Chapter 11 Testing for Differences

Chapter 11Testing for DifferencesDifferences betweens groups or categories of the independent variableStatistical tests of difference reveal whether the differences observed are greater than differences that might occur by chanceChi-squaret-testANOVA1Copyright c 2001 The McGraw-Hill Companies, Inc.Inferential Statistics Statistical test used to evaluate hypotheses and research questionsResults of the sample assumed to hold true for the population if participants areNormally distributed on the dependent variableRandomly assigned to categories of the IV Caveats of application2Copyright c 2001 The McGraw-Hill Companies, Inc.Alternative and Null HypothesesInferential statistics test the likelihood that the alternative hypothesis is true and the null hypothesis is notSignificance level of .05 is generally the criterion for this decisionIf p  .05, then alternative hypothesis acceptedIf p > .05, then null hypothesis is retained3Copyright c 2001 The McGraw-Hill Companies, Inc.Degrees of FreedomRepresented by dfSpecifies how many values vary within a statistical testCollecting data always carries errordf help account for this errorRules for calculating df or each statistical test4Copyright c 2001 The McGraw-Hill Companies, Inc.Four Analytical StepsStatistical test determines if a difference existsExamine results to determine if the difference found is the one predictedIs the difference significant?Evaluate the process and procedures of collecting data5Copyright c 2001 The McGraw-Hill Companies, Inc.Chi-SquareRepresented as χ2Determines if differences among categories are statistically significantCompares the observed frequency with the expected frequencyThe greater the difference between observed and expected, the larger the χ2Data for one or more variables must be nominal or categorical6Copyright c 2001 The McGraw-Hill Companies, Inc.One-Dimensional Chi-SquareDetermines if differences in how cases are distributed across categories of one nominal variable are significantSignificant χ2 indicates that variation of frequency across categories did not occur by chanceDoes not indicate where the significant variation occurs – only that one exists7Copyright c 2001 The McGraw-Hill Companies, Inc.Example of One-Dimensional Chi-Square8Copyright c 2001 The McGraw-Hill Companies, Inc.Contingency AnalysisAlso known as two-way chi-square or two-dimensional chi-squareExamines association between two nominal variables in relationship to one anotherColumns represent frequencies of 1st variableRows represent frequencies of 2nd variableFrequency of cases that satisfy conditions of both variables inserted into each cell9Copyright c 2001 The McGraw-Hill Companies, Inc.Example of Contingency Analysis10Copyright c 2001 The McGraw-Hill Companies, Inc.Limitations of Chi-SquareCan only use nominal data variablesTest may not be accurateIf observed frequency is zero in any cell, If expected frequency is < 5 in any cellCannot directly determine causal relationships11Copyright c 2001 The McGraw-Hill Companies, Inc.t-TestRepresented by tDetermines if differences between two groups of the independent variable on the dependent variable are significantIV must be nominal data of two categoriesDV must be continuous level data at interval or ratio level12Copyright c 2001 The McGraw-Hill Companies, Inc.Commons Forms of t-TestIndependent sample t-testCompares mean scores of IV for two different groups of peoplePaired comparison t-testCompares mean scores of paired or matched IV scores from same participants13Copyright c 2001 The McGraw-Hill Companies, Inc.Types of t-TestsTwo-tailed or nondirectional t-testHypothesis or research question indicates that a difference in either direction is acceptableOne-tailed or directional t-testHypothesis or research question specifies the difference to be found14Copyright c 2001 The McGraw-Hill Companies, Inc.Limitations of t-TestLimited to differences of two groupings of one independent variable on one dependent variableCannot examine complex communication phenomena15Copyright c 2001 The McGraw-Hill Companies, Inc.Analysis of VarianceReferred to with acronym ANOVARepresented by FCompares the influence of two or more groups of IV on the DVOne or more IVs can be tested -- must be nominal -- can be two or more categoriesDV must be continuous level data16Copyright c 2001 The McGraw-Hill Companies, Inc.ANOVA BasicsPlanned comparisons Comparisons among groups indicated in the hypothesisUnplanned comparisons, or post hoc comparisonsNot predicted by hypothesis -- conducted after test reveals a significant ANOVA17Copyright c 2001 The McGraw-Hill Companies, Inc.ANOVA BasicsBetween-groups variance – differences between groupings of IV are large enough to distinguish themselves from one anotherWithin-groups variance – variation among individuals within any category or groupingFor significant ANOVA, between-groups variance is greater than within-groups variance18Copyright c 2001 The McGraw-Hill Companies, Inc.ANOVA BasicsF is calculated to determine if differences between groups exist and if the differences are large enough to be significantly differentA measure of how well the categories of the IV explain the variance in scores of the DVThe better the categories of the IV explain variation in the DV, the larger the F19Copyright c 2001 The McGraw-Hill Companies, Inc.ANOVA Design FeaturesBetween-subjects design Each participant measured at only one level of only one conditionWithin-subject design Each participant measured more than once, usually on different conditionsAlso called repeated measures20Copyright c 2001 The McGraw-Hill Companies, Inc.One-Way ANOVATests for significant differences in DV based on categorical differences of one IVOne IV with at least two nominal categoriesOne continuous level DVSignificant F Difference between groups is larger than difference within groups21Copyright c 2001 The McGraw-Hill Companies, Inc.Two-Way ANOVADetermines relative contributions of each IV to the distribution of the DVTwo nominal IVsOne continuous level DVCan determine main effect of each IVCan determine interaction effect -- if there is a simultaneous influence of both IVs22Copyright c 2001 The McGraw-Hill Companies, Inc.Example of Two-Way ANOVAMaleFemaleOne-sided news reportMales viewing one-sided news reportFemales viewing one-sided news reportTwo-sided news reportMales viewing two-sided news reportFemales viewing two-sided news report23Copyright c 2001 The McGraw-Hill Companies, Inc.Main and Interaction EffectsMain EffectUnique contribution of each IVOne IV influences scores on the DV and this effect is not influenced by other IVInteraction EffectOne IV cannot be interpreted without acknowledging other IVIf interaction effect exists, main effects are ignored24Copyright c 2001 The McGraw-Hill Companies, Inc.Factorial ANOVAAccommodates 3 or 4 IVsStill determines main effects of each IVDetermines all possible interaction effects3 x 2 x 2 ANOVAFirst IV has 3 categoriesSecond IV has 2 categoriesThird IV has 2 categories25Copyright c 2001 The McGraw-Hill Companies, Inc.Limitations of ANOVARestricted to testing IV of nominal or categorical dataWhen 3 or more IVs used, can be difficult and confusing to interpret26Copyright c 2001 The McGraw-Hill Companies, Inc.Tests of Differences27Copyright c 2001 The McGraw-Hill Companies, Inc.