1. Chapter 14 Basic Data Analysis

2. LEARNING OUTCOMES After studying this chapter, you should be able to
Know that analysis consists of summarizing, rearranging, ordering, or manipulating data
Create and interpret simple tabulation and cross-tabulation tables
Understand how cross-tabulations can reveal relationships
Perform basic data transformations
Define hypothesis and significance level
Discuss the steps in the hypothesis-testing procedure
Describe the factors that influence the choice of statistical methods to use for analysis

3. The Nature of Descriptive Analysis
The elementary transformation of raw data in a way that describes the basic characteristics such as central tendency, distribution, and variability.
Histogram
A graphical way of showing a frequency distribution in which the height of a bar corresponds to the observed frequency of the category.

4. EXHIBIT 14.1 Levels of Scale Measurement and Suggested Descriptive Statistics

5. Tabulation Tabulation Frequency Table
The orderly arrangement of data in a table or other summary format showing the number of responses to each response category; tallying.
Frequency Table
A table showing the different ways respondents answered a question.

6. Cross-Tabulation Cross-Tabulation Contingency Table Marginals
Addresses research questions involving relationships among multiple less-than interval variables
Results in a combined frequency table displaying one variable in rows and another variable in columns.
Contingency Table
A data matrix that displays the frequency of some combination of responses to multiple variables.
Marginals
Row and column totals in a contingency table, which are shown in its margins.

7. EXHIBIT 14.2 Cross-Tabulation Tables from a Survey on Ethics in America
From Roger Ricklefs, “Ethics in America,” The Wall Street Journal, October 31, 1983, p. 33, 42; November 1, 1983, p. 33; November 2, 1983, p. 33; and November 3, 1983, pp. 33, 37.

8. EXHIBIT 14.3 Possible Cross-Tabulations of One Question

9. Cross-Tabulation (cont’d)
Percentage Cross-Tabulations
Statistical base: the number of respondents or observations (in a row or column) used as a basis for computing percentages.
Elaboration and Refinement
Elaboration analysis: an analysis of the basic cross-tabulation for each level of a variable not previously considered, such as subgroups of the sample.
Moderator variable: a third variable that changes the nature of a relationship between the original independent and dependent variables.

10. EXHIBIT 14.4 Cross-Tabulation of Marital Status, Sex, and Responses to the Question “Do You Shop at Target?”

11. Cross-Tabulation (cont’d)
How Many Cross-Tabulations?
Every possible response becomes a possible explanatory variable.
When hypotheses involve relationships among two categorical variables, cross-tabulations are the right tool for the job.

12. Data Transformation Data Transformation (also Data Conversion)
The process of changing the data from their original form to a format suitable for performing a data analysis addressing research objectives.
Bimodal

13. Calculating Rank Order
Ranking data can be summarized by performing a data transformation.
The transformation involves multiplying the frequency by the ranking score for each choice to resulting in a new scale.

14. EXHIBIT 14.5 Executive Rankings of Potential Conference Destinations

15. EXHIBIT 14.6 Frequencies of Conference Destination Rankings

16. Tabular and Graphic Methods of Displaying Data
Tables
Are useful for presenting numerical information
Facilitate summarization and communication of data
Can include stubheads and bannerheads that allow the reader to view several cross-tabulations at once
Charts and Graphs
Translate information into visual forms so that relationships may be easily grasped
Can increase the effectiveness of a well-designed presentation
Can create strong visual impressions

17. EXHIBIT 14.7 Table of Regional Airline Usage for Vacation/Pleasure by Income and Education Class

18. EXHIBIT 14.8 A Stubhead Format Table Allowing Several Cross-Tabulations to Be Included in a Single Table
Confidence in Church/Organized Religion Question: I am going to read you a list of institutions in American society. Would you tell me how much confidence you, yourself, have in each one—a great deal, quite a lot, some, or very little? The Church or Organized Religion
*Less than 1 percent. From “Confidence in Church/Organized Religion,” The Gallup Report 238, July 1985, p. 4.

19. EXHIBIT 14.9 The Basic Forms of Graphic Presentation

20. EXHIBIT 14.10 Line Graphs Highlighting Comparisons over Time
Americans spend nine more hours at the office today than they did 27 years ago.
Reprinted from “Time Off ” American Demographics, March 2001, p. 24.

21. Computer Programs for Analysis
Statistical Packages
Spreadsheets
Excel
Statistical software:
SAS
SPSS (Statistical Package for Social Sciences)
MINITAB

22. EXHIBIT 14.11 The Basic Data Analysis Window

23. EXHIBIT 14.12 SAS Computer Output of Descriptive Statistics

24. EXHIBIT 14.13 SPSS Histogram Output

25. EXHIBIT 14.14 Examples of SPSS Output for Cross-Tabulation
From Real Stats Real Easy: SPSS for Windows. Copyright © 1992, SPSS, Inc.

26. Univariate Statistics: Stating a Hypothesis
Unproven proposition: a supposition that tentatively explains certain facts or phenomena
An assumption about nature of the world.
Null Hypothesis (Ho)
Statement about the status quo
No difference in sample and population
Alternative Hypothesis (H1)
Statement that indicates the opposite of the null hypothesis

27. The Hypothesis-Testing Procedure
Process
The specifically stated hypothesis is derived from the research objectives.
A sample is obtained and the relevant variable is measured.
The measured sample value is compared to the value either stated explicitly or implied in the hypothesis.
If the value is consistent with the hypothesis, the hypothesis is supported.
If the value is not consistent with the hypothesis, the hypothesis is not supported.

28. Significance Levels and p-Values
A critical probability associated with a statistical hypothesis test that indicates how likely an inference supporting a difference between an observed value and some statistical expectation is true.
The acceptable level of Type I error.
p-Value
Probability value, or the observed or computed significance level; p-values are compared to significance levels to test hypotheses.
Higher p-values equal more support for an hypothesis.
Critical values
The values that lie exactly on the boundary of the region of rejection.

29. EXHIBIT 14.15 A Sampling Distribution of the Mean Assuming µ = 3.0

30. An Example of Hypothesis Testing
The null hypothesis: the mean is equal to 3.0:
The alternative hypothesis: the mean does not equal to 3.0:

31. An Example of Hypothesis Testing (cont’d)

32. —
EXHIBIT A Hypothesis Test Using the Sampling Distribution of X under the Hypothesis µ = 3.0

33. The Chi-Square Test for Goodness of Fit
Chi-square (χ2) t-test
Tests for statistical significance
Is particularly appropriate for testing hypotheses about frequencies arranged in a frequency or contingency table.
Goodness-of-Fit (GOF)
A general term representing how well some computed table or matrix of values matches some population or predetermined table or matrix of the same size.

34. The Chi-Square Test for Goodness of Fit: The Process
Formulate the null hypothesis and determine the expected frequency of each answer.
Determine the appropriate significance level.
Calculate the χ2 value, using the observed frequencies from the sample and the expected frequencies.
Make the statistical decision by comparing the calculated χ2 value with the critical χ2 value.

35. Chi-Square Formula χ² = chi-square statistic
Oi = observed frequency in the ith cell
Ei = expected frequency on the ith cell
Ri = total observed frequency in the ith row
Cj = total observed frequency in the jth column
n = sample size

36. Degrees of Freedom (d.f.)
(R-1)(C-1)=(2-1)(2-1)=1
d.f.=(R-1)(C-1)

37. EXHIBIT 14.17 One-Way Frequency Table for Brand Awareness
EXHIBIT Table Calculating the Chi-Square Statistic

38. Choosing the Appropriate Statistical Technique
Choosing the correct statistical technique requires considering:
The number of variables involved
The level of scale measurement
The type of question to be answered
Choice of statistical technique influences:
The research design
The type of data collected

39. EXHIBIT 14.19 Descriptive Statistics Permissible with Different Types of Measurement
All statistics appropriate for lower-order scales (nominal is the lowest) are appropriate for higher-order scales (ratio is the highest).

40. EXHIBIT 14.20 Examples of Selecting the Appropriate Univariate Statistical Method

41. Key Terms and Concepts Descriptive analysis Histogram Tabulation
Frequency table
Cross-tabulation
Contingency table
Marginals
Statistical base
Elaboration analysis
Moderator variable
Data transformation
Hypothesis
Null hypothesis
Alternative hypothesis
Significance level
Critical values
Chi-square (χ2) test