Hypothesis

HYPOTHESIS 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

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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

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be used for interval or ratio data

How to Test the Null Hypothesis •

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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 •

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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? 11

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 12

or ratio data