Section 1-1 Analyzing Categorical Data PDF

Preview

Summary

stat...

Description

1.1 Analyzing Categorical Data A. Definitions 1) Statistics: The science of collecting, describing, and interpreting data. 2) Data: Information about individuals. 3) Individuals: Includes people, animals, and objects. 4) Variables: Any characteristic of an individual. A variable can take different values for different individuals. a) Quantitative Variables: Described with a number in such a way that is makes sense to find an average. Ex. Age, height, weight, heart-rate (pulse), GPA,... (Identification numbers or zip codes are often not quantitative variables.) b) Categorical Variables: Place an individual into one of several categories. Ex. Eye color, hair color, politial affiliation, college major, job type, car make/model, composite material,...

B. Bar graphs and pie charts 1) Used with categorical variables

2) Simple example:

3) Deceptive graphs (textbook examples) a) May use varying area instead of varying heights b) Starting points on vertical axes may not be zero.

C. Two way tables and marginal distributions

1) Ex. College enrollment by major.

a) Marginal distribution row and column totals

(row totals)

b) Conditional distributions Focus on one row or one column. (i) Humanities majors: 100 Freshmen 125 Sophomores 140 Juniors 150 Seniors (ii) Seniors:

200 Sci/Eng. 200 Math/CS Segmented Bar Graphs

330 Social Sci. 150 Humanities

D. Organizing a statistical problem 1) State the problem 2) Plan the techniques which will be used 3) Do. That is, execute the plan. Draw graphs, perform calculations. 4) Conclusions. Summarize results and draw inferences

A frequent goal of statistical studies is to determine association between variables. Association: Specific values of one variable tend to occur in common with values of another variable. Examples: a) Study time and grades b) Smoking and lung cancer c) Exercise and overall health

E. Simpson's Paradox Example In 1990 78% of CEOs in 350 companies were men. In 2010 82.57% of CEOs were men. However, among two classes of companies the percentage of male CEOs dropped. Accounting

Technology...