Marketing Research

Aaker, Kumar, DayAaker, Kumar, Day

Seventh EditionSeventh Edition

Instructor’s Presentation Instructor’s Presentation SlidesSlides

Chapter Eighteen

Hypothesis Testing: Hypothesis Testing:

Means and ProportionsMeans and Proportions

Marketing Research 7th Edition Aaker, Kumar, Day©

Hypothesis Testing For Differences Between Means

Commonly used in experimental research

Statistical technique used is analysis of variance (ANOVA)

Marketing Research 7th Edition Aaker, 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 Edition Aaker, 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 ho

Marketing Research 7th Edition Aaker, 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 ho accordingly

Marketing Research 7th Edition Aaker, 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 ho 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 Edition Aaker, 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 Edition Aaker, Kumar, Day©

Analysis of Variance (ANOVA)

Response variable - dependent variable

Factors - independent variables

Treatments - different levels of factors

Marketing Research 7th Edition Aaker, 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

Ho: all treatments have same effect on mean responses

H1 : At least 2 of 1, 2 ... r are different

Marketing Research 7th Edition Aaker, 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

SSr = np (xp - x )2

P=1

Where SSr = treatment sums of squares R = number of groups

Np = sample size in group ‘p’ X = overall Mean

Marketing Research 7th Edition Aaker, 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 (MSSr)

MSSr = SSr/(r-1)

Within-treatment variance

SSu = (xip - xp)2

P i

Marketing Research 7th Edition Aaker, 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 (MSSu)

MSSu = SSu/(N-r)

Where

N = Total Sample Size

Marketing Research 7th Edition Aaker, 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 (SSt)

SSt = SSr + SSu

F-statistic

F=MSSr

MSSu

Marketing Research 7th Edition Aaker, 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 Edition Aaker, 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