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# Understanding and Teaching Unequal Probability of Selection

## Author

Listed:
• Humberto Barreto

(Department of Economics and Management, DePauw University)

• Manu Raghav

(Department of Economics and Management, DePauw University)

## Abstract

This paper focuses on econometrics pedagogy. It demonstrates the importance of including probability weights in regression analysis using data from surveys that do not use simple random samples (SRS). We use concrete, numerical examples and simulation to show how to effectively teach this difficult material to a student audience. We relax the assumption of simple random sampling and show how unequal probability of selection can lead to biased, inconsistent OLS slope estimates. We then explain and apply probability weighted least squares, showing how weighting the observations by the reciprocal of the probability of inclusion in the sample improves performance. The exposition is non-mathematical and relies heavily on intuitive, visual displays to make the content accessible to students. This paper will enable professors to incorporate unequal probability of selection into their courses and allow students to use best practice techniques in analyzing data from complex surveys. The primary delivery vehicle is Microsoft Excel®. Two user-defined array functions, SAMPLE and LINESTW, are included in a prepared Excel workbook. We replicate all results in Stata® and offer a file for easy analysis. Documented code in Excel and Stata allows users to see each step in the sampling and probability weighted least squares algorithms.

## Suggested Citation

• Humberto Barreto & Manu Raghav, 2011. "Understanding and Teaching Unequal Probability of Selection," Working Papers 2011-01, DePauw University, Department of Economics and Management.
• Handle: RePEc:dew:wpaper:2011-01
as

File URL: https://www.depauw.edu/learn/dew/wpaper/workingpapers/DePauw2011-01-Barreto-Raghav.pdf

## References listed on IDEAS

as
1. William J Carrington & John L Eltinge & Kristin McCue, 2000. "An Economist's Primer on Survey Samples," Working Papers 00-15, Center for Economic Studies, U.S. Census Bureau.
2. Barreto,Humberto & Howland,Frank, 2006. "Introductory Econometrics," Cambridge Books, Cambridge University Press, number 9780521843195, May.
Full references (including those not matched with items on IDEAS)

## Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
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Cited by:

1. repec:pal:easeco:v:43:y:2017:i:4:d:10.1057_eej.2015.55 is not listed on IDEAS
2. Humberto Barreto & Manu Raghav, 2013. "Understanding and Teaching Within-Cluster Correlation in Complex Surveys," Working Papers 2013-02, DePauw University, Department of Economics and Management.

### Keywords

complex survey; simulation; unequal probability; weighted regression;

### JEL classification:

• A2 - General Economics and Teaching - - Economic Education and Teaching of Economics
• A22 - General Economics and Teaching - - Economic Education and Teaching of Economics - - - Undergraduate
• A23 - General Economics and Teaching - - Economic Education and Teaching of Economics - - - Graduate
• C80 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - General
• C81 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Microeconomic Data; Data Access
• C83 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Survey Methods; Sampling Methods
• C87 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Econometric Software

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