4. 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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5. 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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6. 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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7. 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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8. 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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9. 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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10. 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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11. 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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12. 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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13. 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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14. 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
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