MR2300: MARKETING RESEARCH

PAUL TILLEY

Unit 10:

Basic Data Analysis

IN THIS VIDEO:

1. Describe the various methods for summarizing data

2. Explain cross tabulations and descriptive statistics

3. Describe the procedures for testing hypotheses

4. Use hypothesis tests

DATA ANALYSIS

Using Data to Answer Research Questions

Marketing researchers edit and code data to provide input that will result in tabulated information for answering the research questions.

With this input, researchers statistically describe project results. Once the data is collected it is important to be able to manipulate it so as analyze its significance.  

In this unit we discuss key data analysis techniques including tabulations, ordering, graphing and hypothesis testing. As well you will have the opportunity to use spreadsheet software to effectively analyze and present information to decision makers.

DESCRIPTIVE ANALYSIS

The transformation of raw data into a form that will make them easy to understand and interpret; rearranging, ordering, and manipulating data to generate descriptive information

SUMMARIZING DATA

In order to present results in a easily understood, meaningful format it is important to have an understanding of the basic tools of data analysis and presentation. What follows is a summary of the basic tools.

CENTRAL TENDENCIES

There are three ways to measure the central tendency, and each has a different meaning.

mean: The mean is simply the arithmetic average. That is, the sum of all the observations divided by the number of observations. Often we will not have enough data to calculate the population mean, so we will calculate a sample mean.

median: The median is the midpoint of the distribution, or the 50th percentile. In other words, the median is the value below which half the values in the sample fall. To calculate the median value, simply arrange the data from highest to lowest number, and locate/select the middle value in the list.

mode: The mode is the measure of central tendency that merely identifies the value that occurs most often.

EXAMPLE: MEAN: 22 students are asked to report the number of children that

live in their house (including brothers and sisters temporarily away at college). The data are recorded below:

1, 3, 4, 3, 1, 2, 2, 2, 1, 2, 2, 3, 4, 5, 1, 2, 3, 2, 1, 2, 3, 6

There are 22 students in this class, and the total number of children in all of their houses is 55, so the mean of this data is 55/22 , or 2.5 children per house.

EXAMPLE: MEDIAN: 22 students are asked to report the number of children that

live in their house (including brothers and sisters temporarily away at college). The data are recorded below:

1, 3, 4, 3, 1, 2, 2, 2, 1, 2, 2, 3, 4, 5, 1, 2, 3, 2, 1, 2, 3, 6

The median is simply the middle number in an ordered set of data. To determine the Median, first sort the numbers into a list and the divide the list into two equal parts. The middle value is the Median.

11111222222

22333334456

Median is MIDDLE VALUE = 2

EXAMPLE: MODE:

22 students are asked to report the number of children that live in their house (including brothers and sisters temporarily away at college). The data are recorded below:

1, 3, 4, 3, 1, 2, 2, 2, 1, 2, 2, 3, 4, 5, 1, 2, 3, 2, 1, 2, 3, 6

The Mode is simply the most often occurring value in the set of data. Sort the data and then count the groups of numbers. The biggest group is the MODE

1

1

1

1

1

2

2

2

2

2

2

2

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3

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3

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2 is the Mode -Most Often occurring number

TABULATION

Tabulation - Orderly arrangement of data in a table or other summary format

Frequency table

Percentages

FREQUENCY TABLE & CHART

The arrangement of statistical data in a row-and-column format that exhibits the count of responses or observations for each category assigned to a variable

Data Frequency

1   1   1  51   1   2   2   2   2  82   2   2   2   3   3   3  53   3   4  24   5  16  1

Frequency87654321

# of Children per household

PERCENTAGES

Whether the data are tabulated by computer or by hand, percentages, cumulative percentages, and frequency distributions are useful.

Frequency Percentages111 5 23%112222 8 36%2222333 5 23%334 2 9%45 1 5%6 1 5%

TABULATION

Tabulation refers to the orderly arrangement of data in a table or other summary format.

Counting the number of responses to a question and putting them into a frequency distribution is a simple tabulation, or marginal tabulation, which provides the most basic form of information for the researcher.

A frequency table is the arrangement of statistical data in a row and column format that exhibits the count of responses or observations for each of the categories or codes assigned to a variable.

CROSS-TABULATION

A technique for organizing data by groups, categories, or classes, thus facilitating comparisons; a joint frequency distribution of observations on two or more sets of variables

Contingency table- The results of a cross-tabulation of two variables, such as survey questions

CROSS-TABULATION Example:

Question 1: Are you Male Female

Question 2: Do you buy Diet Coke

RESULTS 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22SummaryMale or Female M M M M M M M F F F F F F F F F F F F F F F 7 Males / 15 FemalesBuy Diet Coke Yes No No No No No No Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No No No No No 11 Yes / 11 No

Initial analysis:N=22Males = 7Females = 15 ½ of those surveyed buy Diet Coke

CROSS-TABULATION

Example: Question 1: Are you Male Female

Question 2: Do you buy Diet Coke

RESULTS 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22SummaryMale or Female M M M M M M M F F F F F F F F F F F F F F F 7 Males / 15 FemalesBuy Diet Coke Yes No No No No No No Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No No No No No 11 Yes / 11 No

Cross tabulation indicates:1 in 7 males (in our study) buy Diet Coke (only 15% of males buy Diet Coke)10 in 15 females buy Diet Coke (68% of females buy Diet Coke)CONCLUSION: Diet Coke is mostly purchased by Females

DATA TRANSFORMATION

Data conversion

Changing the original form of the data to a new format

More appropriate data analysis

New variables

COLLAPSING A FIVE-POINT SCALE

Strongly Agree 10 Agree 10 Neither Agree nor 5

Disagree Disagree 20 Strongly Disagree15

Strongly Agree/Agree 20

Neither Agree nor 5 Disagree

Disagree/Strongly Disagree 35

Data Transformation example

INDEX NUMBERS

Score or observation recalibrated to indicate how it relates to a base number

CPI - Consumer Price Index

Current item price ($) = (base year price) * (Current CPI) / (Base year CPI)

EXCEL FOR ANALYSIS Microsoft Excel is a popular spreadsheet package that allows

for entering and editing data with minimal effort. It also incorporates descriptive analysis, graphic analysis, and limited statistical analysis.

In Excel statistical calculations can be performed using the Data Analysis and Paste Function menus.

HYPOTHESIS TESTING & ERROR The process of hypothesis testing goes as follows:

1) Determine a statistical hypothesis.

2) Take an actual sample and calculate the sample mean. (The sample value should reflect the true value of the population parameter. The difference between the sample mean and the actual population mean is called the Error)

3) Determine if the deviation between the obtained value of the sample mean and its expected value would have occurred by chance alone—that is, if the statistical hypothesis is true. If the sample mean is significantly different – reject the null hypotheses

The researcher runs the risk of committing two types of errors. A Type I error, which has the probability alpha —the level of significance that we have set up—is an error caused by the rejection of the null hypothesis when it is true.

A Type II error has the probability of beta and it is an error caused by the failure to reject the null hypothesis when the alternative hypothesis is true.