## The Annals of Applied Statistics

- Ann. Appl. Stat.
- Volume 5, Number 3 (2011), 1726-1751.

### Are private schools better than public schools? Appraisal for Ireland by methods for observational studies

Danny Pfeffermann and Victoria Landsman

#### Abstract

In observational studies the assignment of units to treatments is not under
control. Consequently, the estimation and comparison of treatment effects based
on the empirical distribution of the responses can be biased since the units
exposed to the various treatments could differ in important unknown pretreatment
characteristics, which are related to the response. An important example studied
in this article is the question of whether private schools offer better quality
of education than public schools. In order to address this question, we use data
collected in the year 2000 by OECD for the *Programme for International
Student Assessment* (PISA). Focusing for illustration on scores in
mathematics of 15-year-old pupils in Ireland, we find that the raw average score
of pupils in private schools is higher than of pupils in public schools.
However, application of a newly proposed method for observational studies
suggests that the less able pupils tend to enroll in public schools, such that
their lower scores are not necessarily an indication of bad quality of the
public schools. Indeed, when comparing the average score in the two types of
schools after adjusting for the enrollment effects, we find quite surprisingly
that public schools perform better on average. This outcome is supported by the
methods of instrumental variables and latent variables, commonly used by
econometricians for analyzing and evaluating social programs.

#### Article information

**Source**

Ann. Appl. Stat., Volume 5, Number 3 (2011), 1726-1751.

**Dates**

First available in Project Euclid: 13 October 2011

**Permanent link to this document**

https://projecteuclid.org/euclid.aoas/1318514283

**Digital Object Identifier**

doi:10.1214/11-AOAS456

**Zentralblatt MATH identifier**

1228.62156

**Keywords**

Average treatment effect goodness of fit identifiability instrumental variables private-dependent schools propensity scores sample distribution

#### Citation

Pfeffermann, Danny; Landsman, Victoria. Are private schools better than public schools? Appraisal for Ireland by methods for observational studies. Ann. Appl. Stat. 5 (2011), no. 3, 1726--1751. doi:10.1214/11-AOAS456. https://projecteuclid.org/euclid.aoas/1318514283

#### Supplemental materials

- Supplementary material: Supplement to: “Are private schools better than
public schools? Appraisal for Ireland by methods for observational
studies”. This supplement contains a PDF which is divided into five
sections: Supplement A develops the probability weighted estimators of the
ATE. Supplement B describes the maximization of the likelihood (4.3).
Supplement C contains the proof of Lemma 1. Supplement D contains the proof
of Result 1. Supplement E describes the data file, which is provided. The
data file PISA_math2000.R contains the data.Digital Object Identifier: doi:10.1214/11-AOAS456SUPP