Aron chpt 5 ed revised

Introduction to Hypothesis TestingIntroduction to Hypothesis Testing

Chapter 5

Copyright © 2011 by Pearson Education, Inc. All rights reserved

Chapter OutlineChapter OutlineA Hypothesis-Testing ExampleThe Core Logic of Hypothesis TestingThe Hypothesis-Testing ProcessOne-Tailed and Two-Tailed Hypothesis

TestsDecision Errors


Hypothesis TestingHypothesis Testing

TheoryA 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

HypothesisA specific prediction intended to be tested in a research study

Can be based on informal observation or theory



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



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


The Core Logic of Hypothesis The Core Logic of Hypothesis TestingTesting

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


The Core Logic of Hypothesis The Core Logic of Hypothesis Testing Testing

ISSUES!!1. 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”

2. It is impossible statistically to demonstrate something is true.

Statistical techniques are better at demonstrating that something is not true


Confusing but

Important

The Core Logic of Hypothesis The Core Logic of Hypothesis TestingTesting

Null Hypothesis (H0)◦ The hypothesis predicting that no difference

exists between groups being compared. Children in academic after-school programs will not have


Research Hypothesis (Alternative Hypothesis) (Ha)◦ The hypothesis that the researcher wants to

support predicting that a significant difference exists between the groups being compared.

Children in academic after-school programs will have higher IQ scores than children in the general population.

Confusing but

Important

Null HypothesisNull HypothesisThe purposes of the null hypothesis

1. 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

2. 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 The Hypothesis-Testing ProcessProcess

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 1Hypothesis Testing: Step 1Restate the question as a research hypothesis and a null hypothesis about the populations

◦ Research hypothesis Children in academic after-school programs will have


◦ Null hypothesis Children in academic after-school programs will not have


.

Hypothesis Testing: Step Hypothesis Testing: Step 22Determine 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.

Hypothesis Testing: Step 3Hypothesis Testing: Step 3

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 Hypothesis Testing: Step 3 (cont.)(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 Hypothesis Testing: Step 3 (cont.)(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.

Hypothesis Testing: Step Hypothesis Testing: Step 44

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:

Hypothesis Testing: Step Hypothesis Testing: Step 55Decide 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 Implications of Rejecting of Failing to Reject the Null Failing to Reject the Null HypothesisHypothesis

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 Implications of Rejecting of Failing to Reject the Null Failing to Reject the Null HypothesisHypothesis

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 ExampleAnother Example


-1.64

One-Tailed and Two-Tailed One-Tailed and Two-Tailed Hypothesis TestsHypothesis 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 Determining Cutoff Scores with Two-Tailed TestsTwo-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-When to Use One-Tailed or Two-Tailed TestsTailed 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 ErrorsDecision ErrorsWhen the right procedures lead to the

wrong decisionsIn 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 ErrorType I ErrorRejecting 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 ErrorType I ErrorThe 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 ErrorType II ErrorWith 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 Relationship Between Type I and Type II Errorsand 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

H0 True Ha True

Ha Supported (H0 Rejected)Error Type I Correct Decision

Inconclusive (H0 Not Rejected)Correct Decision Error Type II

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