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

        Chapter Seventeen

                          Hypothesis Testing:
                      Basic Concepts and Tests of
                             Association                 Marketing Research 10th Edition

       Hypothesis Testing: Basic Concepts
           • Assumption (hypothesis) made about a population
             parameter (not sample parameter)

           • Purpose of Hypothesis Testing
                ▫ To make a judgment about the difference between two sample
                  statistics or between sample statistic and a hypothesized
                  population parameter

           • Evidence has to be evaluated statistically before arriving
             at a conclusion regarding the hypothesis.
                ▫ Depends on whether information generated from the sample is
                  with fewer or larger observations                                     Marketing Research 10th Edition

       Hypothesis Testing
           • The null hypothesis (Ho) is tested against the
             alternative hypothesis (Ha).

           • At least the null hypothesis is stated.

           • Decide upon the criteria to be used in making
             the decision whether to “reject” or "not reject"
             the null hypothesis.                          Marketing Research 10th Edition

       Hypothesis Testing Process
                                         Problem Definition

                                Clearly state the null and alternative
                                                                            Determine the
                                  Choose the relevant test and the        degrees of freedom
                                 appropriate probability distribution
                                                                          Decide if one-or two-
    Determine the
                                                                               tailed test
  significance level                  Choose the critical value

  Compute relevant              Compare test statistic & critical value
    test statistic
                                           the test statistic
                                           fall in the critical              Do not reject null

                                             Reject null                                                  Marketing Research 10th Edition

       Basic Concepts of Hypothesis Testing
         Three Criteria Used To Decide Critical Value
          (Whether To Accept or Reject Null Hypothesis):

         • Significance Level

         • Degrees of Freedom

         • One or Two Tailed Test                   Marketing Research 10th Edition

        Significance Level
         • Indicates the percentage of sample means that is outside the cut-off limits
           (critical value)

         • The higher the significance level () used for testing a hypothesis, the higher
           the probability of rejecting a null hypothesis when it is true (Type I error)

         • Accepting a null hypothesis when it is false is called a Type II error and its
           probability is ()

         • When choosing a level of significance, there is an inherent tradeoff between
           these two types of errors

         • A good test of hypothesis should reject a null hypothesis when it is false                                               Marketing Research 10th Edition

        Relationship between Type I & Type II Errors               Marketing Research 10th Edition
        Relationship between Type I &
        Type II Errors (Contd.)           Marketing Research 10th Edition
        Relationship between Type I &
        Type II Errors (Contd.)           Marketing Research 10th Edition

        Choosing The Critical Value
       • Power of hypothesis test
            ▫ (1 - ) should be as high as possible

       • Degrees of Freedom
            ▫ The number or bits of "free" or unconstrained data used
              in calculating a sample statistic or test statistic
            ▫ A sample mean (X) has `n' degree of freedom
            ▫ A sample variance (s2) has (n-1) degrees of freedom                             Marketing Research 10th Edition
        Hypothesis Testing &
        Associated Statistical Tests          Marketing Research 10th Edition

        One or Two-tail Test
         • One-tailed Hypothesis Test
              ▫ Determines whether a particular population parameter
                is larger or smaller than some predefined value
              ▫ Uses one critical value of test statistic

         • Two-tailed Hypothesis Test
              ▫ Determines the likelihood that a population parameter
                is within certain upper and lower bounds
              ▫ May use one or two critical values                               Marketing Research 10th Edition

        Basic Concepts of Hypothesis Testing (Contd.)
         • Select the appropriate probability distribution
           based on two criteria
              ▫ Size of the sample

              ▫ Whether the population standard deviation is known or
                not                             Marketing Research 10th Edition

       Hypothesis Testing

                                                  Data Analysis Outcome

                                        Accept Null Hypothesis Reject Null Hypothesis

             Null Hypothesis is True       Correct Decision         Type I Error

             Null Hypothesis is False       Type II Error         Correct Decision                                            Marketing Research 10th Edition

        Cross-tabulation and Chi Square
         In Marketing Applications, Chi-square Statistic is
         used as:
         • Test of Independence
              ▫ Are there associations between two or more variables in a study?

         • Test of Goodness of Fit
              ▫ Is there a significant difference between an observed frequency
                distribution and a theoretical frequency distribution?

         • Statistical Independence
              ▫ Two variables are statistically independent if a knowledge of one
                would offer no information as to the identity of the other                                        Marketing Research 10th Edition

        The Concept of Statistical Independence

             If n is equal to 200 and Ei is the number of outcomes expected in cell i,                                            Marketing Research 10th Edition

        Chi-Square As a Test of Independence         Marketing Research 10th Edition
       Chi-Square As a Test of
       Independence (Contd.)

         Null Hypothesis Ho
         • Two (nominally scaled) variables are statistically

         Alternative Hypothesis Ha
         • The two variables are not independent

         Use Chi-square distribution to test.                              Marketing Research 10th Edition

        Chi-square Distribution
         • A probability distribution
         • Total area under the curve is 1.0
         • A different chi-square distribution is associated with different degrees
           of freedom
                                Cutoff points of the chi-square distribution function                                                           Marketing Research 10th Edition

        Chi-square Distribution (Contd.)
          Degrees of Freedom
          • Number of degrees of freedom, v = (r - 1) * (c - 1)
                       r = number of rows in contingency table
                       c = number of columns

          • Mean of chi-squared distribution = Degree of freedom (v)

          • Variance = 2v                                     Marketing Research 10th Edition

        Chi-square Statistic (2)
         • Measures of the difference between the actual numbers observed in cell i (Oi), and
           number expected (Ei) under assumption of statistical independence if the null
           hypothesis were true
                                                    (Oi  Ei ) 2
                                             
                                               i 1     Ei
                  With (r-1)*(c-1) degrees of freedom

                  Oi = observed number in cell i

                  Ei = number in cell i expected under independence
                  r = number of rows
                  c = number of columns

         •   Expected frequency in each cell, Ei = pc * pr * n
                      Where     pc and pr are proportions for independent variables
                                n is the total number of observations                                                         Marketing Research 10th Edition

        Chi-square Step-by-Step

                                                  Calculate row &          Calculate
             Formulate          Calculate row &
                                                      column                expected
             Hypothesis          column totals
                                                   proportions          frequencies (Ei)

           Make decision        Obtain critical     Calculate
                                                                           Calculate χ2
          regarding Null-        value from         degrees of
            hypothesis              table            freedom                                       Marketing Research 10th Edition

        Strength of Association
         • Measured by contingency coefficient

         • 0 = no association (i.e., Variables are statistically
         • Maximum value depends on the size of table
         • Compare only tables of same size                                Marketing Research 10th Edition

        Limitations of Chi-square as an
        Association Measure

        • It is basically proportional to sample size
                 Difficult to interpret in absolute sense and compare
                  cross-tabs of unequal size

        • It has no upper bound
                 Difficult to obtain a feel for its value
                 Does not indicate how two variables are related                                  Marketing Research 10th Edition

        Measures of Association for Nominal Variables

         • Measures based on Chi-Square


                           Cramer’s V                   Marketing Research 10th Edition

        Chi-square Goodness of Fit
         • Used to investigate how well the observed pattern fits the
           expected pattern
         • Researcher may determine whether population
           distribution corresponds to either a normal, Poisson or
           binomial distribution

              To determine degrees of freedom:

                  • Employ (k-1) rule
                  • Subtract an additional degree of freedom for each population
                    parameter that has to be estimated from the sample data                                            Marketing Research 10th Edition

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