METHODS IN BEHAVIORAL RESEARCH NINTH EDITION PAUL C. COZBY Copyright © 2007 The McGraw-Hill Companies, Inc.

CHAPTER 13 UNDERSTANDING RESEARCH RESULTS: STATISTICAL INFERENCE

LEARNING 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 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 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 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 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 HYPOTHESES Null Hypothesis: Population Means are Equal Research Hypothesis: Population Means are Not Equal

PROBABILITY AND SAMPLING DISTRIBUTIONS Probability: The Case of ESP Sampling Distributions Sample Size

EXAMPLE: THE t AND F 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 t VALUES

EXAMPLE: THE t AND F TESTS Degrees of Freedom One-Tailed Versus Two-Tailed Tests F Test (analysis of variance) Systematic variance Error variance

EXAMPLE: THE t AND F TESTS Calculating Effect Size Confidence Intervals and Statistical Significance Statistical Significance: An Overview

TYPE I AND TYPE II ERRORS Type I Errors Made when the null hypothesis is rejected but the null hypothesis is actually true Obtained when a large value of t or F is obtained

TYPE I AND TYPE II ERRORS Type II Errors Made when the null hypothesis is accepted although in the population the research hypothesis is true Factors related to making a Type II error Significance (alpha) level Sample size Effect size

THE EVERYDAY CONTEXT OF TYPE I AND TYPE II ERRORS

CHOOSING A SIGNIFICANCE LEVEL 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: POWER 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 REPLICATIONS 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 r CORRELATION COEFFICIENT Is the relationship statistically significant? Ho: r = 0 and H1: r ≠ 0

COMPUTER ANALYSIS OF DATA Software Programs SPSS SAS Minitab Microsoft Excel Steps in analysis Input data Conduct analysis Interpret output

SELECTING THE APPROPRIATE SIGNIFICANCE TEST One Independent Variable– Two Groups Only Nominal Scale Data Ordinal Scale Data Interval or Ratio Scale Data

SELECTING THE APPROPRIATE SIGNIFICANCE TEST One Independent Variable– Three or More Groups Nominal Scale Data Ordinal Scale Data Interval or Ratio Scale Data

SELECTING THE APPROPRIATE SIGNIFICANCE TEST Two or More Independent Variables Nominal Scale Data - chi-square Ordinal Scale Data – no appropriate test is available Interval or Ratio Scale Data – two-way analysis of variance