bmgt 311 chapter_12

BMGT 311: Chapter 12

Using Descriptive Analysis, Performing Population Estimates, and Testing Hypotheses

Learning Objectives

• To learn about the concept of data analysis and the functions it provides

• To appreciate the five basic types of statistical analysis used in marketing research

• To use measures of central tendency and dispersion customarily used in describing data

• To understand the concept of statistical inference

• To learn how to estimate a population mean or percentage

• To test a hypothesis about a population mean or percentage

Types of Statistical Analyses Used in Marketing Research

• Descriptive analysis

• Inferential analysis

• Differences analysis

• Associative analysis

• Predictive analysis

Descriptive Analysis

• Used by marketing researchers to describe the sample dataset in such a way as to portray the “typical” respondent and to reveal the general pattern of responses

Inference Analysis

• Used when marketing researchers use statistical procedures to generalize the results of the sample to the target population it represents

Difference Analysis

• Used to determine the degree to which real and generalizable differences exist in the population to help the manager make an enlightened decision on which advertising theme to use

Association Analysis

• Investigates if and how two variables are related

Predictive Analysis

● Statistical procedures and models to help make forecasts about future events ● Big data is making this

highly accurate ● This is the future of

marketing and research

Understanding Data via Descriptive Analysis

• Two sets of measures are used extensively to describe the information obtained in a sample.

• Measures of central tendency or measures that describe the “typical” respondent or response

• Measures of variability or measures that describe how similar (dissimilar) respondents or responses are to (from) “typical” respondents or responses

Measures of Central Tendency: Summarizing the “Typical” Respondent

• The basic data analysis goal involved in all measures of central tendency is to report a single piece of information that describes the most typical response to a question.

• Central tendency applies to any statistical measure used that somehow reflects a typical or frequent response.

Measures of Central Tendency: Summarizing the “Typical” Respondent

• Measures of central tendency:

• Mode: a descriptive analysis measure defined as that value in a string of numbers that occurs most often

• Median: expresses that value whose occurrence lies in the middle of an ordered set of values

• Mean (or average):

Measures of Variability: Visualizing the Diversity of Respondents

• All measures of variability are concerned with depicting the “typical” difference between the values in a set of values.

• There are three measures of variability:

• Frequency distribution

• Range

• Standard deviation

• A frequency distribution is a tabulation of the number of times that each different value appears in a particular set of values.

• The conversion is accomplished simply through a quick division of the frequency for each value by the total number of observations for all values, resulting in a percent, called a percentage distribution.

• Range: identifies the distance between lowest value (minimum) and the highest value (maximum) in an ordered set of values

• Standard deviation: indicates the degree of variation or diversity in the values in such a way as to be translatable into a normal or bell-shaped curve distribution

Coding Data and the Data Code Book

• Typical Question: How satisfied are you with the gas mileage in the Ford Fiesta

Highly Satisfied Satisfied Somewhat

Satisfied

Neither Satisfied or dissatisfied

Somewhat Dissatisfied Dissatisfied Not Satisfied

at all

Coding Data and the Data Code Book

• Once the items are coded - you can build a frequency distribution table

Highly Satisfied Satisfied Satisfied

at all

7 6 5 4 3 2 1

Building the Frequency Distribution

Satisfaction Rating Count

Total 10

Frequency: Number of times a number (response) is in the data set

Frequency Distribution: Summary of how many times each possible response

to a question appears in the data set

Satisfaction Rating Count Sum

7 2 14

6 2 12

5 4 20

Total 10 54

Mean 5.4

Mean: Arithmetic Average of all responses

!(7+5+6+4++6+5+7+5+4+5) = 54

!54/10 = 5.4

Satisfaction Rating Count Sum Percentage

7 2 14 20%

6 2 12 20%

5 4 20 40%

4 2 8 20%

Total 10 54

Percentage = Frequency/total count

Satisfaction Rating Count Sum Percentage Cumulative %

7 2 14 20% 20%

6 2 12 20% 40%

5 4 20 40% 80%

4 2 8 20% 100%

Total 10 54

Cumulative Percentage = Each individual percentage added to the

previous to get a total

Median: Descriptive statistic that splits the data into a hierarchal

pattern where half the data is above the median value and half is below

!Look for 50% or what includes

50% in the cumulative %

Median = 5

7 2 14 20% 20%

6 2 12 20% 40%

5 4 20 40% 80%

4 2 8 20% 100%

Total 10 54

Mode: Most Frequently occurring response to a given set of questions

7 2 14 20% 20%

6 2 12 20% 40%

5 4 20 40% 80%

4 2 8 20% 100%

Total 10 54

Mode = 5

Range: Statistic that represents the spread of the data and the distance

between the largest and smallest values of a frequency distribution

Range = 7 - 4 = 3

7 2 14 20% 20%

6 2 12 20% 40%

5 4 20 40% 80%

4 2 8 20% 100%

Total 10 54

Descriptive Analysis: Building the Distribution Table from a real life example

• Example Question from a Survey:

• Question: Overall, how satisfied are you with the Real World Experience Adjunct Professors bring to the table here at Point Park University

Satisfied

at all

7 6 5 4 3 2 1

Step 1: Collect the Raw Data

Respondent Number Satisfaction Rating

Satisfied

at all

7 6 5 4 3 2 1

Distribution Table: Fill in Data Sets

• Record the Data

• Mean =

• Mode =

• Median =

• Range =

Satisfaction Rating

Count Sum Percentage Cumulative %

7 0 0 0% 0%

6 0 0 0% 0%

5 0 0 0% 0%

4 0 0 0% 0%

3 0 0 0% 0%

2 0 0 0% 0%

1 0 0 0% 0%

Total 11 0

Mean 0.00

Class Work: Try to Develop a Distribution Table from the following Data Sets

• Question: Overall, how satisfied are you with the cafe food at Point Park University?

Respondent Number Satisfaction Rating

Satisfied

at all

7 6 5 4 3 2 1

In Class Example #2

• What is the mean?

• What is the median?

• What is the mode?

• What was the range? What does this tell you?

• Overall, what do these results tell you? What would you recommend?

Hypothesis Tests

• Tests of an hypothesized population parameter value:

• Test of an hypothesis about a percent

• Test of an hypothesis about a mean

• The crux of statistical hypothesis testing is the sampling distribution concept.

Hypothesis Tests

Hypothesis Tests: Example: Page 314 and 315

• Rex hypothesizes interns will make about $2,750 their first semester

• Sample Survey:

• n=100 (Total Students Surveyed)

• Sample Mean = $2,800

• Standard Deviation = $350

• Does his hypothesis support this?

• z = (x - u)/standard error of the mean

• z = (2,800 - 2,750)/350/Sq Root 100

• z = 50/35 = 1.43

• Is this Hypothesis Supported? Yes. Why?

bmgt 311 chapter_12

concept of data analysis

inference analysis

difference analysis

association analysis

percentage distribution

descriptive analysis

sets of measures

frequency distribution

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