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Chapter Seventeen HYPOTHESIS TESTING

Chapter Seventeen HYPOTHESIS TESTING. 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

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Chapter Seventeen HYPOTHESIS TESTING

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  1. Chapter SeventeenHYPOTHESIS 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 TestingContinued • 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 • 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 SignificanceContinued • 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 TestsContinued • 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 • Z or t test (pp. 535-536) • Chi-square test (pp. 536-537) • Two sample tests • Interdependent samples • Z or t test (pp. 539-540) • Chi-square test (pp. 540-542) • Related samples • Z or t test (pp. 543-544) • Chi-square test (McNemar test on pp. 545-546)

  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

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