# Understanding and teaching unequal probability of selection

## Author

Listed:
• Barreto Humberto

(DePauw University, 7 E. Larabee St, Harrison Hall 206, Greencastle, IN 46135, USA)

• Raghav Manu

()

## 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 do-file for easy analysis in Stata. Documented code in Excel and Stata allows users to see each step in the sampling and probability weighted least squares algorithms. All files and code are available at www.depauw.edu/learn/stata.

## Suggested Citation

• Barreto Humberto & Raghav Manu, 2013. "Understanding and teaching unequal probability of selection," Journal of Econometric Methods, De Gruyter, vol. 2(1), pages 101-112, July.
• Handle: RePEc:bpj:jecome:v:2:y:2013:i:1:p:101-112:n:6
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File URL: https://www.degruyter.com/view/j/jem.2013.2.issue-1/jem-2012-0017/jem-2012-0017.xml?format=INT

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## 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

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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.

### JEL classification:

• A22 - General Economics and Teaching - - Economic Education and Teaching of Economics - - - Undergraduate
• A23 - General Economics and Teaching - - Economic Education and Teaching of Economics - - - Graduate
• C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs
• C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

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