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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