Statistics for the Social Sciences

Areas of Expertise:Contemporary Middle East, especially Arab-Israel RelationsQuantitative Methods

• 1. How We ReasonKEY CONCEPTSPROLOGUE AND INTRODUCTIONSETTING THE STAGESCIENCETHE SCIENTIFIC METHODTESTING HYPOTHESESFROM HYPOTHESES TO THEORIESTYPES OF RELATIONSHIPSASSOCIATION AND CAUSATIONTHE UNIT OF ANALYSISCONCLUSIONEXERCISES2. Levels of Measurement and Forms of DataKEY CONCEPTSPROLOGUE AND INTRODUCTIONMEASUREMENTNOMINAL LEVEL OF MEASUREMENTORDINAL LEVEL OF MEASUREMENTLIKERT SCALESSCORES VERSUS FREQUENCIESINTERVAL AND RATIO LEVELS OF MEASUREMENTTABLES CONTAINING NOMINAL LEVEL OF MEASUREMENTCONCLUSIONEXERCISES3. Defining VariablesKEY CONCEPTSPROLOGUE AND INTRODUCTIONGATHERING THE DATAOPERATIONAL DEFINITIONSINDEX AND SCALE CONSTRUCTIONVALIDITYRELIABILITYCONCLUSIONEXERCISES4. Measuring Central TendencyKEY CONCEPTSPROLOGUE AND INTRODUCTIONCENTRAL TENDENCYTHE MEANTHE MEDIANUSING CENTRAL TENDENCYTHE MODEINTERPRETING GRAPHSCENTRAL TENDENCY AND LEVELS OF MEASUREMENTSKEWNESSOTHER GRAPHIC REPRESENTATIONSCONCLUSIONSUMMARY OF MAJOR FORMULASEXERCISES5. Measuring DispersionKEY CONCEPTSPROLOGUE AND INTRODUCTIONVISUALIZING DISPERSIONTHE RANGETHE MEAN DEVIATIONTHE VARIANCE AND STANDARD DEVIATIONTHE COMPUTATIONAL FORMULAS FOR VARIANCEVARIANCE AND STANDARD DEVIATION FOR DATA IN FREQUENCY DISTRIBUTIONSCONCLUSIONSUMMARY OF MAJOR FORMULASEXERCISES6. Constructing and Interpreting Contingency TablesKEY CONCEPTSPROLOGUE AND INTRODUCTIONCONTINGENCY TABLESREGROUPING VARIABLESGENERATING PERCENTAGESINTERPRETINGCONTROLLING FOR A THIRD VARIABLEPARTIAL TABLESCAUSAL MODELSCOMPUTER APPLICATIONSCONCLUSIONEXERCISES7. Statistical Inference and Tests of SignificanceKEY CONCEPTSPROLOGUE AND INTRODUCTIONWHAT IS STATISTICAL INFERENCE?RANDOM SAMPLESCOMPARING MEANSTHE TGEST STATISTICPROBABILITIESDECISION MAKINGDIRECTIONAL VERSUS NONDIRECTIONAL ALTERNATIVE HYPOTHESES (ONE-TAILED VERSUS TWO-TAILED TESTS)CONCLUSIONSUMMARY OF MAJOR FORMULASEXERCISES8. Probability Distributions and One-Sample z and t TestsKEY CONCEPTSPROLOGUE AND INTRODUCTIONNORMAL DISTRIBUTIONSTHE ONE-SAMPLE z TEST FOR STATISTICAL SIGNIFICANCETHE CENTRAL LIMIT THEOREMTHE NORMALITY ASSUMPTIONTHE ONE-SAMPLE t TESTDEGREES OF FREEDOMTHE t TABLEAN ALTERNATIVE t FORMULAA z TEST FOR PROPORTIONSINTERVAL ESTIMATIONCONFIDENCE INTERVALS FOR PROPORTIONSMORE ON PROBABILITYPERMUTATIONS AND COMBINATIONSCONCLUSIONSUMMARY OF MAJOR FORMULASEXERCISES9. Two-Sample t TestsKEY CONCEPTSPROLOGUE AND INTRODUCTIONINDEPENDENT SAMPLES VERSUS DEPENDENT SAMPLESTHE TWO-SAMPLE t TEST FOR INDEPENDENTLY DRAWN SAMPLESADJUSTMENTS FOR SIGMA-HAT SQUARED (^ 2)INTERPRETING A COMPUTER-GENERATED t TESTCOMPUTER APPLICATIONSTHE TWO-SAMPLE t TEST FOR DEPENDENT SAMPLESSTATISTICAL SIGNIFICANCE VERSUS RESEARCH SIGNIFICANCESTATISTICAL POWERCONCLUSIONSUMMARY OF MAJOR FORMULASEXERCISES10. One-Way Analysis of VarianceKEY CONCEPTSPROLOGUE AND INTRODUCTIONHOW ANALYSIS OF VARIANCE IS USEDANALYSIS OF VARIANCE IN EXPERIMENTAL SITUATIONSF – AN INTUITIVE APPROACHANOVA TERMINOLOGYTHE ANOVA PROCEDURECOMPARING F WITH tANALYSIS OF VARIANCE WITH EXPERIMENTAL DATAPOST HOC TESTINGCOMPUTER APPLICATIONSTWO-WAY ANALYSIS FOR VARIANCECONCLUSIONSUMMARY OF MAJOR FORMULASEXERCISES11. Measuring Association in Contingency TablesKEY CONCEPTSPROLOGUE AND INTRODUCTIONMEASURES FOR TWO-BY-TWO TABLESMEASURES FOR n-BY-nCURVILINEARITYOTHER MEASURES OF ASSOCIATIONINTERPRETING AN ASSOCIATION MATRIXCONCLUSIONSUMMARY OF MAJOR FORMULASEXERCISES12. The Chi-Square TestKEY CONCEPTSPROLOGUE AND INTRODUCTIONTHE CONTEXT FOR THE CHI-SQUARE TESTOBSERVED VERSUS EXPECTED FREQUENCIESUSING THE TABLE OF CRITICAL VALUE OF CHI-SQUARECALCULATING THE CHI-SQUARE VALUEYATES’ CORRECTIONVALIDITY OF CHI-SQUAREDIRECTIONAL ALTERNATIVE HYPOTHESESTESTING SIGNIFICANCE OF ASSOCIATION MEASURESCHI-SQUARE AND PHICOMPUTER APPLICATIONSCONCLUSIONSUMMARY OF MAJOR FORMULASEXERCISES13. Correlation and Regression AnalysisKEY CONCEPTSPROLOGUE AND INTRODUCTIONTHE SETTINGCARTESIAN COORDINATESTHE CONCEPT OF LINEARITYLINEAR EQUATIONSLINEAR REGRESSIONCOMPUTER APPLICATIONSCORRELATION MEASURES FOR ANALYSIS OF VARIANCECONCLUSIONSUMMARY OF MAJOR FORMULASEXERCISES14. Additional Aspects of Correlation and Regression AnalysisKEY CONCEPTSPROLOGUE AND INTRODUCTIONSTATISTICAL SIGNIFICANCE FOR r AND bSIGNIFICANCE OF rPARTIAL CORRELATIONS AND CAUSAL MODELSMULTIPLE CORRELATION AND THE COEFFICIENT OF MULTIPLE DETERMINATIONMULTIPLE REGRESSIONTHE STANDARDIZED PARTIAL REGRESSION SLOPEUSING A REGRESSION PRINTOUTSTEPWISE MULTIPLE REGRESSIONCOMPUTER APPLICATIONSCONCLUSIONSUMMARY OF MAJOR FORMULASEXERCISESAppendix 1: Proportions of Area Under Standard Normal CurveAppendix 2: Distribution of tAppendix 3: Critical Values of F for p = .05Appendix 4: Critical Values of Chi-SquareAppendix 5: Critical Values of the Correlation CoefficientAnswers to Selected ExercisesIndexAbout the Author