2 Statistical Analysis - Overview Every set of data collected needs some summary information that describes the numbers it containsCentral tendency and dispersionRelationships of the sample dataHypothesis testing
3 Measures of Central Tendency MeanThe arithmetic average of the sampleAll values of a distribution of responses are summed and divided by the number of valid responsesMedianThe middle value of a rank-ordered distributionExactly half of the responses are above and half are below the median valueModeThe most common value in the set of responses to a questionThe response most often given to a question
4 Dialog Boxes for Calculating the Mean, Median, and Mode (in ‘Frequencies’ function)
5 Measures of Dispersion RangeThe distance between the smallest and largest values in a set of responsesStandard deviationThe average distance of the distribution values from the meanVarianceThe average squared deviation about the mean of a distribution of values
8 Univariate Statistical Tests Used when the researcher wishes to test a proposition about a sample characteristic against a known or given standardAppropriate for interval or ratio dataTest: “Is a mean significantly different from some number?”Example: “Is the ‘Reasonable Prices’ average different from 4.0?”
9 Univariate Hypothesis Test Using X-16 – Reasonable Prices
10 Bivariate Statistical Tests Test hypotheses that compare the characteristics of two groups or two variablesThree types of bivariate hypothesis testsChi-squaret-testAnalysis of variance (ANOVA)
11 Cross-Tabulation (“Cross-tabs”) Used to examine relationships and report findings for two categorical (i.e. ‘nominal’) variablesPurpose is to determine:if differences exist between subgroups of the total sample on a key measurewhether there is an association between two categorical variablesA frequency distribution of responses on two or more sets of variables
13 Chi-Square AnalysisAssesses how closely the observed frequencies fit the pattern of the expected frequenciesReferred to as a “goodness-of-fit”Tests for statistical significance between the frequency distributions of two or more nominally scaled (i.e. “categorical”) variables in a cross-tabulation table to determine if there is any kind of association between the variables
14 SPSS Chi-Square Crosstab Example Do males and females recall the ads differently?
15 Comparing Means: Independent Versus Related Samples Independent samples: Two or more groups of responses that supposedly come from different populationsRelated samples: Two or more groups of responses that supposedly originated from the same populationAlso called “Matched” or “Dependent” samplesSPSS calls them “Paired” samplesPractical tip: Ask yourself, “Were the subjects re-used (“Paired”) or not re-used (“Independent”) in order to obtain the data?
16 Using the t -Test to Compare Two Means t-test: A hypothesis test that utilizes the t distributionUsed when the sample size is smaller than 30 and the standard deviation is unknownWhere,
17 Comparing two means with Paired Samples t-Test Do average scores on variables X-18 and X-20 differ from each other?
18 Do males and females differ with respect to their satisfaction? Comparing Two Means with Independent Samples t-TestDo males and females differ with respect to their satisfaction?
19 Analysis of Variance (ANOVA) ANOVA determines whether three or more means are statistically different from each otherThe dependent variable must be either interval or ratio dataThe independent variable(s) must be categorical (i.e. nominal or ordinal)“One-way ANOVA” means that there is only one independent variable“n-way ANOVA” means that there is more than one independent variable (i.e. ‘n’ IVs)
20 Analysis of Variance (ANOVA) F-test: The test used to statistically evaluate the differences between the group means in ANOVA
21 Example of One-Way ANOVA Does distance driven affect customers’ likelihood of returning?
22 Analysis of Variance (ANOVA) ANOVA does not tell us where the significant differences lie – just that a difference existsFollow-up (Post-hoc) tests: Analysis that flags the specific means that are statistically different from each otherPerformed after an ANOVA determines there is an “Omnibus” differenc between meansSome Pairwise Comparison Tests (there are others)TukeyDuncanScheffé
24 n-Way ANOVAANOVA that analyzes several independent variables at the same timeAlso called “Factorial Design”Multiple independent variables in an ANOVA can act in concert together to affect the dependent variable – this is called Interaction Effect
25 n-way ANOVA: ExampleMen and women are shown humorous and non-humorous ads and then attitudes toward the brand are measured.IVs (factors) = (1) gender (male vs. female), and (2) ad type (humorous vs. non-humorous)DV = attitude toward brandNeed 2-way ANOVA design here (also called “factorial design”) because we have two factors2 x 2 design (2 levels of gender x 2 levels of ad type)
26 n-Way ANOVA ExampleDoes distance driven and gender affect customers’ likelihood of recommending Santa Fe Grill?