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

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

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

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

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

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

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

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

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

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

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

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