSS (as demonstrated in the following video cases) to calculate the test statistic or critical value.

5. Determine the value needed to reject the null hypothesis.

• Based on the degrees of freedom and the level of risk and calculated by a software package such as SPSS (as demonstrated in the following video cases).

6. Compare the test statistic to the value needed to reject the null hypothesis

7. Accept or Reject

• If the test statistic is more extreme than the critical value - reject the null hypothesis. In other words, the research statistic is more attractive and there is a difference between the means.
• If the test statistic is less extreme than the critical value - accept the null hypothesis. In this case, it is statistically likely that the means are the same.

INDEPENDENT-SAMPLES T-TEST

Let's assume we have a cookie business and want to determine how our chocolate chip cookies compare to a competitor. One way we could do this is by comparing the average (mean) number of chocolate chips per cookie for our product against our competitor.

STATISTICAL ANALYSIS (SPSS)

Using this data set, the following video describes how to determine whether or not there is a statistical difference between the average number of chocolate chips in samples of the competitor and the House Brand.

PAIRED-SAMPLES T-TEST

The vendor providing chocolate chip cookies went out of business and a new supplier provides a sample for testing. Chips are distributed to the different manufacturing sites and used to produce new batches of cookies. In order to test for equivalency between the two chips, the average (mean) number of chocolate chips per cookie will be compared to the average (mean) number of chocolate chips per cookie using samples from the new supplier. There are ten manufacturing sites and data will be collected for each, pre- and post- vendor change.

STATISTICAL ANALYSIS (SPSS)

Using this data set, the following video describes how to determine whether or not there is a statistical difference between the average number of chocolate chips pre- and post- vendor change.

Additional Helpful Resources:

Barnard College's Emperical Reasoning Center: SPSS Resource on T-Tests

APA Formatting for Independent-Saples T-Test and Paired-Samples T-Tes