t-test, Two Dependent Samples (Jump to: Lecture | Video )

Let's perform a dependent samples t-test: Researchers want to test a new anti-hunger weight loss pill. They have 10 people rate their hunger both before and after taking the pill. Does the pill do anything? Use alpha = 0.05

Figure 1.

Steps for Dependent Samples t-Test
1. Define Null and Alternative Hypotheses 2. State Alpha 3. Calculate Degrees of Freedom 4. State Decision Rule 5. Calculate Test Statistic 6. State Results 7. State Conclusion

Let's begin.

1. Define Null and Alternative Hypotheses

Figure 2.

2. State Alpha

Alpha = 0.05

3. Calculate Degrees of Freedom

Figure 3.

4. State Decision Rule

Using an alpha of 0.05 with a two-tailed test with 9 degrees of freedom, we would expect our distribution to look something like this:

Figure 4.

Use the t-table to look up a two-tailed test with 9 degrees of freedom and an alpha of 0.05. We find a critical value of 2.2622. Thus, our decision rule for this two-tailed test is:

If t is less than -2.2622, or greater than 2.2622, reject the null hypothesis.

5. Calculate Test Statistic

The first step is for us to calculate the difference score for each pairing:

Figure 5.

Now, we can calculate our t value:

Figure 6.

6. State Results

t = 3.61

Result: Reject the null hypothesis.

7. State Conclusion

The anti-hunger weight loss pill significantly affected hunger, t = 3.61, p < 0.05.

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