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17-1 Part Four ANALYSIS AND PRESENTATION OF DATA 17-2 McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc.,All Rights Reserved. Chapter Seventeen HYPOTHESIS TESTING 17-3 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 17-4 Types of Hypotheses • Null – 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. 17-5 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 17-6 Decision Errors in Testing • Type I error – a true null hypothesis is rejected • Type II error – one fails to reject a false null hypothesis 17-7 Testing for Statistical Significance • • • • • • 17-8 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 17-9 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 17-10 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 17-11 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 17-12 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? 17-13 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 17-14