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17-2McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc.,All Rights

Reserved.

Part FourANALYSIS AND

PRESENTATION OF DATA

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Chapter SeventeenHYPOTHESIS TESTING

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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

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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.

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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

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Decision Errors in Testing

• Type I error– a true null hypothesis is rejected

• Type II error– one fails to reject a false null hypothesis

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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

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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

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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

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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

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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

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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?

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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