Chapter 11 Testing for relationships

Testing for relationshipsChapter 11Basic assumptionsData collected from sample to draw conclusion about populationData from normally distributed populationAppropriate variables are selected to be tested using theoretical modelsParticipants randomly selectedAlternative 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 retainedFour analytical stepsStatistical test determines if a relationship existsExamine results to determine if the relationship found is the one predictedIs the relationship significant?Evaluate the process and procedures of collecting datacorrelationAlso known as Pearson product-moment correlation coefficientRepresented by rCorrelation reveals one of the following:Scores on both variables increase or decreaseScores on one variable increase while scores on the other variable decreaseThere is no pattern or relationship correlationCorrelation coefficient or r reveals the degree to which two continuous level variables are relatedParticipants provide measures of two variablesIf p of the r statistic is  .05relationship is significanthypothesis or research question acceptedCorrelation cannot necessarily determine causationInterpreting the coefficientDirection of relationshipPositive– both variables increase or both variables decreaseNegative – one variable increases while the other decreasesRelationship strength.70 – strong or dependable relationshipScale of correlationDegree of shared variancer2 – represents the percentage of variance two variables have in commonKnown as coefficient of determinationFound by squaring r.2 or -.2 = .04 r2.3 or -.3 = .09 r2.4 or -.4 = .16 r2.5 or -.5 = .25 r2.6 or -.6 = .36 r2.7 or -.7 = .49 r2.8 or -.8 = .64 r2.9 or -.9 = .81 r2Correlation matrixLimits of correlationExamines relationship between only 2 variablesAny relationship is presumed to be linearLimited in the degree to which inferences can be madeCorrelation does not necessarily equal causationCausation depends on the logic of relationshipregressionPredicts some variables by knowing othersAssesses influence of several continuous level predictor, or IVs, on a single continuous criterion, or DVUsed to examine causation without experimentation“Variance accounted for” the % of variance in the criterion variable accounted for by the predictor variableLinear regressionRegression line – line drawn through the data points that best summarizes the relationship between the IV and DV The better the fit of the line, the higher RAdjusted R2– the proportion of variance explained or accounted for on the DV by the IVBeta weightsAlso known as beta coefficientsRepresented by βAllows comparison among variables of different measuring unitsRange from +1.00 to –1.00Multiple regressionTests for significant relationship between one DV and multiple IVsIndependentlyAs a groupUse beta weights to interpret the relative contribution of each IVStructural equation modelingAlso known as SEMMultiple variablesExogenous variableNot cause by another variable in the modelEndogenous variableCaused by another variable in the modelTests for a theoretical or hypothesized associationsIs the theoretical model different from associations found in the data?Identifying appropriate statistical test of relationshipCaution in using statisticsUse and interpretation of statistical tests is subjectiveMany variations of each testResearcher must interpret statistical resultAre the results worth interpreting statistically?Was appropriate statistical test selected and used?Are the results statistically significant?Are the results socially significant?