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Unit 11 Intro: Dependent Samples t-test
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- Unit 11: Getting Started with Dependent Sample t-Tests
- After this module, you will be able to…
Explain when to use the dependent samples t test
Explain the difference between the dependent and independent samples t-test
Explain the effect of using the dependent samples test on the likelihood of rejecting H0
Compute the observed t value given a set of data
Interpret the t value, comparing it to t critical values, to complete a hypothesis test
Use the Excel to carry out dependent sample t-tests
Read and interpret dependent t-Test results in research reports - Concepts to review and carry forward
t distribution and curve
Degrees of freedom df
Steps of Hypothesis testing
Summation notation - What are related or dependent samples?
Related samples
Same subjects at two points in time (before/after)
Related subjects, such as twins, or members of a married couple, or father-son, mother-daughter comparisons
Two scores for each case (a pair=1 case) - When the dependent samples test is used
Comparing differencesof related sets ofscores.
Before/after
Twins
Couples
Differencescore (D) is computed.
Determining the correct test statistic - Computing the Test Statistic – Part 1
- Instead of individual scores, a Difference score D is computed for each set of scores: After – Before = D
- Equation for t uses (?D)2 and ?D2
- For (?D)2 sum the D scores first, then square the result
- For ?D2 square each D first, then sum the results
- Computing the Test Statistic – Part 2
Compute Difference score D for each case
Compute D2 for each case
Equation for t is relatively easy - Degrees of Freedom
- Degrees of freedom approximate the sample size
- For the Dependent sample t-test
- n – 1
- The n used is the number of pairs of observations
- Example: four people, measured before-and-after
- There are 8 scores (4 before, 4 after)
- There are 4 Difference scores (D)
- df = 4 – 1 = 3
- So How Do I Interpret…
- t(24) = 2.45
24 is the number of degrees of freedom
25 pairs of cases were used
25 individuals if a before-and-after test
50 matched individuals (e.g., 50 twins in 25 pairs)
2.45 is the obtained value of t (from the formula)
p < .05 indicates the probability level chosen
What would these results mean for the null hypothesis? - Deciding about the null hypothesis
The Critical Value (two-tailed) for df=24 from Table B.2 is 2.064
The Obtained t = 2.45
Obtained t is greater than the Critical Value
Null hypothesis of no difference between groups would be rejected
Decision: There is a statistically significant difference between the groups (t(11)=2.45, p<0.05). - Effect size
When the null hypothesis is rejected, the size of the effect must also be reported.
The same equation for r2 that was used in Unit 10will work here.
In this example, about 20% of the variability in difference scores is related to the treatment. - Next steps
Read Salkind Chapter 11
Do Time to Practice Problems 1 and 3 (hand)
Do Time to Practice Problems 2 and 4 (Excel)
Do Excel Assignment #3
Try the online Practice Problems
Do Quiz 11 - Unit 11: Getting Started with Dependent Sample t-Tests
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