## S. Senn: Lauding Lord (Guest Post)

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Stephen Senn
Consultant Statistician
Edinburgh, Scotland

# A Diet of Terms

A large university is interested in investigating the effects on the students of the diet provided in the university dining halls and any sex difference in these effects. Various types of data are gathered. In particular, the weight of each student at the time of his arrival in September and their weight the following June are recorded.(P304)

This is how Frederic Lord (1912-2000) introduced the paradox (1) that now bears his name. It is justly famous (or notorious). However, the addition of sex as a factor adds nothing to the essence of the paradox and (in my opinion) merely confuses the issue. Furthermore, studying the effect of diet needs some sort of control. Therefore, I shall consider the paradox in the purer form proposed by Wainer and Brown (2), which was subtly modified by Pearl and Mackenzie in The Book of Why (3) (See pp212-217). Continue reading

## S. Senn: The Many Halls Problem (Guest Post)

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Stephen Senn
Consultant Statistician
Edinburgh, Scotland

The Many Halls Problem
It’s not that paradox but another

Generalisation is passing…from the consideration of a restricted set to that of a more comprehensive set containing the restricted one…Generalization may be useful in the solution of problems. George Pólya [1] (P108)

## S. Senn: To infinity and beyond: how big are your data, really? (guest post)

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Stephen Senn
Consultant Statistician
Edinburgh

### What is this n you boast about?

Failure to understand components of variation is the source of much mischief. It can lead researchers to overlook that they can be rich in data-points but poor in information. The important thing is always to understand what varies in the data you have, and to what extent your design, and the purpose you have in mind, master it. The result of failing to understand this can be that you mistakenly calculate standard errors of your estimates that are too small because you divide the variance by an n that is too big. In fact, the problems can go further than this, since you may even pick up the wrong covariance and hence use inappropriate regression coefficients to adjust your estimates.

I shall illustrate this point using clinical trials in asthma. Continue reading

## Stephen Senn: On the level. Why block structure matters and its relevance to Lord’s paradox (Guest Post)

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Stephen Senn
Consultant Statistician
Edinburgh

Introduction

In a previous post I considered Lord’s paradox from the perspective of the ‘Rothamsted School’ and its approach to the analysis of experiments. I now illustrate this in some detail giving an example.

What I shall do

I have simulated data from an experiment in which two diets have been compared in 20 student halls of residence, each diet having been applied to 10 halls. I shall assume that the halls have been randomly allocated the diet and that in each hall 10 students have been randomly chosen to have their weights recorded at the beginning of the academic year and again at the end. Continue reading