Tag: statistics

What’s the difference between fixed and random effects?

Gelman (2005, p. 21) to the rescue.

We prefer to sidestep the overloaded terms “fixed” and “random” with a cleaner distinction […]. We define effects (or coefficients) in a multilevel model as constant if they are identical for all groups in a population and varying if they are allowed to differ from group to group.

Gelman A. (2005). Analysis of variance—why it is more important than ever. Annals of Statistics, 33(1), 1–53

How to get someone’s g

“Intelligence”, “IQ”, “g” (due to Spearman), are terms that are bandied around.

The following may be helpful: the gist of how to calculate someone’s g score, which is often used as the measure of someone’s “intelligence”.

For example, that’s the “IQ”/”intelligence” referred to in the recentish BBC article on research linking childhood intelligence and adult vegetarianism (clever children grow into clever vegetarian adults).

  1. Give hundreds or thousands of people a dozen tests of ability.
  2. Zap everyone’s scores with PCA or factor analysis.
  3. g is the first component and usually explains around half the variance.  Here’s an example genre of analysis of g with other facets to psychometric intelligence.
  4. Use the component to calculate a score.  For factor analysis there are many ways to do this, e.g. Thompson’s scores, Bartlett’s weighted least-squares.  The gist is that for each person you compute a weighted sum of their scores, where the weights are a function of how loaded the particular test score was on g.
  5. To get something resembling an IQ score, scale it so it has a mean of 100 and an SD of 15.
  6. Talk about it as if it were a substantive psychological construct, rather than a statistical artefact 😉

What is this mysterious g thing?

Florence Nightingale

A bio of Florence Nightingale, statistician and nurse. Excerpt:

“Nightingale helped to promote what was then a revolutionary idea (and a religious one for her) that social phenomena could be objectively measured and subjected to mathematical analysis. Her work with medical statistics was so impressive that she was elected (in 1858) to membership in the Statistical Society of England. One of the pioneers in the graphic method of presentation of data, she invented colorful polar-area diagrams to dramatize medical data. Although other methods of persuasion had failed, her statistical approach convinced military authorities, Parliament, and Queen Victoria to carry out her proposed hospital reforms.”

[Photo of her Polar Area Diagram (“coxcomb”) from over here.]