## Statistical Science

- Statist. Sci.
- Volume 29, Number 2 (2014), 267-284.

### Comments on the Neyman–Fisher Controversy and Its Consequences

Arman Sabbaghi and Donald B. Rubin

#### Abstract

The Neyman–Fisher controversy considered here originated with the 1935 presentation of Jerzy Neyman’s *Statistical Problems in Agricultural Experimentation* to the Royal Statistical Society. Neyman asserted that the standard ANOVA F-test for randomized complete block designs is valid, whereas the analogous test for Latin squares is invalid in the sense of detecting differentiation among the treatments, when none existed on average, more often than desired (i.e., having a higher Type I error than advertised). However, Neyman’s expressions for the expected mean residual sum of squares, for both designs, are generally incorrect. Furthermore, Neyman’s belief that the Type I error (when testing the null hypothesis of zero average treatment effects) is higher than desired, whenever the expected mean treatment sum of squares is greater than the expected mean residual sum of squares, is generally incorrect. Simple examples show that, without further assumptions on the potential outcomes, one cannot determine the Type I error of the F-test from expected sums of squares. Ultimately, we believe that the Neyman–Fisher controversy had a deleterious impact on the development of statistics, with a major consequence being that potential outcomes were ignored in favor of linear models and classical statistical procedures that are imprecise without applied contexts.

#### Article information

**Source**

Statist. Sci., Volume 29, Number 2 (2014), 267-284.

**Dates**

First available in Project Euclid: 18 August 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.ss/1408368581

**Digital Object Identifier**

doi:10.1214/13-STS454

**Mathematical Reviews number (MathSciNet)**

MR3264542

**Zentralblatt MATH identifier**

1332.62007

**Keywords**

Analysis of variance Latin squares nonadditivity randomization tests randomized complete blocks

#### Citation

Sabbaghi, Arman; Rubin, Donald B. Comments on the Neyman–Fisher Controversy and Its Consequences. Statist. Sci. 29 (2014), no. 2, 267--284. doi:10.1214/13-STS454. https://projecteuclid.org/euclid.ss/1408368581

#### Supplemental materials

- Supplementary material: Supplementary materials for “Comments on the Neyman–Fisher Controversy and its Consequences”. The supplementary material contains our reworking of Neyman’s calculations, specifically expectations and variances of sample averages, and expectations of sums of squares for RCB and LS designs. These calculations form the basis of all results presented in this article. The supplementary material can be accessed via the following link: http://www.people.fas.harvard.edu/~sabbaghi/sabbaghi_rubin_supplement.pdf.Digital Object Identifier: doi:10.1214/13-STS454SUPP