市場調(diào)查方式英文版第十五章

1、市場調(diào)查方式英文版第十五章LEARNING OUTCOMESUnderstand what multivariate statistical analysis involves and know the two types of multivariate analysisInterpret results from multiple regression analysis.Interpret results from multivariate analysis of variance (MANOVA)Interpret basic exploratory factor analysis res

2、ultsAfter studying this chapter, you should be able to2What Is the Appropriate Test of Difference?Test of DifferencesAn investigation of a hypothesis that two (or more) groups differ with respect to measures on a variable.Behavior, characteristics, beliefs, opinions, emotions, or attitudesBivariate

3、Tests of DifferencesInvolve only two variables: a variable that acts like a dependent variable and a variable that acts as a classification variable.Differences in mean scores between groups or in comparing how two groups scores are distributed across possible response categories.3EXHIBIT 15.1Choosi

4、ng the Right Statistic4EXHIBIT 15.1Choosing the Right Statistic (contd)5Type of MeasurementDifferences between two independent groupsDifferences among three or more independent groupsOrdinalMann-Whitney U-testWilcoxon testKruskal-Wallis testCommon Bivariate TestsNominalZ-test (two proportions)Chi-sq

5、uare testChi-square testInterval and ratioIndependent groups:t-test or Z-testOne-way ANOVA6Cross-Tabulation Tables: The 2 Test for Goodness-of-FitCross-Tabulation (Contingency) TableA joint frequency distribution of observations on two more variables.2 DistributionProvides a means for testing the st

6、atistical significance of a contingency table.Involves comparing observed frequencies (Oi) with expected frequencies (Ei) in each cell of the table.Captures the goodness- (or closeness-) of-fit of the observed distribution with the expected distribution.7Example: Papa Johns RestaurantsUnivariate Hyp

7、othesis:Papa Johns restaurants are more likely to be located in a stand-alone location or in a shopping center.Bivariate Hypothesis: Stand-alone locations are more likely to be profitable than are shopping center locations.8Chi-Square Test = chi-square statisticOi = observed frequency in the ith cel

8、lEi = expected frequency on the ith cellRi = total observed frequency in the ith rowCj = total observed frequency in the jth columnn = sample size9Degrees of Freedom (d.f.)(R-1)(C-1)=(2-1)(2-1)=1d.f.=(R-1)(C-1)10The t-Test for Comparing Two MeansIndependent Samples t-TestA test for hypotheses statin

9、g that the mean scores for some interval- or ratio-scaled variable grouped based on some less than interval classificatory variable.11The t-Test for Comparing Two Means (contd)Determining when an independent samples t-test is appropriate:Is the dependent variable interval or ratio?Can the dependent

10、variable scores be grouped based upon some categorical variable?Does the grouping result in scores drawn from independent samples?Are two groups involved in the research question?12The t-Test for Comparing Two Means (contd)Pooled Estimate of the Standard ErrorAn estimate of the standard error for a

11、t-test of independent means that assumes the variances of both groups are equal.13The t-Test for Comparing Two Means (contd)14EXHIBIT 15.2Independent Samples t-Test Results15What Is ANOVA?Analysis of Variance (ANOVA)An analysis involving the investigation of the effects of one treatment variable on

12、an interval-scaled dependent variableA hypothesis-testing technique to determine whether statistically significant differences in means occur between two or more groups.A method of comparing variances to make inferences about the means.ANOVA tests whether “grouping observations explains variance in

13、the dependent variable.16Simple Illustration of ANOVAHow much coffee respondents report drinking each day based on which shift they work (GY stands for Graveyard shift).Day 1Day 3Day 4Day 0Day 2GY 7GY 2GY 1GY 6Night 6Night 8Night 3Night 7Night 617EXHIBIT 15.3Illustration of ANOVA Logic18Partitioning

14、 Variance in ANOVATotal VariabilityGrand meanThe mean of a variable over all observations.SSTThe total observed variation across all groups and individual observationsSST = Total of (observed value-grand mean)219Partitioning Variance in ANOVABetween-groups VarianceThe sum of differences between the

15、group mean and the grand mean summed over all groups for a given set of observations.SSBSystematic variation of scores between groups due to manipulation of an experimental variable or group classifications of a measured independent variable or between-group variance.SSB = Total of ngroup(Group Mean

16、 Grand Mean)220Partitioning Variance in ANOVAWithin-group Error or VarianceThe sum of the differences between observed values and the group mean for a given set of observations; also known as total error variance.SSEVariation of scores due to random error or within-group variance due to individual d

17、ifferences from the group mean.This is the error of prediction.SSE = Total of (Observed Mean Group Mean)221The F-TestF-TestIs used to determine whether there is more variability in the scores of one sample than in the scores of another sample.Variance components are used to compute f-ratiosSSE, SSB,

18、 SST22EXHIBIT 15.4Interpreting ANOVA23Correlation Coefficient AnalysisCorrelation coefficientA statistical measure of the covariation, or association, between two at-least interval variables.CovarianceExtent to which two variables are associated systematically with each other.24Simple Correlation Co

19、efficientCorrelation coefficient (r)Ranges from +1 to -1Perfect positive linear relationship = +1Perfect negative (inverse) linear relationship = -1No correlation = 0Correlation coefficient for two variables (X,Y)25Correlation, Covariance, and CausationWhen two variables covary, they display concomi

20、tant variation.This systematic covariation does not in and of itself establish causality.Roosters crow and the rising of the sunRooster does not cause the sun to rise.26Coefficient of DeterminationCoefficient of Determination (R2)A measure obtained by squaring the correlation coefficient; the propor

21、tion of the total variance of a variable accounted for by another value of another variable.Measures that part of the total variance of Y that is accounted for by knowing the value of X.27Regression AnalysisSimple (Bivariate) Linear RegressionA measure of linear association that investigates straigh

22、t-line relationships between a continuous dependent variable and an independent variable that is usually continuous, but can be a categorical dummy variable.The Regression Equation (Y = + X )Y = the continuous dependent variableX = the independent variable = the Y intercept (regression line intercep

23、ts Y axis) = the slope of the coefficient (rise over run)28The Regression EquationParameter Estimate Choices is indicative of the strength and direction of the relationship between the independent and dependent variable. (Y intercept) is a fixed point that is considered a constant (how much Y can ex

24、ist without X)Standardized Regression Coefficient ()Estimated coefficient of the strength of relationship between the independent and dependent variables.Expressed on a standardized scale where higher absolute values indicate stronger relationships (range is from -1 to 1).29EXHIBIT 15.5The Advantage

25、 of Standardized Regression Weights30The Regression Equation (contd)Parameter Estimate Choices (contd)Raw regression estimates (b1)Raw regression weights have the advantage of retaining the scale metricwhich is also their key disadvantage.If the purpose of the regression analysis is forecasting, the

26、n raw parameter estimates must be used.This is another way of saying when the researcher is interested only in prediction.Standardized regression estimates (1)Standardized regression estimates have the advantage of a constant scale.Standardized regression estimates should be used when the researcher

27、 is testing explanatory hypotheses.31Multiple Regression AnalysisMultiple Regression AnalysisAn analysis of association in which the effects of two or more independent variables on a single, interval-scaled dependent variable are investigated simultaneously.Dummy variableThe way a dichotomous (two g

28、roup) independent variable is represented in regression analysis by assigning a 0 to one group and a 1 to the other.32Multiple Regression Analysis (contd)A Simple ExampleAssume that a toy manufacturer wishes to explain store sales (dependent variable) using a sample of stores from Canada and Europe.

29、 Several hypotheses are offered:H1:Competitors sales are related negatively to sales.H2:Sales are higher in communities with a sales office thanwhen no sales office is present.H3:Grammar school enrollment in a community is relatedpositively to sales.33Multiple Regression Analysis (contd)Statistical

30、Results of the Multiple RegressionRegression Equation:Coefficient of multiple determination (R2): 0.845F-value= 14.6; p.0534Multiple Regression Analysis (contd)Regression Coefficients in Multiple RegressionPartial correlationThe correlation between two variables after taking into account the fact th

31、at they are correlated with other variables too.R2 in Multiple RegressionThe coefficient of multiple determination in multiple regression indicates the percentage of variation in Y explained by all independent variables.35Multiple Regression Analysis (contd)Coefficients of Partial RegressionbnIndepe

32、ndent variables correlated with one anotherThe percentage of variance in the dependent variable that is explained by a single independent variable, holding other independent variables constantR2The percentage of variance in the dependent variable that is explained by the variation in the independent variables.36Multiple Regression Analysis (contd)Statistical Significance in Multiple RegressionF-testTests