1. t-Tests

2. Overview of t-Tests How a t-Test Works Single-Sample t
Independent Samples t
Paired t
Effect Size

3. How a t-Test Works The t-test is used to compare means.
The difference between means is divided by a standard error.
The t statistic is conceptually similar to a z-score.

4. How a t-Test Works

5. How a t-Test Works

6. The t-Test as Regression
bo is the mean of one group
b1 is the difference between means
If b1 is significant, then there is a significant difference between means

7. Single Sample t-test
Compare a sample mean to a hypothesized population mean (test value based on previous research or norms)

8. Assumptions for Single-Sample t
1. Independent observations
2. Normal distribution or large N
3. Interval or ratio level data

9. Sampling Distribution of the Mean
The t distribution is symmetrical but flatter than a normal distribution.
The exact shape depends on degrees of freedom.

10. normal distribution
t distribution

11. Degrees of Freedom Amount of information in the sample
Changes depending on the design and statistic
For a one-group design, df = N-1
The last score is not “free to vary”

12. Independent Samples t-test
Also called: Unpaired t-test
Use with between-subjects, unmatched designs

13. Sampling Distribution of the Difference Between Means
We are collecting two sample means and finding out how big the difference is between them.
The mean of this sampling distribution is the Ho difference between population means, which is zero.

14. sampling distribution of the difference between means
m1- m2
x1-x2

15. Independent Samples t -test Assumptions
Interval/ratio data
Normal distribution or N at least 30
Independent observations
Homogeneity of variance - equal variances in the population

16. Levene’s Test Test for homogeneity of variance
If the test is significant, the variances of the two populations should not be assumed to be equal

17. Independent Samples t-test Interpretation
Sign of t depends on the order of entry of the two groups
df = N1 + N2 - 2
Use Bonferroni correction for multiple tests
Divide alpha level by the number of tests

18. Paired t-Test Also called: Dependent Samples or Related Samples t-test
Compares two conditions with paired scores:
Within subjects design
Matched groups design

19. Paired Samples t-Test Assumptions
Interval/ratio data
Normal distribution or N at least 30
Independent observations

20. Paired Samples t-test - Interpretation
The sign of the t depends on the order in which the variables are entered
df = N-1
Use Bonferroni correction for multiple tests

21. Effect Size
Statistical significance is about the Null Hypothesis, not about the size of the difference.
A small difference may be significant with sufficient power.
A significant but small difference may not be important in practice.

22. Effect Size with r2
Compute the correlation between the independent and dependent variables.
This will be a point-biserial correlation.
Square the r to get the proportion of variance explained.

23. Computing r2 from t

24. Example APA Format Sentence
A paired samples t-test indicated a significant difference between the number of incorrect items (M = 2.64, SD = 2.54) and the number of lures recalled (M = 3.30, SD = 1.83), t(97) = 2.54, p = .013, r2 = .06.

25. Take-Home Points
Every t-test compares a systematic difference to a measure of error.
Effect size should be reported along with whether a difference is significant.