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DATA ANALYSIS

AND

INTERPRETATION

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SOME PROBLEMS OF UNDERSTANDING

• This slide is dedicated to those who feel any discussion of mathematics or statistics with a feeling of withdrawal.

• A few statements are given on the next two slides, acceptance of which may reduce such apprehensions so that they will not interfere with increasing one’s research ability with regard to analytical tools.

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FOLLOWING STATEMENTS ARE TRUE

• Sheer unfamiliarity with mathematical language presents a serious obstacle that disappears as one employs it.

• Mathematical expressions are simply an alternative to verbal ones. They are much more efficient in being able to say quickly in numbers and nonverbal symbols what would require many words.

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• Mathematical expressions are clear and specific. They avoid ambiguities that obscure our verbal communication.

• Numbers and formulas are abstractions and thus should offer no inherent confusions.

• If you regard quantitative analytical methods as possible keys to unlock the meaning of data and expand your interpretive powers, you will welcome their assistance and adopt a positive attitude towards them.

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NATURE AND FUNCTIONS OF STATISTICAL ANALYSIS

• STATISTICAL ANALYSIS: The refinement and manipulation of data that prepares them for the application of logical inferences.

• Statistical analytical methods may be used in valid ways or in specious ways. This depends both on the honesty of the researcher in selecting the appropriate formulas and data inputs, and on his or her understanding of the formulas and their outputs.

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NATURE AND FUNCTIONS OF STATISTICAL ANALYSIS – Contd.

• For each analytical method, there is an appropriate sequence that can be used.

• However, there are three chief phases for analysis:

–Bringing the raw data into order (arrays, tabulations, establishing categories, percentages)

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NATURE AND FUNCTIONS OF STATISTICAL ANALYSIS – Contd.

–Summarising the data: measures of central tendency and dispersion, and graphical presentation

–Applying analytical methods to manipulate the data so that their interrelationships and quantitative meaning become evident. For this purpose an appropriate analytical method is to be selected: Selection criteria

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INTERRELATIONSHIP BETWEEN ANALYSIS AND INTERPRETATION

(a) Consider the following exchange regarding survey data:

• RESEARCHER: Look at the answers to a question, “If you were buying an electric range or a gas range completely equipped with all modern features, what would it price be?” Average price given for electric range was Rs. 11,900 and for gas range was Rs. 10,250. I think, it is advantageous for the gas range.

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INTERRELATIONSHIP BETWEEN ANALYSIS AND INTERPRETATION

• MARKETING MANAGER: I wouldn’t say that at all. It seems to me what that shows is, that most women just cannot conceive of a gas range that has all the features of a modern range. So, that is a mark against gas.

• As per the researcher, the company would have gone for gas ranges. In light of the data collected, a proper analysis has been made by the researcher. However, the interpretation made was faulty because the data were not properly related to other information that the Marketing Manager had injected.

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INTERRELATIONSHIP BETWEEN ANALYSIS AND INTERPRETATION

(b) Suppose that a detergent manufacturer is trying to decide which of three advertisements would be the most effective in increasing sales of their detergent. They test the three ads by running each at different times in newspapers in six different cities. Sales are

Advertise 1 2 3

Sales of boxes 2,396 3,654 2,576

This indicates that the ad 2 is the most effective.

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INTERRELATIONSHIP BETWEEN ANALYSIS AND INTERPRETATION

• Looking to the big difference, the researcher felt that there may be another variable. Hence, following table was prepared:

Advt. A B C D E F TOTAL

1 379 400 420 380 421 396 2,396

2 401 384 1527 424 447 471 3,654

3 429 351 451 425 487 433 2,576

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INTERRELATIONSHIP BETWEEN ANALYSIS AND INTERPRETATION

• There was an unusual demand during advertisement 2 in city C, otherwise three advertisements did not differ significantly in any city.

• If the researcher had used the combined data, it would have been an improper analysis, but correct interpretation.

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INTERPRETIVE PROCESS

• Our perceptions can be distorted and limited very easily, and our thinking processes can take wrong turns too easily.

• There is no truth in the adage that “figures speak for themselves”.

• When people have the figures to interpret, they state what the figures mean, and dangerous errors are often committed.

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INTERPRETIVE PROCESS

• Firm discipline over one’s mental processes and the ability to work as dispassionately as possible are necessary.

• For this purpose, every researcher will have to follow certain maxims. They can be:

1. Produce honest and sober interpretations.

2. Keep objectives and simple principles in the forefront.

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INTERPRETIVE PROCESS

3. Beware of the limitations of small samples.

4. Give fair weight to all evidence.

5. Give due attention to infrequent significant answers.

6. Recognise averages as mere tendencies.

7. Distinguish between opinion and fact.

8. Look for causes and do not confuse them with effects.

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BRINGING THE DATA INTO ORDER

• Simplest way in which data can be brought into order is an array. This is a simple tabulation.- Minimum and maximum can be found.- Range can be found.- Quartiles can be found.- Mode can be found.

• When there are only a few observations, setting up an array may not be too tedious.

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BRINGING THE DATA INTO ORDER

• In spite of the advantages of data array, this would be inefficient with a sizable array of data such as is usually obtained in a marketing study. For such data, suitable classifications are to be established. Then, we can place individual observations in those categories. This is called a simple tabulation. It is also referred to as a ‘one-way’ or a ‘marginal’ tabulation.

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BRINGING THE DATA INTO ORDER

• Many research questions may be answered by simple tabulation of data. However, simple tabulation merely shows a distribution of one variable at a time, and may not yield the full value of data. Most data can be further organised to yield additional information. Cross-tabulation is an extension of one dimensional form in which the researcher can investigate the relationship between two or more variables by simultaneously counting the number of responses that fall in each of the classifications.

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Types of Statistical Analyses Used in Marketing Research

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Prentice HallPrentice Hall

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Types of Statistical Analyses Used in Marketing Research

• Five Types of Statistical Analysis:

1. Descriptive analysis: used to describe the data set

2. Inferential analysis: used to generate conclusions about the population’s characteristics based on the sample data

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Types of Statistical Analyses Used in Marketing Research

3. Differences analysis: used to compare

the mean of the responses of one group to that of another group

4. Associative analysis: determines the strength and direction of relationships between two or more variables

5. Predictive analysis: allows one to make forecasts for future events

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A Classification of Univariate Techniques

Independent RelatedIndependent Related

* Two- Group test* Z test * One-Way

ANOVA

* Paired t test * Chi-Square

* Mann-Whitney* Median* K-S* K-W ANOVA

* Sign* Wilcoxon* McNemar* Chi-Square

Metric Data Non-numeric Data

Univariate Techniques

One Sample Two or More Samples

One Sample Two or More Samples

* t test* Z test

* Frequency* Chi-Square* K-S* Runs* Binomial

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A Classification of Multivariate Techniques

More Than One Dependent

Variable* Multivariate

Analysis of Variance and Covariance

* Canonical Correlation

* Multiple Discriminant Analysis

* Cross- Tabulation

* Analysis of Variance and Covariance

* Multiple Regression

* Conjoint Analysis

* Factor Analysis

One Dependent Variable

Variable Interdependence

Interobject Similarity

* Cluster Analysis* Multidimensional

Scaling

Dependence Technique

Interdependence Technique

Multivariate Techniques

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WHEN TO USE A PARTICULAR STATISTIC

Copyright © 2010 Pearson Education, Inc. Copyright © 2010 Pearson Education, Inc. publishing as Prentice Hallpublishing as Prentice Hall

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Statistics Associated with Cross-Tabulation Phi Coefficient

• The phi coefficient (φ) is used as a measure of the strength of association in the special case of a table with two rows and two columns (a 2 x 2 table).

• The phi coefficient is proportional to the square root of the chi-square statistic:

• It takes the value of 0 when there is no association, which would be indicated by a chi-square value of 0 as well. When the variables are perfectly associated, phi assumes the value of 1 and all the observations fall just on the main or minor diagonal.

φ = χ2

n

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Statistics Associated with Cross-TabulationContingency Coefficient

• While the phi coefficient is specific to a 2 x 2 table, the contingency coefficient (C) can be used to assess the strength of association in a table of any size.

• The contingency coefficient varies between 0 and 1. • The maximum value of the contingency coefficient

depends on the size of the table (number of rows and number of columns). For this reason, it should be used only to compare tables of the same size.

C = χ 2

χ 2 + n

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Statistics Associated with Cross-TabulationCramer’s V

• Cramer's V is a modified version of the phi correlation coefficient, φ, and is used in tables larger than 2 x 2.

or

V = φ2

min (r-1), (c-1)

V = χ2/n

min (r-1), (c-1)