METHODS IN BEHAVIORAL METHODS IN BEHAVIORAL RESEARCHRESEARCH

NINTH EDITION

PAUL C. COZBYCopyright © 2007 The McGraw-Hill Companies, Inc.

CHAPTER 13CHAPTER 13

UNDERSTANDING RESEARCH RESULTS: STATISTICAL

INFERENCE

LEARNING OBJECTIVESLEARNING OBJECTIVES

Explain how researchers use inferential statistics to evaluate sample data

Distinguish between the null hypothesis and the research hypothesis

Discuss probability in statistical inference, including the meaning of statistical significance

LEARNING OBJECTIVESLEARNING OBJECTIVES

Describe the t test, and explain the difference between one-tailed and two-tailed tests

Describe the F test, including systematic variance and error variance

Distinguish between Type I and Type II errors

LEARNING OBJECTIVESLEARNING OBJECTIVES

Discuss the factors that influence the probability of a Type II error

Discuss the reasons a researcher may obtain nonsignificant results

Define power of a statistical test Describe the criteria for selecting an

appropriate statistical test

SAMPLES AND POPULATIONSSAMPLES AND POPULATIONS

Inferential statistics are necessary because the results of a given study are based on data obtained from a single sample of researcher participants

Allows conclusions on the basis of sample data

INFERENTIAL STATISTICSINFERENTIAL STATISTICS

Allows researchers to make inferences about the true difference in the population on the basis of the sample data

Gives the probability that the difference between means reflects random error rather than a real difference

NULL AND RESEARCH NULL AND RESEARCH HYPOTHESESHYPOTHESES

Null Hypothesis: Population Means are Equal

Research Hypothesis: Population Means are Not Equal

PROBABILITY AND SAMPLING PROBABILITY AND SAMPLING DISTRIBUTIONSDISTRIBUTIONS

Probability: The Case of ESP Sampling Distributions Sample Size

EXAMPLE: THE EXAMPLE: THE tt AND AND FF TESTS TESTS

t value is a ratio of two aspects of the data, the difference between the group means and the variability within groups

t = group difference within group variability

SAMPLING DISTRIBUTION OF SAMPLING DISTRIBUTION OF tt VALUES VALUES

EXAMPLE: THE EXAMPLE: THE tt AND AND FF TESTS TESTS

Degrees of Freedom One-Tailed Versus Two-Tailed Tests F Test (analysis of variance)

Systematic varianceError variance

EXAMPLE: THE EXAMPLE: THE tt AND AND FF TESTS TESTS

Calculating Effect Size Confidence Intervals and Statistical

Significance Statistical Significance: An Overview

TYPE I AND TYPE II ERRORSTYPE I AND TYPE II ERRORS

Type I ErrorsMade when the null hypothesis is rejected but

the null hypothesis is actually trueObtained when a large value of t or F is

obtained

TYPE I AND TYPE II ERRORSTYPE I AND TYPE II ERRORS

Type II ErrorsMade when the null hypothesis is accepted

although in the population the research hypothesis is true

Factors related to making a Type II errorSignificance (alpha) levelSample sizeEffect size

THE EVERYDAY CONTEXT OF THE EVERYDAY CONTEXT OF TYPE I AND TYPE II ERRORSTYPE I AND TYPE II ERRORS

CHOOSING A SIGNIFICANCE CHOOSING A SIGNIFICANCE LEVELLEVEL

Researchers traditionally have used either a .05 or a .01 significance level in the decision to reject the null hypothesis

Researchers generally believe that the consequences of making a Type I error are more serious than those associated with a Type II error

CHOOSING A SAMPLE SIZE: CHOOSING A SAMPLE SIZE: POWER ANALYSISPOWER ANALYSIS

• Power is a statistical test that determines optimal sample size based on probability of correctly rejecting the null hypothesis

Power = 1 – p (Type II error)

• Effect sizes range and desired power• Smaller effect sizes require larger samples to be significant• Higher desired power demands a greater sample size• Researchers usually use a power between .70 and .90

IMPORTANCE OF IMPORTANCE OF REPLICATIONSREPLICATIONS

• Scientists attach little importance to results of a single study

• Detailed understanding requires numerous studies examining same variables

• Researchers look at the results of studies that replicate previous investigations

SIGNIFICANE OF PEARSON SIGNIFICANE OF PEARSON r r CORRELATION COEFFICIENTCORRELATION COEFFICIENT

• Is the relationship statistically significant?• Ho: r = 0 and H1: r ≠ 0

COMPUTER ANALYSIS OF COMPUTER ANALYSIS OF DATADATA

Software ProgramsSPSSSASMinitabMicrosoft Excel

Steps in analysis Input dataConduct analysis Interpret output

SELECTING THE APPROPRIATE SELECTING THE APPROPRIATE SIGNIFICANCE TESTSIGNIFICANCE TEST

One Independent Variable– Two Groups OnlyNominal Scale Data Ordinal Scale DataInterval or Ratio Scale Data

SELECTING THE APPROPRIATE SELECTING THE APPROPRIATE SIGNIFICANCE TESTSIGNIFICANCE TEST

One Independent Variable– Three or More GroupsNominal Scale DataOrdinal Scale DataInterval or Ratio Scale Data

SELECTING THE APPROPRIATE SELECTING THE APPROPRIATE SIGNIFICANCE TESTSIGNIFICANCE TEST

Two or More Independent VariablesNominal Scale Data - chi-squareOrdinal Scale Data – no appropriate test is

availableInterval or Ratio Scale Data – two-way analysis

of variance