1. Essentials of Marketing Research (Second Edition)
Kumar Aaker & Day
Instructor’s Presentation Slides
Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day

2. Basic Concepts and Tests of Association, Means and Proportion
Chapter Thirteen
Hypothesis Testing:
Basic Concepts and Tests of Association, Means and Proportion
Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day

3. Hypothesis Testing: Basic Concepts
Assumption (hypothesis) made about a population parameter (not sample parameter)
Purpose of Hypothesis Testing
To make a judgement about the difference between two sample statistics or the sample statistic and a hypothesized population parameter
Evidence has to be evaluated statistically before arriving at a conclusion regarding the hypothesis.
Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day

4. Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day
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.
Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day

5. The Logic of Hypothesis Testing
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
Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day

6. Clearly state the null and alternative hypotheses.
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 and critical value
Reject null
Does the test statistic fall in the critical region?
Determine the significance level
Compute relevant test statistic
Determine the degrees of freedom
Decide if one-or two-tailed test
Do not reject null
Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day

7. Basic Concepts of Hypothesis Testing (Contd.)
The Three Criteria Used Are
Significance Level
Degrees of Freedom
One or Two Tailed Test
Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day

8. Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day
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 ()
Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day

9. Significance Level (Contd.)
When choosing a level of significance, there is an inherent tradeoff between these two types of errors
Power of hypothesis test (1 - )
A good test of hypothesis ought to reject a null hypothesis when it is false
1 -  should be as high a value as possible
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10. Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day
Degree 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
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11. Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day
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
Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day

12. 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
Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day

13. Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day
Hypothesis Testing
DATA ANALYSIS
OUTCOME
In Population
Accept Null
Hypothesis
Reject Null
Null Hypothesis
True
Correct Decision
Type I Error
False
Type II Error
Correct
Decision
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14. Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day
Hypothesis Testing
Tests in this class
Statistical Test
Frequency Distributions 2
Means (one) z (if  is known)
t (if  is unknown)
Means (two) t
Means (more than two) ANOVA
Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day

15. 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
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16. Chi-Square As a Test of Independence
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
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17. Chi-square As a Test of Independence (Contd.)
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
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18. Chi-square As a Test of Independence (Contd.)
Degree 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
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19. Chi-square Statistic (2)
Measures of the difference between the actual numbers observed in cell i (Oi), and number expected (Ei) under independence if the null hypothesis were true
With (r-1)*(c-1) degrees of freedom
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 and n is the total number of observations i n E O 2 1 ) ( - S = c
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20. Chi-square Step-by-Step
1) Formulate Hypotheses
2) Calculate row and column totals
3) Calculate row and column proportions
4) Calculate expected frequencies (Ei)
5) Calculate 2 statistic
6) Calculate degrees of freedom
7) Obtain Critical Value from table
8) Make decision regarding the Null-hypothesis
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21. Example of Chi-square as a Test of Independence
Class
1 2
A 10 8
Grade B C
D 16 6
E 9 2
This is a ‘Cell’
Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day

22. Chi-square As a Test of Independence - Exercise
Own Income
Expensive Low Middle High
Automobile
Yes No
Task: Make a decision whether the two variables are independent!
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23. The chi-square distribution
df = 4
F(x2)
Critical value = 9.49
5% of area under curve
 = .05 x2
Probability distributions that are continuous, have one mode, and are skewed to the right.
Exact shape varies according to the number of degrees of freedom.
The critical value of a test statistic in a chi-square distribution is determined by specifying a significance level and the degrees of freedom.
Ex: Significance level = .05
Degrees of freedom = 4
CVx2 = 9.49
The decision rule when testing hypotheses by means of chi-square distribution is:
If x2 is <= CVx2, accept H0 Thus, for 4 df and  = .05
If x2 is > CVx2, reject H0 If If x2 is <= 9.49, accept H0
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24. Cross Tabulation Example
In a nationwide study of 1,402 adults a question was asked about institutions:
“I am going to name some institutions in this country. As far as the people running these institutions are concerned, would you say have a great deal of confidence, only some confidence, or hardly any confidence at all in them?”
One of the institutions was television.
Answers to the question about television are cross-tabulated with three levels of income below.
Annual Family Income
Amount of confidence in television
Under
$10,000
$10,000 – 20,000
Over $20,000 95 57 39
191
272
274
214
760
140
163
148
451
507
494
401
1,402
A great deal
Only some
Hardly any
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25. Calculations for income-confidence data
Cell
Observed
Expected
Contribution
(Ou – Eu)2/ Eu
Cell11 95
69.1
9.71
Cell12 57
67.3
1.58
Cell13 39
54.6
4.46
Cell21
272
274.8
.03
Cell22
274
267.8
.14
Cell23
214
217.4
.05
Cell31
140
163.1
3.27
Cell32
163
158.9
.11
Cell33
148
129.0
2.80
X2ts = 22.15
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26. Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day
 = .05
df = [(r-1) (c-1)]
n = 1402
X2cv = 9.5
X2ts = 22.15
F(x2)
X2cv = 9.5
df = 4
5% of area under curve
 = .05
22.15
Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day

27. Strength of Association
Measured by contingency coefficient
C = x o< c < 1
 x2 + n
0 - no association (i.e. Variables are statistically independent)
Maximum value depends on the size of table-compare only tables of same size
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28. Limitations 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
Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day

29. 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
Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day

30. Chi-square 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
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31. Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day
Goodness-of-Fit Test
Suppose a researcher is investigating preferences for four possible names of a new lightweight brand of sandals: Camfo, Kenilay, Nemlads, and Dics. Since the names are generated from random combinations of syllables, thre researcher expects preferences will be equally distributed across the four names (that is, each name will receive 25 percent of the available preferences). After sampling 300 people at reandom and asking them which one of the four names was most preferred, the following distribution resulted (each expected value is 300 * .25 = 75).
Possible Name
Observed Preferences
Expected Preferences
Camfo 30 75
Kenilay 80
Nemlads
120
Dics 70
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32. Goodness-of-Fit Test (cont.)
There are (d – 1) or three degrees of freedom in this instance. If  is specified as 0.01, the critical value is from Statistical Appendix Table Given this information, the hypothesis to be tested can be stated as:
H0: preferences are equal for the names
Ha: preferences are not equal for the names
And the decision rule is
If x2 is <= , accept H0.
If x2 is > , reject H0.
The test statistic is calculated as
x2 = (30-75)2 / 75 + (80-75)2 / 75 + (120-75)2 / 75 + (70-75)2 / 75 =
= 54.66
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33. Hypothesis Testing For Differences Between Means
Commonly used in experimental research
Statistical technique used is analysis Of variance (ANOVA)
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
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34. The Probability Values (P-value) Approach to Hypothesis Testing
P-value provides researcher with alternative method of testing hypothesis without pre-specifying 
Largest level of significance at which we would not reject ho
Difference Between Using  and p-value
Hypothesis testing with a pre-specified 
Researcher is trying to determine, "is the probability of what has been observed less than ?"
Reject or fail to reject ho accordingly
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35. Essentials of Marketing Research ,Second Edition Kumar , Aaker & 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 pre-specified significance level
In general, the smaller the p-value, the greater is the researcher's confidence in sample findings
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
Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day

36. Hypothesis Testing About a Single Mean - Step-by-Step
1) Formulate Hypotheses
2) Select appropriate formula
3) Select significance level
4) Calculate z or t statistic
5) Calculate degrees of freedom (for t-test)
6) Obtain critical value from table
7) Make decision regarding the Null-hypothesis
Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day

37. Hypothesis Testing About a Single Mean - Example 1
Ho:  = 5000 (hypothesized value of population)
Ha:   5000 (alternative hypothesis)
n = 100
X = 4960
 = 250
 = 0.05
Rejection rule: if |zcalc| > z/2 then reject Ho.
Population case: therefore z-test
Standard error of mean: x =  /sqrt(n) = 250/10 = 25
z= ( ) / 25 = -1.6
z/2 = 1.96
if |zcalc| > z/2 then reject Ho
since |-1.6| < do not reject Ho.
Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day

38. Hypothesis Testing About a Single Mean - Example 2
Ho:  = 1000 (hypothesized value of population)
Ha:   1000 (alternative hypothesis)
n = 12
X =
s = 191.6
 = 0.01
Rejection rule: if |tcalc| > tdf, /2 then reject Ho.
Softdrink manufacturer plans to introduce new soft drink. 12 supermarkets are selected at random and soft drink is offered in these supermarkets for limited time.Average existing softdrink sales are 1000, new softdrink sales are
Sample < 60 therefore t-test
Standard error of mean: sx = s /sqrt(n) = 191.6/sqrt(12) = 55.31
tcalc= ( ) / = 1.57
df = 12-1 = 11
t11,/2 = 3.106
if |tcalc| > t/2 then reject Ho
since |1.57| < do not reject Ho.
Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day

39. Hypothesis Testing About a Single Mean - Example 3
Ho:   1000 (hypothesized value of population)
Ha:  > 1000 (alternative hypothesis)
n = 12
X =
s = 191.6
 = 0.05
Rejection rule: if tcalc > tdf,  then reject Ho.
One sided test
Sample < 30 therefore t-test
Standard error of mean: x =  /sqrt(n) = 191.6/sqrt(12) = 55.31
tcalc= ( ) / = 1.57
df = 12-1 = 11
t11,/2 = 1.796
if tcalc > t then reject Ho
since 1.57 < do not reject Ho.
Rejection rule for opposite directionality:
if tcalc < -t then reject Ho
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40. Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day
Confidence Intervals
Hypothesis testing and Confidence Intervals are two sides of the same coin.
interval   estimate of  x s X t ) ( m - = = x ts X
Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day

41. Confidence Interval Estimation
If  = .95 then,
Problem:
n = 75  = .01
Since CI is for both sides, z-value is got for /2 = .005
Z /2 = 2.58
Test the hypothesis that the true mean weight of the Hawkeyes football team is greater than or equal to 300 pounds with  = .05 n Z X s 95 . ) ( = + - n z X u Z P s 99 . ) 46
294 54
285 ( )) 75 15 58 2
290 = + - u P 75 15 = n s
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42. Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day
H0: uW  300
H1: uW < 300
At  = 0.05, CVZ = (for a one-tailed test)
Since Zts falls in the critical region
We ______________________ the null hypothesis
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43. Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day
Test the hypothesis that the true mean weight of the Hawkeyes football team is equal to 286 pounds with  = 0.01
H0: uW = 286
uW  286
AT  = .01
CVZ = 2.58
Since Zts < CvZ we __________________ the null hypothesis
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44. Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day
H0: PA = PB
HA: PA not equal to PB
Chain N
Proportion of Stores Open for 24 hours A 40
-45 B 75
-40
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45. Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day
And
df = n1+n2-2
(n1-1) + (n2-1)
= .05
df = 113
= weighted average of sample proportions
Computation of tts would proceed as follows:
Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day

46. Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day42 .
115 30 18 75 40 ) (. 45 ˆ = + p
Since
then
and
-1.96
+1.96
.025
.025 - +
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47. Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day
Descriptive Statistics for two samples of students, liberal arts majors (n = 317) and engineering majors (n = 592) include
The smaller the mean, the more students agree with the statement. The formula for a t-test of mean differences for independent samples is
With being the standard error of the mean difference
Where
Is a weighted average of sample standard deviations. In this situation the hypothesis:
Liberal arts majors
Engineering majors X
2.59
2.29 S
1.00
1.10
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48. Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day
Pooled Std. dev
= 1.07
Tts= / .07 = .30 / .07 = 4.29
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49. Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day
Statistical techniques
Analysis of Variance (ANOVA)
Correlation Analysis
Regression Analysis
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50. Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day
Analysis of Variance
ANOVA mainly used for analysis of
experimental data
Ratio of “between-treatment” variance
and “within- treatment” variance
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51. Analysis of Variance (ANOVA)
Response variable - dependent variable (Y)
Factor(s) - independent variables (X)
Treatments - different levels of factors (r1, r2, r3, …)
Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day

52. 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
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53. Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day
Example (Book p.495)
Product Sales
Total Xp
39 ¢
Price
Level 44 ¢
49 ¢ ]
Overall sample mean: X = 8.333
Overall sample size: n = 15
No. of observations per price level: np = 5
Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day

54. Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day
Example (Book p.495)
Essentials of Marketing Research ,Second Edition Kumar , Aaker & Day

55. One - Factor ANOVA - Intuitively
If: Between Treatment Variance
Within Treatment Variance
 is large then there are differences between treatments
 is small then there are no differences between treatments
To Test Hypothesis, Compute the Ratio Between the "Between Treatment" Variance and "Within Treatment" Variance
 =
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56. One - Factor ANOVA Table
Source of Variation Degrees of Mean Sum F-ratio
Variation (SS) Freedom of Squares
Between SSr r-1 MSSr =SSr/r-1 MSSr
(price levels) MSSu
Within SSu n-r MSSu=SSu/n-r
(price levels)
Total SSt n-1
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57. One - Factor Analysis of Variance
Between Treatment Variance
SSr =  np (Xp - X)2 = 23.3
Within-treatment variance
SSu =   (Xip - Xp)2 = 34
Where
SSr = treatment sums of squares r = number of groups
np = sample size in group ‘p’ Xp = mean of group p
X = overall mean Xip =sales at store i at level p r
np r
i=1 p=1
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58. One - Factor Analysis of Variance
Between variance estimate (MSSr)
MSSr = SSr/(r-1) = 23.3/2 = 11.65
Within variance estimate (MSSu)
MSSu = SSu/(n-r) = 34/12 = 2.8
Where
n = total sample size r = number of groups
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59. One - Factor Analysis of Variance
Total variation (SSt): SSt = SSr + SSu = = 57.3
F-statistic: F = MSSr / MSSu = /2.8 = 4.16
DF: (r-1), (n-r) = 2, 12
Critical value from table: CV(, df) = 3.89
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