Why this is useful  Failure as a statistician/ analyst often is failure to clearly communicate  Need to communicate results to non-technical decision- makers – politicians, judges  Can provide insight into data for both internal (YOU) and external uses

Descriptive uses of categorical data  Describe sample  Check Data Quality  Answer Descriptive Questions

Please pay attention …. Categorical data can be either nominal or ordinal. It is perfectly reasonable to discuss whether ordinal data are skewed (and often, one of the most interesting findings is that it is) With categorical data, it is also useful to look at distributions

Questions related to distributions What is the distribution of students’ expectations about their own likely educational attainment? Is the distribution of students’ expectations about their own likely educational attainment skewed?

Easy creation of charts & tables with SAS Enterprise Guide  Just pointing and clicking  Also available free to university researchers and students via SAS on-demand  Characterize data tasks gives frequency distributions for all categorical variables and charts for ALL variables

Answer the questions The distribution of students’ expectations for educational attainment are shown above. The median expectation was to finish a Bachelor’s degree. Only 17.1% of students expected to complete less than a four-year degree. The distribution of educational expectations is very skewed.

Categorical data that is in order The distribution of homework hours is somewhat positively skewed Mean = 2.68 Median = 1-2 hours ( Category 3) Mode = 2

Getting the data Figure 1.1 FILE> OPEN> DATA

Tasks> describe> characterize data Figure 1.5 ALWAYS DO THIS !!

Just click through the windows and accept all of the defaults.

Some Coding ODS GRAPHICS ON ; * PROC FREQ DATA = dsname ; TABLES varname ; Will produce histograms and one-way tables * Not needed in SAS 9.3

(Sounds more impressive than it is) Bi-variate categorical data analysis

Homes without computers have fewer books

Children of mother’s with more education are less likely to fail Notice how the further down the column you go, the smaller the column percentages

Bi-variate distributions  Is there a relationship between school failure and mother’s education?  Is there a relationship between the number of books (this was a category) in the home and whether a family has a computer  Is there a relationship between mother’s education and father’s education

Answer by trend, proportion, odds  The trend of the data showed a lower likelihood of a student failing a grade the higher the educational level of the moms surveyed.  At the 0-11 yrs of education level 73% of the students never failed a grade while at 16 yrs or more it was 88% never having failed.  Students whose mothers had not finished high school were more than twice as likely to fail a grade as children of college graduate mothers

Mothers tend to be married to fathers with similar education Note that the highest row percentages tend to be in the diagonals where the parents’ education is the same

Some More Coding PROC FREQ DATA = dsname ; TABLES varname1 * varname2 / AGREE ; FOR CORRELATED DATA

Correlated Data

McNemar’s Test

Correlated Data

Cohen’s Kappa 1.0 = perfect agreement Negative Kappa is not an error, it means the two agree less than chance = Probability observed – Probability expected 1 – Probability expected

Chi-square (wrong) Notice you do NOT get identical p-value

Fisher (wrong) Notice you do NOT get identical p-value

Some More Coding PROC FREQ DATA = dsname ; TABLES varname1 * varname2 / chisq ;

Chi-square (right)

Right