1. Lecture 1. Introduction Outlines for Today 1.Types of Variables
2. Categorical Data
3. SA3202 Data Sets
4. Categorical Data Analysis
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SA3202, Lecture 1

2. a). Binary Variable: take only two possible values
Types of Variables:
a). Binary Variable: take only two possible values
e.g. Sex
e.g. Marital Status
b). Nominal Variable: take several unordered values
e.g. Nationality
e.g. Race
c). Ordinal Variable: take several ordered values
e.g. Grade
e.g. Social class
e.g. Political view
1/18/2019
SA3202, Lecture 1

3. d). Discrete Variable: take a countable number of possible values
e.g. # of students in a class
e.g. # of fishes in a pond
e). Continuous Variable: take any possible value in a interval
e.g. Height
e.g. Income
Categorical Variable: take a finite number of possible values, including types of a)-c), and possibly d). The possible values of a categorical variable is referred to as its categories or levels.
e.g. Type of blood
e.g. Grade of a class
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SA3202, Lecture 1

4. Contingency Table: A table presenting the categorical data
Categorical Data: data collected based on one or several categorical variables. Other terms: count data, frequency data,discrete data, qualitative data, cross-classified data.
Contingency Table: A table presenting the categorical data
Cells-----correspond to different combinations of the categories (levels)
Entry in a cell----- frequency of the cell
Dimension # of the categorical variables
e.g One-way Table
e.g Two-way Table
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SA3202, Lecture 1

5. SA Data Sets
1. Random Number Data The following table shows the frequency of each digit when 100 “random digits” were generated on a pocket calculator:
Digit Total
Frequency
2. Suicide Data The following table shows the classification of suicides in France by day of the week. Based on these data, Durkheim (1897) concludes that suicide diminishes at the end of the week, beginning on Friday. He also notes that the suicide rate is not lower on Sunday than on Saturday.
Day Monday Tuesday Wednesday Thursday Friday Saturday Sunday Total
# of Suicides
3. Homicide Data The following table shows the monthly distribution of homicides in the USA in 1970.
Month Jan. Feb. Mar. Apr. May Jun. Jul. Aug Sept. Oct. Nov. Dec. Total
# of Homicides
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SA3202, Lecture 1

6. 4. Political Views Data The following table shows the political views of 1397 Americans in 1975.
Response Code Frequency
Extremely Liberal
Liberal
Slightly Liberal
Moderate
Slightly Conservative
Conservative
Extremely Conservative
Total
5. Number of Boys Data The following table shows the number of boys among the first 4 children in 3343 Swedish families of size 4 or more.
Number of boys Total
Frequency
6. World Cup Data The following table shows the number of goals scored per team per game, for the 32 matches played in the 1996 Football World Cup.
Number of Goals Total
Frequency
1/18/2019
SA3202, Lecture 1

7. 7. Vitamin C Data The following table is based on 1961 French study regarding the therapeutic value of ascorbic (Vitamin C). The study was double blind, with one group of 140 skiers receiving a placebo while a second group of 139 received 1 gram of ascorbic acid per day. Of interest is the relative occurrence of colds for the two groups
Placebo Vitamin C
Cold
Not Cold
Total
8. Seal Belt Data The following table is based on the records of accidents in Florida, USA, in 1988.
Safety Equipment
Injury Seal Belt None Total
Fatal
Nonfatal
Total
9. Death Penalty Data The following table is based on a study concerning the effects of racial characteristics on whether individuals convicted of homicide receive the death penalty . It shows that the defendant’s race (white, black) and the verdict (death penalty, no death penalty) in 326 cases of homicide in Florida, USA during
Defendant’s Race
Death Penalty White Black Total
Yes No
Total
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SA3202, Lecture 1

8. 10. University Admission Data The following table shows admission results for the six largest graduate departments at the University of California at Berkeley, for the fall 1973 session.
Applicant’s Gender
Whether Admitted Male Female
Yes No
Total
11. Smoking and Lung Cancer Data The following table is based on a retrospective study of lung cancer and tobaco smoking among patients in hospitals in serveral English cities. The table compares male lung cancer patients with control patients having other diseases, according to the average number of cigarettes smoked daily over a ten-year period preceding the onsets of the disease
Daily Average # of Cigarettes Lung Cancer Patients Control Patients
None
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12. Smoking Habit Data The following table is from a study concerning smoking habits of high school students in Arizona, USA
Student Smokes Students Not Smoke
Both parents smoke
One parent smokes
Neither parent smokes
1/18/2019
SA3202, Lecture 1

9. 13. Income and Job Satisfaction Data The following table is taken from the 1984 General Social Survey of the National Data program in the US. The variables are income and job satisfaction. Income has four levels: <$6000, between $6000 and $15000, between $15000 and $25000, and over $ Job satisfaction g=has four levels: very dissatisfied (VD), little dissatisfied (LD), moderately satisfied (MS), and very satisfied (VS):
Job Satisfaction
Income VD LD MS VS
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British Social Mobility Data The following table relates father’s and son’s occupational status for a sample of 3500 British father-son pairs.
Son’s Status
Father’s Status
1/18/2019
SA3202, Lecture 1

10. 15. Danish Social Mobility Data The following table presents data on intergenerational mobility in Denmark, similar to the British Social Mobility Data:
Son’s Status
Father’s Status
The “Complete” Death Penalty Data. The following table gives the victim’s race (black, white), as well as the defendant’s race and the verdict, for the Death Penalty Data presented earlier.
Defendant’s Race Victim’s Race Death Penalty Not Death Penalty
White White
Black
Black White
Black
The “Complete” University Admission Data. The following table gives the admission decisions for each of the six largest graduate departments for the University Admission Data.
Male ( Whether Admitted) Female
Department Yes No Yes No A B C D E F
Total
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SA3202, Lecture 1

11. Method 1: Pearson’s Goodness of Fit Test The test statistic is
Categorical Data Analysis: the analysis of the categorical data, usually referred to fitting a statistical model to the data: first postulate a model for the underlying population via
formulating a statistical hypothesis, and then test whether or not the model fits the data.
This is also known as the hypothesis test of contingency table: compare the observed frequencies with their “expected frequencies” (the frequencies expected under the model) to see how close they are.
Method 1: Pearson’s Goodness of Fit Test The test statistic is
Degrees of freedom:
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SA3202, Lecture 1

12. Method 2: Wilk’s Likelihood Ratio Test The test statistic is
Degrees of freedom:
Method 1 and Method 2 are asymptotically equivalent.
1/18/2019
SA3202, Lecture 1