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

Hypothesis Testing:
Basic Concepts and Tests of
Association

http://www.drvkumar.com/mr10/                 Marketing Research 10th Edition
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Hypothesis Testing: Basic Concepts
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
http://www.drvkumar.com/mr10/                                     Marketing Research 10th Edition
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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.

http://www.drvkumar.com/mr10/                          Marketing Research 10th Edition
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Hypothesis Testing Process
Problem Definition

Clearly state the null and alternative
hypotheses
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
Does
the test statistic
fall in the critical              Do not reject null
region?

Reject null
http://www.drvkumar.com/mr10/                                                  Marketing Research 10th Edition
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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

http://www.drvkumar.com/mr10/                   Marketing Research 10th Edition
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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

http://www.drvkumar.com/mr10/                                               Marketing Research 10th Edition
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Relationship between Type I & Type II Errors

http://www.drvkumar.com/mr10/               Marketing Research 10th Edition
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Relationship between Type I &
Type II Errors (Contd.)

http://www.drvkumar.com/mr10/           Marketing Research 10th Edition
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Relationship between Type I &
Type II Errors (Contd.)

http://www.drvkumar.com/mr10/           Marketing Research 10th Edition
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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

http://www.drvkumar.com/mr10/                             Marketing Research 10th Edition
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Hypothesis Testing &
Associated Statistical Tests

http://www.drvkumar.com/mr10/          Marketing Research 10th Edition
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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

http://www.drvkumar.com/mr10/                               Marketing Research 10th Edition
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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

http://www.drvkumar.com/mr10/                             Marketing Research 10th Edition
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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

http://www.drvkumar.com/mr10/                                            Marketing Research 10th Edition
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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

http://www.drvkumar.com/mr10/                                        Marketing Research 10th Edition
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The Concept of Statistical Independence

If n is equal to 200 and Ei is the number of outcomes expected in cell i,

http://www.drvkumar.com/mr10/                                            Marketing Research 10th Edition
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Chi-Square As a Test of Independence

http://www.drvkumar.com/mr10/         Marketing Research 10th Edition
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Chi-Square As a Test of
Independence (Contd.)

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

Alternative Hypothesis Ha
• The two variables are not independent

Use Chi-square distribution to test.

http://www.drvkumar.com/mr10/                              Marketing Research 10th Edition
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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

http://www.drvkumar.com/mr10/                                                           Marketing Research 10th Edition
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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

http://www.drvkumar.com/mr10/                                     Marketing Research 10th Edition
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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
n
 
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

http://www.drvkumar.com/mr10/                                                         Marketing Research 10th Edition
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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
statistic
hypothesis              table            freedom

http://www.drvkumar.com/mr10/                                       Marketing Research 10th Edition
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Strength of Association
• Measured by contingency coefficient

• 0 = no association (i.e., Variables are statistically
independent)
• Maximum value depends on the size of table
• Compare only tables of same size

http://www.drvkumar.com/mr10/                                Marketing Research 10th Edition
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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

http://www.drvkumar.com/mr10/                                  Marketing Research 10th Edition
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Measures of Association for Nominal Variables

• Measures based on Chi-Square

Phi-squared

Cramer’s V

http://www.drvkumar.com/mr10/                   Marketing Research 10th Edition
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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

http://www.drvkumar.com/mr10/                                            Marketing Research 10th Edition

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