# Measures of Variability/Central Tendency For Certain Categories

1. Mar 6, 2013

### Soaring Crane

1. The problem statement, all variables and given/known data

Suppose that I have the following groups/categories with how each is measured next to them:

Response to light – measured on a scale of 1 to 4
HDL levels – continuous value from 1 to 100
Smoker status - smoker or non-smoker

The question is as follows:

What are the highest-level measures of central tendency and variability that can be used?

2. Relevant equations

If descriptive, equations would not apply.

3. The attempt at a solution

I know that central tendency includes mean, mode, and median and variability includes variance and standard deviation, but could someone please tell me what is meant by “highest-level measures”? Do I include the descriptive term (for example, central tendency answer "mean") or an actual measurement?

Thank you.

2. Mar 7, 2013

### ajkoer

By “highest-level measures” I would assume that all the data is incorporated in the mean/variance estimate.

Solutions:

Answer 1: Use standard regression theory although the error terms (difference between fitted and observed) is not precisely normal (a mixture of dummy variables, categorical data and continuous). The Standard Error of Regression is the risk measure, the mean is given by the linear regression equation.

Answer 2: Use the error terms from answer 1 as an input to a Box-Cox Analysis of transformation. Use the proposed transformation on the y-variable to correct (or approximately adjust) for normality issues.

Answer 3: Use Least-Absolute deviations in place of a Least-Squares criteria. Apply risk measures (like average median deviation) and a median point estimate as discussed in the literature.

Last edited: Mar 7, 2013
3. Mar 8, 2013