1. Chapter 5 Introduction to Hypothesis Testing
Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall

2. Hypothesis Testing
Procedure for deciding whether the outcome of a study supports a particular theory or practical innovation
Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall

3. Core Logic of Hypothesis Testing
Approach can seem curious or even backwards
Researcher considers the probability that the experimental procedure had no effect and that the observed result could have occurred by chance alone
If that probability is sufficiently low, researcher will…
Reject the notion that experimental procedure had no effect
Affirm the hypothesis that the procedure did have an effect
Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall

4. The Null Hypothesis and the Research Hypothesis
Opposite of desired result
Usually that manipulation had no effect
Research hypothesis
Also called the “alternative hypothesis”
Opposite of the null hypothesis
What the experimenter desired or expected all along—that the manipulation did have an effect
Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall

5. The Hypothesis Testing Process
Step 1. Restate the question as a research hypothesis and a null hypothesis about the populations
Step 2. Determine characteristics of the “comparison distribution”
A distribution of the sort you would have if the null hypothesis were true
Used for figuring probability of getting your result if the null hypothesis were true
Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall

6. The Hypothesis Testing Process
Step 3. Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected
The score the sample would need to have in order to decide against the null hypothesis
Also called the “critical value”
In general, researchers use a cutoff with probability of 5% or less or sometimes 1% or less
Corresponds to p-values of p < .05 and p < .01
Conventional levels of significance
Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall

7. The Hypothesis Testing Process
Step 4. Determine your sample’s score on the comparison distribution
Convert sample’s raw score to a Z score on the comparison distribution
Step 5. Decide whether to reject the null hypothesis
If sample’s Z score is more extreme than the cutoff score, reject the null
Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall

8. The Hypothesis Testing Process: A Review of the Steps
Restate the question as a research hypothesis and a null hypothesis about the populations
Determine characteristics of the comparison distribution
Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected
Determine your sample’s score on the comparison distribution
Decide whether to reject the null hypothesis
Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall

9. Important Point about Hypothesis Testing
The null hypothesis can never be rejected completely
Instead, it can only be shown to be very unlikely that one would have gotten the observed results if the null were true
As a result, research results can never prove a theory
Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall

10. One-tailed vs. Two-tailed Hypothesis Tests
Directional prediction
Researcher expects experimental procedure to have an effect in a particular direction
One-tailed significance tests may be used
Nondirectional prediction
Research expects experimental procedure to have an effect but does not predict a particular direction
Two-tailed significance test appropriate
Takes into account that the sample could be extreme at either tail of the comparison distribution
Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall

11. Significance Level Cutoffs for One- and Two-Tailed Tests
The .05 significance level
The .01 significance level
Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall

12. One-tailed vs. Two-tailed Hypothesis Tests
Two-tailed tests
More conservative than one-tailed tests
Some believe that two-tailed tests should always be used, even when an experimenter makes a directional prediction
Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall