Chapter 10 Testing for Differences

Testing for differencesChapter 10 Inferential statisticsStatistical 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 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 retainedDegrees of freedomRepresented by dfSpecifies how many values vary within a statistical testCollecting data always carries errorRules for calculating df for each statistical testFour 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 dataChi-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 must be nominal or categoricalOne dimensional chi-squareAre there significant differences in how cases are distributed across categories of one nominal variable?Significant χ2 indicates that across categories did not occur by chanceDoes not indicate where the significant variation occursOne dimensional chi-square exampleContingency analysisAlso known as two-way chi-square or two-dimensional chi-squareExamines association between two nominal variables relative to one anotherColumns represent 1st variableRows represent 2nd variableFrequency of cases that satisfy conditions of both variables inserted into each cellContingency analysis exampleLimitations 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 relationshipst-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 levelForms of t-testIndependent sample t-testCompares mean scores of IV for two different groups of peopleExample: Those with public speaking experience in one group; those without in another groupPaired comparison t-testCompares mean scores of paired or matched IV scores from same participantsExample: Those without public speaking experience are tested and tested again after trainingTypes of t-TESTTwo-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 foundDoesn’t predict which category of the IV will result in larger or smaller DVDoes predict which category of the IV will result in a larger or smaller DVLimitations of t-testLimited to differences of two groupings of one independent variable on one dependent variableCannot examine complex communication phenomenaAnalysis 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 testedmust be nominal can be two or more categoriesDV must be continuous level dataWhat kind of comparisons are you making?Planned comparisons Comparisons among groups indicated in the hypothesisUnplanned comparisons, or post hoc comparisonsNot predicted by hypothesis—conducted after test reveals a significant ANOVAAnova basicsBetween-groups variancedifferences between groupings of IV are large enough to distinguish themselves from one anotherWithin-groups variancevariation among individuals within any category or groupingFor significant ANOVAbetween-groups variance is greater than within-groups varianceCalculating fF 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 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 measuresOne-way anovaTests for significant differences in DV based on categorical differences of one IVOne IV with at least two nominal categoriesOne continuous level DVSignificant FDifference between groups is larger than difference within groupsTwo-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 IVsWhich effect is found?Main EffectInteraction EffectUnique contribution of each IVOne IV influences scores on the DV and this effect is not influenced by other IVOne IV cannot be interpreted without acknowledging other IVIf interaction effect exists, main effects are ignoredFactorial anovaMore than 2 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 categories1 DVLimitations of anovaRestricted to testing IV of nominal or categorical dataWhen 3 or more IVs used, can be difficult and confusing to interpretIdentifying the appropriate statistical test of difference