mkt research

Essentials of Marketing Research Kumar, Aaker, Day

Essentials of Marketing Research

Kumar, Aaker, DayKumar, Aaker, Day

InstructorInstructor’’s Presentation Slidess Presentation Slides


Chapter Fourteen

Fundamentals of Data Fundamentals of Data AnalysisAnalysis


Fundamentals of Data Analysis


Data Analysis

A set of methods and techniques used to obtain information and insights from data

Helps avoid erroneous judgements and conclusions

Can constructively influence the research objectives and the research design


Preparing the Data for Analysis

Data editing

Coding

Statistically adjusting the data


Preparing the Data for Analysis (Contd.)

Data Editing

Identifies omissions, ambiguities, and errors in responses

Conducted in the field by interviewer and field supervisor and by the analyst prior to data analysis



Problems Identified With Data Editing

Interviewer Error

Omissions

Ambiguity

Inconsistencies

Lack of Cooperation

Ineligible Respondent



Coding

Coding closed-ended questions involves specifying how the responses are to be entered

Open-ended questions are difficult to code Lengthy list of possible responses is generated



Statistically Adjusting the Data + Weighting Each response is assigned a number according to a pre-

specified rule

Makes sample data more representative of target population on specific characteristics

Modifies number of cases in the sample that possess certain characteristics

Adjusts the sample so that greater importance is attached to respondents with certain characteristics



Statistically Adjusting the Data + Variable Re-specification

Existing data is modified to create new variables

Large number of variables collapsed into fewer variables

Creates variables that are consistent with study objectives

Dummy variables are used (binary, dichotomous, instrumental, quantitative variables)

Use (d-1) dummy variables to specify (d) levels of qualitative variable



Statistically Adjusting the Data + Scale Transformation

Scale values are manipulated to ensure comparability with other scales

Standardization allows the researcher to compare variables that have been measured using different types of scales

Variables are forced to have a mean of zero and a standard deviation of one

Can be done only on interval or ratio scaled data


Simple Tabulation

Consists of counting the number of cases that fall into various categories

Use of Simple Tabulation

Determine empirical distribution (frequency distribution) of the variable in question

Calculate summary statistics, particularly the mean or percentages

Aid in "data cleaning" aspects


Frequency Distribution

Reports the number of responses that each question received

Organizes data into classes or groups of values

Shows number of observations that fall into each class

Can be illustrated simply as a number or as a percentage or histogram

Response categories may be combined for many questions

Should result in categories with worthwhile number of respondents


Descriptive Statistics

Statistics normally associated with a frequency distribution to help summarize information in the frequency table

Measures of central tendency mean, median and mode

Measures of dispersion (range, standard deviation, and coefficient of variation)

Measures of shape (skewness and kurtosis)


Analysis for Various Population Subgroups

Differences between means or percentages of two subgroup responses can provide insights

Difference between means is concerned with the association between two questions

Question upon which means are based are intervally scaled


Cross Tabulations

Statistical analysis technique to study the relationships among and between variables

Sample is divided to learn how the dependent variable varies from subgroup to subgroup

Frequency distribution for each subgroup is compared to the frequency distribution for the total sample

The two variables that are analyzed must be nominally scaled


Factors Influencing the Choice of Statistical Technique

Type of Data Classification of data involves nominal, ordinal,

interval and ratio scales of measurement

Nominal scaling is restricted to the mode as the only measure of central tendency

Both median and mode can be used for ordinal scale

Non-parametric tests can only be run on ordinal data

Mean, median and mode can all be used to measure central tendency for interval and ratio scaled data


Factors Influencing the Choice of Statistical Technique (Contd.)Research Design

Dependency of observations

Number of observations per object

Number of groups being analyzed

Control exercised over variable of interest

Assumptions Underlying the Test Statistic If assumptions on which a statistical test is based are

violated, the test will provide meaningless results


Overview of Statistical Techniques

Univariate Techniques Appropriate when there is a single measurement of each of

the 'n' sample objects or there are several measurements of each of the `n' observations but each variable is analyzed in isolation

Nonmetric - measured on nominal or ordinal scale

Metric-measured on interval or ratio scale

Determine whether single or multiple samples are involved

For multiple samples, choice of statistical test depends on whether the samples are independent or dependent


Overview of Statistical Techniques (Contd.)

Multivariate Techniques

A collection of procedures for analyzing association between two or more sets of measurements that have been made on each object in one or more samples of objects

Dependence or interdependence techniques



Multivariate Techniques (Contd.)

Dependence Techniques

One or more variables can be identified as dependent variables and the remaining as independent variables

Choice of dependence technique depends on the number of dependent variables involved in analysis



Multivariate Techniques (Contd.)

Interdependence Techniques

Whole set of interdependent relationships is examined

Further classified as having focus on variable or objects



Why Use Multivariate Analysis?

To group variables or people or objects

To improve the ability to predict variables (such as usage)

To understand relationships between variables (such as advertising and sales)


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.


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.


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 ()


Hypothesis Testing

Tests in this classStatistical Test

Frequency Distributions 2

Means (one) z (if is known)

t (if is unknown)

Means (two or more) ANOVA


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?


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.


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

iin

i E

EO 2

1

2 )(


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


Example of Chi-square as a Test of Independence

Class

1 2

A 10 8

Grade B 20 16

C 45 18

D 16 6

E 9 2

This is a ‘Cell’


Chi-square As a Test of Independence - Exercise

Own Income

Expensive Low Middle High

Automobile

Yes 45 34 55

No 52 53 27

Task: Make a decision whether the two variables are independent!


Hypothesis Testing About a Single Mean

Make judgement about a single sample parameter.

Hypothesis testing depends on whether the population is known on not known

if population variance if population varianceis known is not known, or

if sample size < 60

x

Xz

)(

xs

Xt

)(


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


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.



Ho: = 1000 (hypothesized value of population)

Ha: 1000 (alternative hypothesis)

n = 12 X = 1087.1 s = 191.6 = 0.01

Rejection rule: if |tcalc| > tdf, /2 then reject Ho.



Ho: 1000 (hypothesized value of population)

Ha: > 1000 (alternative hypothesis)

n = 12 X = 1087.1 s = 191.6 = 0.05

Rejection rule: if tcalc > tdf, then reject Ho.


Confidence Intervals

Hypothesis testing and Confidence Intervals are two sides of the same coin.

interval estimate of xs

Xt

)( xtsX


Analysis of Variance (ANOVA)

Response variable - dependent variable (Y)

Factor(s) - independent variables (X)

Treatments - different levels of factors (r1, r2, r3, …)


Example (Book p.495)

Product Sales

1 2 3 4 5 Total Xp

39¢ 8 12 10 9 11 50 10

Price

Level 44 ¢ 7 10 6 8 9 40 8

49 ¢ 4 8 7 9 7 35 7

Overall sample mean: X = 8.333

Overall sample size: n = 15

No. of observations per price level: np = 5


Example (Book p.495)

Grand Mean


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


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


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



Between Treatment Variance

SSr = np (Xp - X)2 = 23.3

Within-treatment variance

SSu = (Xip - Xp)2 = 34

WhereSSr = treatment sums of squares r = number of groupsnp = sample size in group ‘p’ X = mean of group pX = overall mean Xip =sales at store i at level p

r

p=1

i=1 p=1

np r



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

Wheren = total sample size r = number of groups



Total variation (SSt): SSt = SSr + SSu = 23.3+34 = 57.3

F-statistic: F = MSSr / MSSu = 11.65/2.8 = 4.16

DF: (r-1), (n-r) = 2, 12

Critical value from table: CV(, df) = 3.89

mkt research

Technology