Download Statistics for Behavioral and Social Sciences

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
• Null 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
1. Restate the question as a research hypothesis and
a null hypothesis about the populations
2. Determine characteristics of the comparison
distribution
3. Determine the cutoff sample score on the
comparison distribution at which the null
hypothesis should be rejected
4. Determine your sample’s score on the
comparison distribution
5. 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