Part Four ANALYSIS AND PRESENTATION OF DATA McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc.,All Rights Reserved.

Chapter Seventeen HYPOTHESIS TESTING

Approaches to Hypothesis Testing Classical Statistics sampling-theory approach objective view of probability decision making rests on analysis of available sampling data Bayesian Statistics extension of classical statistics consider all other available information

Types of Hypotheses Null Alternative that no statistically significant difference exists between the parameter and the statistic being compared Alternative logical opposite of the null hypothesis that a statistically significant difference does exist between the parameter and the statistic being compared.

Logic of Hypothesis Testing Two tailed test nondirectional test considers two possibilities One tailed test directional test places entire probability of an unlikely outcome to the tail specified by the alternative hypothesis

Decision Errors in Testing Type I error a true null hypothesis is rejected Type II error one fails to reject a false null hypothesis

Testing for Statistical Significance State the null hypothesis Choose the statistical test Select the desired level of significance Compute the calculated difference value Obtain the critical value Interpret the test

Classes of Significance Tests Parametric tests Z or t test is used to determine the statistical significance between a sample distribution mean and a population parameter Assumptions: independent observations normal distributions populations have equal variances at least interval data measurement scale

Classes of Significance Tests Nonparametric tests Chi-square test is used for situations in which a test for differences between samples is required Assumptions independent observations for some tests normal distribution not necessary homogeneity of variance not necessary appropriate for nominal and ordinal data, may be used for interval or ratio data

How to Test the Null Hypothesis Analysis of variance (ANOVA) the statistical method for testing the null hypothesis that means of several populations are equal

Multiple Comparison Tests Multiple comparison procedures test the difference between each pair of means and indicate significantly different group means at a specified alpha level (<.05) use group means and incorporate the MSerror term of the F ratio

How to Select a Test Which does the test involve? one sample, two samples k samples If two or k samples,are the individual cases independent or related? Is the measurement scale nominal, ordinal, interval, or ratio?

K Related Samples Test Use when: The grouping factor has more than two levels Observations or participants are matched . . . or the same participant is measured more than once Interval or ratio data