Analyzing Categorical Data

1
Chapter 3

• Analyzing Categorical Data

2
Recoding Data

• In some instances, we want to produce data in
• a different format. For example,
• We may want to create a variable so that 1
  Male, 2 Female.
• We may want to create a variable, say agegrp,
  will be 1 if age 50 inclusive and 3 otherwise.
• There are a few ways to go about this.

3
Example 1

• data example
• input g
• if g1 then genderMale
• else genderFemale
• datalines
• 1
• 2
• 2
• 1
• 1
• We created a variable so that 1Male, 2Female.

4
Example 2

• data example
• input gender age
• if gendermale and ageyoung then grp1
• else if genderfemale and ageyoung then
  grp2
• else if gendermale and ageold then
  grp3
• else genderfemale and ageold then grp4
• datalines
• male old
• male old
• female young
• female old
• male young
• 4 groups created (male and young), (female and
  young), (male and
• old), (female and old)

5
Example 3 - Inequalities

• data example
• input age
• if age
• else if age
• else agegrp3
• datalines
• 44
• 31
• 15
• 22
• 23
• Other inequalities include , , . is
  used
• for not equal.

6
Adding Labels

• Since SAS restricts variable names from being
• more than 8, we sometimes cant be as
• descriptive as wed like.
• We can make labels for the variables which will
• show up in the output for procedures.

7
Example

• data new
• input ageenter gender gpahs
• label ageenter Age Upon Entering College
• gpahs High School GPA
• datalines
• 20 male 3.4
• 19 female 2.91
• 22 male 3.8
• proc means
• var ageenter
• run

8
Proc Format

• Suppose that categorical variables have been
• coded with numbers.
• For example,
• Major 1Math,2English,3Accounting
• Gender1Male,2Female
• Hair Color1Blonde,2Brown,3Red,4Black
• We want to recode these numbers.

9

• proc format
• value majfmt 1Math 2English
  3Accounting
• value genfmt 1Male 2Female
• value hairfmt 1Blonde 2Brown
  3Red
• 4Black
• run
• data new
• input major gender hairc
• format major majfmt. gender genfmt. hairc
  hairfmt.
• datalines

10
Two Way Frequency Table

• To have SAS create a table similar to the
  following
• use proc freq

11

• data new
• input gender party count
• datalines
• male dem 20
• male rep 15
• female dem 30
• female rep 40
• proc freq
• tables gender party genderparty
• weight count
• run

12
Math 210 - Review

• Suppose we want to test at the
  0.05
• significance level. We can draw a conclusion in
• 3 possible ways
• Compare the test statistic (TS) to the critical
  value (CV)
• Compare the p-value to the level of significance.
• Obtain a 95 confidence interval for the
  population mean and check to see if 4 is in the
  interval.

13
Chi-Square Test

• Example A survey of 436 workers showed that
• 192 of them feel that it is seriously unethical
  to
• monitor employee email. When 121
• senior-level bosses were surveyed, 40 said that
• it was seriously unethical.

14
(No Transcript)
15
Total Independence

• Note that
• The response of a worker doesnt affect the
  response of any other work random sample!
• The response of a boss doesnt affect the
  response of any other boss random sample!
• Also, the response of a worker doesnt affect the
  response of any boss and vice versa.

16

• The question of interest Is the proportion of
• workers that think its seriously unethical to
• monitor employee email equal to the proportion
• of senior-level bosses that think its seriously
• unethical to monitor employee email?

17
To run the Chi-Square test

• data chisqex
• input emptype resp count
• datalines
• worker agree 192
• worker disagree 244
• boss agree 40
• boss disagree 81
• proc freq datachisqex
• weight count
• tables emptyperesp / chisq
• run

18

• SAS will provide a test statistic and p-value.
  Reject the null hypothesis if the p-value is less
  than the significance level.
• This same test was seen in Math 210 except a
  different test statistic was used. The standard
  normal distribution was used to calculate the
  p-value rather than the Chi-Square distribution.

19

• The Chi-Square test can also be used to determine
  if the row and column variables are independent.
• For example, there might be a dependence between
  hair color and eye color.
• But there wont be a dependence between hair
  color and university major.

20
McNemars Test For Paired Data

• Example Forty-five couples are asked whether
• they approve of one of their U.S. Senators.

21

• The question is this Is the proportion of wives
• that support one of their U.S. Senators equal to
• the proportion of husbands that support one of
• their U.S. Senators?
• In the Chi-Square test before, we had
• independence.

22

• The response of one husband doesnt affect any
  other husband.
• The response of one wife doesnt affect the
  response of any other wife.
• However, the response of one husband may affect
  the response of his own wife and vice versa.
  Seems reasonable that they may talk about
  politics.

23
To run McNemars test

• data mcnex
• input husbresp wiferesp count
• datalines
• yes yes 20
• yes no 5
• no yes 10
• no no 10
• proc freq datamcnex
• weight count
• tables husbrespwiferesp / agree
• run

24

• SAS will supply a test statistic and p-value.
• As with any statistical test, we reject the null
• hypothesis if the p-value is less than a
• pre-determined level of significance, say 0.01,
• 0.05,etc.

25
Odds Ratio

• Suppose that there is a p10 chance of rain
• tomorrow. Then the odds of it raining is defined
• as
• So the odds of it raining is 1 to 9 (or 19).
  The
• odds of it not raining is 9 to 1( or 91).

26

• Example Suppose that in a random sample of
• 100 men, 90 have drunk beer and in a sample
• of 100 women, 20 have drunk beer.

27

• The proportion of men that drink beer is
  90/1000.9 and the proportion of women that drink
  beer is 20/1000.2
• The odds that a man drinks beer is 0.9/0.19.
• The odds that a woman drinks beer is
  0.2/0.80.25.
• So the odds ratio is OR9/0.2536.

28

• The odds ratio can be any value between 0 and
  infinity.
• If OR drink beer.
• If OR 1, then men and women are equally likely
  to drink beer.
• If OR 1, then men are more likely than women to
  drink beer.
• Since OR36, men are much more likely than women
  to drink beer.

29

• The question of interest Who is more likely to
  drink beer?
• data oddsr
• input gender beerresp count
• datalines
• men 1-yes 90
• men 2-no 10
• women 1-yes 20
• women 2-no 80
• proc freq dataoddsr
• weight count
• tables genderbeerresp / chisq cmh
• run

30

• In the output, SAS will provide a confidence
• interval for the population odds ratio. If the
• confidence interval contains 1, then
  statistically
• speaking we can say that men and women are
• equally likely to drink beer.

31

• In the SAS code, notice that I used 1-yes/2-no
• rather than simply using yes/no.
• The reason is that I want the odds for both men
• and women to represent the odds of drinking
• beer rather than the odds of not drinking beer.
• N comes before Y alphabetically but by using
• 1-yes and 2-no, I have the correct ordering.

32

• If I was interested in obtaining an odds ratio
• with women in the numerator, Id have to use
• 1-women/2-men because M comes before W
• alphabetically.
• The results wouldnt be any less correct without
• this trick but in some instances we want results
• in a particularly meaningful order.

33
Relative Risk (RR)

• Relative Risk is a statistic commonly used in
• clinical trials to determine the risk of one
  group
• getting a certain disease, for instance, versus
• another group.

34

• Suppose that 20 of smokers develop lung
• cancer while 10 of non-smokers develop lung
• cancer. The relative risk is defined as
• which is to say that smokers are twice as likely
• to develop lung cancer than non-smokers.

35

• Example A group of 90 patients suffering from
• respiratory problems were selected for a study.
• They were randomly divided into 2 groups.
• One group received a new treatment (TRT)
• and the other group received a placebo. After
• a period of time, it was determined whether
• each patient showed improvement.

36

37

• For the TRT group, the proportion that showed
  improvement is 29/450.6444.
• For the placebo group, the proportion that showed
  improvement is 14/450.3111.
• The relative risk for improvement is
  0.6444/0.31112.0713.
• SAS will provide the RR for improvement but it
  will also provide the RR for not improving.

38

• data rr
• input group respimp count
• datalines
• 1-trt 1-yes 29
• 1-trt 2-no 16
• 2-plac 1-yes 14
• 2-plac 2-no 31
• proc freq datarr
• weight count
• tables grouprespimp / all nocol nopct
• run

39

• Again, notice the trick of using 1-trt/2-plac and
• 1-yes/2-no.