Aron chpt 5 ed revised

Introduction to Hypothesis Testing
Chapter 5
Copyright © 2011 by Pearson Education, Inc. All rights reserved

Chapter Outline
A Hypothesis-Testing Example
The Core Logic of Hypothesis Testing
The Hypothesis-Testing Process
One-Tailed and Two-Tailed Hypothesis Tests
Decision Errors

Hypothesis Testing
Theory
A set of principles that attempts to explain one or more facts, relationships, or events
Usually gives rise to various specific hypotheses that can be tested in research studies
Hypothesis
A specific prediction intended to be tested in a research study
Can be based on informal observation or theory

Hypothesis Testing
A systematic procedure for deciding whether the results of a research study supports a hypothesis that applies to a population

Hypothesis Testing
Researchers want to draw conclusions about a particular population.
e.g., babies in general
Conclusions will be based on results of studying a sample.
e.g., one baby

Research is usually designed to answer a specific question
Do students who attend an after-school program that is academically oriented (math, writing, computer use) score higher on an intelligence test than students who do not attend such a program?
Researcher forms a hypothesis
Children in academic after-school programs will have higher IQ scores than children in the general population.
Researcher sets criteria and runs experiment

ISSUES!!
Karl Popper (1902-1994)
Philosophy of Falsification
Can only falsify a hypothesis-cannot prove a hypothesis
Need only one case to disprove something
e.g. –”All birds are blue”
It is impossible statistically to demonstrate something is true.
Statistical techniques are better at demonstrating that something is not true
Copyright © 2011 by Pearson Education, Inc. All rights reserved Confusing but Important

Null Hypothesis (H 0 )
The hypothesis predicting that no difference exists between groups being compared.
Children in academic after-school programs will not have higher IQ scores than children in the general population.
Research Hypothesis (Alternative Hypothesis) (H a )
The hypothesis that the researcher wants to support predicting that a significant difference exists between the groups being compared.
Confusing but Important

Null Hypothesis
The purposes of the null hypothesis
Acts as a starting point
Until researchers can verify that there is a difference between two groups, it must be assumed that there is no difference
Provides a benchmark
The null hypothesis helps define a range within any observed differences between groups can be attributed to chance or are due to something other than chance

The Hypothesis-Testing Process
Step 1: Restate the question as a research hypothesis and a null hypothesis about the population.
Step 2: Determine the characteristics of the comparison distribution.
Step 3: Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected.
Step 4: Determine your sample’s score on the comparison distribution.
Step 5: Decide whether to reject the null hypothesis.

Hypothesis Testing: Step 1
Restate the question as a research hypothesis and a null hypothesis about the populations
Research hypothesis
Null hypothesis
Children in academic after-school programs will not have higher IQ scores than children in the general population.
.

Determine the characteristics of the comparison distribution
Comparison distribution (sampling distribution)
distribution used in hypothesis testing
represents the population distribution if the null hypothesis is true
distribution to which you compare the score based on your sample’s results
Find out the key information about the comparison distribution
e.g., population mean, population SD, shape of the distribution (does it follow a normal curve?)
M = 100, SD = 15
If the null hypothesis is true:
Population 1 and Population 2 are the same.

Set a cutoff sample score or critical value
This is a target against which you will compare the results of your study
By setting a cutoff score, you are deciding how extreme a sample score would need to be in order to be too unlikely to get such an extreme score if the null hypothesis were true.

Hypothesis Testing: Step 3 (cont.)
Researchers use Z scores and percentages to set the cutoff scores.
For instance, a researcher might decide that if a result was less likely than 5%, she would reject the null hypothesis
In this case, researchers would look at the normal curve table and find the Z score cutoff for scores in the top 5% of a normal curve, which is 1.64

Hypothesis Testing: Step 3 (cont.)
Generally, researchers in the social and behavioral sciences use conventional levels of significance, which are cutoff scores of either 5% or 1%.
When a sample score is at least as extreme as the cutoff score, then the result is considered statistically significant.

Determine your samples score on the comparison distribution.
Figure the Z score for the sample’s raw score based on the comparison distribution’s mean and standard deviation
If your sample’s raw score = 125, the population mean = 100, and the population standard deviation = 15
The Z score for your sample would be:

Decide Whether to Accept or Reject the Null Hypothesis.
Compare your sample’s Z score to the cutoff Z score
Cutoff Z = 1.64
Sample Z = 1.67
Reject Null Hypothesis
“ Children in academic after-school programs will not have higher IQ scores than children in the general population.”
Found Support for Research Hypothesis
“ Children in academic after-school programs will have higher IQ scores than children in the general population.”

Implications of Rejecting of Failing to Reject the Null Hypothesis
When you reject the null hypothesis, all you are saying is that your results support the research hypothesis.
The results never prove the research hypothesis or show that your hypothesis is true.
Research studies and their results are based on the probability or chance of getting your result if the null hypothesis were true.

Implications of Rejecting of Failing to Reject the Null Hypothesis
When the results are not extreme enough to reject the null hypothesis, you do not say that the results support the null hypothesis.
You say that the results are not statistically significant, or that the results are inconclusive.
We are basing research on probabilities, and the fact that we did not find a result in this study does not mean that the null hypothesis is true.

Another Example

Another Example -1.64

Another Example

One-Tailed and Two-Tailed Hypothesis Tests
Directional Hypothesis
focuses on a specific direction of effect
e.g., that reading levels would be greater in students participating in a reading program
one-tailed test
To reject the null hypothesis, a sample score needs to be in a particular tail of the distribution (e.g., the top 1% of the distribution).
Non-Directional Hypothesis
a hypothesis that predicts an effect, but does not specify whether the score will be high or low
The null hypothesis would be that there would be no change, or that the scores would not be extreme at either tail of the comparison distribution.

Determining Cutoff Scores with Two-Tailed Tests
For a two-tailed test, you have to divide the significance percentage between two tails.
For a 5% significance level, the null hypothesis would be rejected if the sample score was in either the top 2.5% or the bottom 2.5% of the comparison distribution.

When to Use One-Tailed or Two-Tailed Tests
Use a one-tailed test when you have a clearly directional hypothesis.
Use a two-tailed test when you have a clearly non-directional hypothesis.
With a one-tailed test, if the sample score is extreme—but in the opposite direction—the null cannot be rejected.
Often researchers will use two-tailed tests even if the hypothesis is directional.

Decision Errors
When the right procedures lead to the wrong decisions
In spite of calculating everything correctly, conclusions drawn from hypothesis testing can still be incorrect.
This is possible because you are making decisions about populations based on information in samples.
Hypothesis testing is based on probability.

Type I Error
Rejecting the null hypothesis when the null hypothesis is true
You find an effect when in fact there is no effect.
A Type I error is a serious error as theories, research programs, treatment programs, and social programs are often based on conclusions of research studies.

Type I Error
The chance of making a Type I error is the same as the significance level.
If the significance level was set at p < .01, there is less than a 1% chance that you could have gotten your result if the null hypothesis was true.
To reduce the chance of making a Type I error, researchers can set a very stringent significance level (e.g., p < .001).

Type II Error
With a very extreme significance level, there is a greater probability that you will not reject the null hypothesis when the research hypothesis is actually true.
e.g. concluding that there is dangerous drug effects when there is actually no dangerous effect
The probability of making a Type II error can be reduced by setting a very lenient significance level (e.g., p < .10).

Relationship Between Type I and Type II Errors
Decreasing the probability of a Type I error increases the probability of a Type II error.
The compromise is to use standard significance levels of p < .05 and p < .01.
Real Situation H 0 True H a True H a Supported (H 0 Rejected) Error Type I Correct Decision Inconclusive (H 0 Not Rejected) Correct Decision Error Type II

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Aron chpt 5 ed revised

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