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

2. Basic Concepts and Tests of Association
Chapter Seventeen
Hypothesis Testing:
Basic Concepts and Tests of Association

3. 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

4. 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.

5. Hypothesis Testing Process
Problem Definition
Clearly state the null and alternative hypotheses
Choose the relevant test and the appropriate probability distribution
Choose the critical value
Compare test statistic & critical value
Reject null
Determine the significance level
Compute relevant test statistic
Determine the degrees of freedom
Decide if one-or two-tailed test
Do not reject null
Does
the test statistic
fall in the critical
region?

6. 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

7. Significance Level Look at book page 473: explain Type I/II error
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
Look at book page 473: explain Type I/II error

8. Relationship between Type I & Type II Errors

9. Relationship between Type I & Type II Errors (Contd.)

10. Relationship between Type I & Type II Errors (Contd.)

11. 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

12. Hypothesis Testing & Associated Statistical Tests

13. 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

14. 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

15. 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

16. 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

17. The Concept of Statistical Independence
If n is equal to 200 and Ei is the number of outcomes expected in cell i,

18. Chi-Square As a Test of Independence

19. 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.

20. 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

21. 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

22. 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
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

23. Chi-square Step-by-Step
Formulate Hypothesis
Calculate row & column totals
Calculate row & column proportions
Calculate expected frequencies (Ei)
Calculate χ2 statistic
Calculate degrees of freedom
Obtain critical value from table
Make decision regarding Null-hypothesis

24. 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

25. 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

26. Measures of Association for Nominal Variables
Measures based on Chi-Square
Phi-squared
Cramer’s V

27. 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