Marketing Research Aaker, Kumar, Day Seventh Edition Instructor’s Presentation Slides

Chapter Eighteen Hypothesis Testing: Means and Proportions

© Marketing Research 7th EditionAaker, Kumar, Day Hypothesis Testing For Differences Between Means Commonly used in experimental research Statistical technique used is analysis of variance (ANOVA)

© Marketing Research 7th EditionAaker, Kumar, Day Hypothesis Testing For Differences Between Means (Cont.) Hypothesis Testing Criteria Depends on Whether the samples are obtained from different or related populations Whether the population is known on not known If the population standard deviation is not known, whether they can be assumed to be equal or not

© Marketing Research 7th EditionAaker, Kumar, Day The Probability Values (P- value) Approach to Hypothesis Testing P-value provides researcher with alternative method of testing hypothesis without prespecifying  Largest level of significance at which we would not reject h o

© Marketing Research 7th EditionAaker, Kumar, Day The Probability Values (P-value) Approach to Hypothesis Testing (Contd.) Difference Between Using  and p-value Hypothesis testing with a prespecified  Researcher is trying to determine, "is the probability of what has been observed less than  ?" Reject or fail to reject h o accordingly

© Marketing Research 7th EditionAaker, Kumar, Day The Probability Values (P- value) Approach to Hypothesis Testing (Contd.) Using the p-Value Researcher can determine "how unlikely is the result that has been observed?" Decide whether to reject or fail to reject h o without being bound by a prespecified significance level In general, the smaller the p-value, the greater is the researcher's confidence in sample findings

© Marketing Research 7th EditionAaker, Kumar, Day The Probability Values (P-value) Approach to Hypothesis Testing (Contd.) P-value is generally sensitive to sample size A large sample should yield a low p- value P-value can report the impact of the sample size on the reliability of the results

© Marketing Research 7th EditionAaker, Kumar, Day Analysis of Variance (ANOVA) Response variable - dependent variable Factors - independent variables Treatments - different levels of factors

© Marketing Research 7th EditionAaker, Kumar, Day One - Factor Analysis of Variance Studies the effect of 'r' treatments on one response variable Determine whether or not there are any statistically significant differences between the treatment means  1,  2,...  R H o : all treatments have same effect on mean responses H 1 : At least 2 of  1,  2...  r are different

© Marketing Research 7th EditionAaker, Kumar, Day One - Factor Analysis of Variance (Contd.) To Test Hypothesis, Compute the Ratio Between the "Between Treatment" Variance and "Within Treatment" Variance Between treatment variance SS r =  n p (x p - x ) 2 P=1 Where SS r = treatment sums of squares R = number of groups N p = sample size in group ‘p’ X = overall Mean

© Marketing Research 7th EditionAaker, Kumar, Day One - Factor Analysis of Variance (Contd.) To Test Hypothesis, Compute the Ratio Between the "Between Treatment" Variance and "Within Treatment" Variance (Contd.) Between variance estimate (MSS r ) MSS r = SS r /(r-1) Within-treatment variance SS u =   (x ip - x p ) 2 P i

© Marketing Research 7th EditionAaker, Kumar, Day One - Factor Analysis of Variance (Contd.) To Test Hypothesis, Compute the Ratio Between the "Between Treatment" Variance and "Within Treatment" Variance (Contd.) Within variance estimate (MSS u ) MSS u = SS u /(N-r) Where N = Total Sample Size

© Marketing Research 7th EditionAaker, Kumar, Day One - Factor Analysis of Variance (Contd.) To Test Hypothesis, Compute the Ratio Between the "Between Treatment" Variance and "Within Treatment" Variance (Contd.) Total variation (SS t ) SS t = SS r + SS u F-statistic F=MSS r MSS u

© Marketing Research 7th EditionAaker, Kumar, Day One - Factor Analysis of Variance (Contd.) P-value Probability that the F-ratio* would be larger than the calculated F-ratio*, given the null hypothesis

© Marketing Research 7th EditionAaker, Kumar, Day Interaction Effect Impact of one treatment will not be the same for each condition of the other treatment Hypothesis of no interaction can be tested using F-ratio for interaction F-ratio = MSS interaction MSS unexplained