2 Approaches to Hypothesis Testing Classical Statistics vs. Bayesian ApproachClassical Statisticssampling-theory approachMaking inference about a population based on sample evidenceobjective view of probabilityAllowing how much error is likely to occurdecision making rests on analysis of available sampling data
3 Approaches to Hypothesis Testing Continued Bayesian Statisticsextension of classical statisticsIn 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 comparedAlternative Hypothesislogical opposite of the null hypothesisthat 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 testnondirectional testconsiders two possibilities (change could be increase or decrease)One tailed testdirectional testplaces 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 hypothesisChoose the statistical test (t, Z, Chi-square, ANOVA, etc.)Select the desired level of significance (α)Confidence level =1- αCompute the calculated valueObtain the critical value
8 Testing for Statistical Significance Continued Interpret the test and make decisionCompare 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 hypothesisIf 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 parametert test is for smaller sample and/or when population standard deviation is unknown.Assumptions:independent observationsnormal distributionspopulations have equal variancesat 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 requiredAssumptionsindependent observations for some testsnormal distribution not necessaryhomogeneity of variance not necessaryappropriate 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 testsInterdependent samplesZ or t test (pp )Chi-square test (pp )Related samplesZ 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 testtest the difference between each pair of means and indicate significantly different group means at a specified alpha leveluse 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 levelsObservations or participants arematched orthe same participant is measured more than onceInterval or ratio data