1. Chapter Seventeen HYPOTHESIS TESTING

2. Approaches to Hypothesis Testing
Classical Statistics vs. Bayesian Approach
Classical Statistics
sampling-theory approach
Making inference about a population based on sample evidence
objective view of probability
Allowing how much error is likely to occur
decision making rests on analysis of available sampling data

3. Approaches to Hypothesis Testing Continued
Bayesian Statistics
extension of classical statistics
In addition, consider additional elements of prior information such as subjective probability estimates to improve the decision maker’s judgment.
Statistically more sophisticated

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

5. Logic of Hypothesis Testing
Depending on how the alternative hypothesis is defined, two tailed or one tailed test.
Two tailed test
nondirectional test
considers two possibilities (change could be increase or decrease)
One tailed test
directional test
places entire probability of an unlikely outcome to the tail specified by the alternative hypothesis (change is either increase or decrease)

6. Decision Errors in Testing
Type I error (α)
a true null hypothesis is rejected (or a innocent person is unjustly convicted)
Type II error (β)
one fails to reject a false null hypothesis (or a guilty person is acquitted)
Greater emphasis is given on not committing Type I error.

7. Testing for Statistical Significance
State the null hypothesis
Choose the statistical test (t, Z, Chi-square, ANOVA, etc.)
Select the desired level of significance (α)
Confidence level =1- α
Compute the calculated value
Obtain the critical value

8. Testing for Statistical Significance Continued
Interpret the test and make decision
Compare the calculated value and critical value and make a decision.
If the calculated actual value > the critical value, reject the null hypothesis.
If the calculated actual value < the critical value, do not reject the null hypothesis.
Or compare p value (probability of the sample value falling into the rejection area) and α.
If p < α, then reject the null hypothesis
If p > α, then do not reject the null hypothesis.

9. Classes of Significance Tests
Parametric tests (Z or t tests)
Z or t test is used to determine the statistical significance between a sample mean and a population parameter
t test is for smaller sample and/or when population standard deviation is unknown.
Assumptions:
independent observations
normal distributions
populations have equal variances
at least interval data measurement scale

10. Classes of Significance Tests Continued
Nonparametric tests (χ2 test)
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

11. Applications One sample tests Two sample tests
Z or t test (pp )
Chi-square test (pp )
Two sample tests
Interdependent samples
Z or t test (pp )
Chi-square test (pp )
Related samples
Z or t test (pp )
Chi-square test (McNemar test on pp )

12. ANOVA (Analysis of Variance)
One-way ANOVA (k independent samples test)
the statistical method (F-test) for testing the null hypothesis that means of several populations are equal by a single grouping variable (or factor)
Two-way ANOVA (k related samples test)
The statistical method (F-test) for testing the null hypothesis that means of several populations are equal by two grouping variables (factors)

13. ANOVA (analysis of Variance) Continued
Multiple comparison test
test the difference between each pair of means and indicate significantly different group means at a specified alpha level
use group means and incorporate the mean square error term of the F ratio

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