## Thursday, 22 July 2010

### Correlation coefficients and p-values

The original edition of The Spirit Level did not show correlation coefficients or p-values for any of the graphs, but when I wrote The Spirit Level Delusion, I included r-squared coefficients to show the strength of the associations.

Later editions of The Spirit Level include an appendix which shows Pearson Correlation Coefficients and two-sided p-values. As the Pearson coefficient shows a different figure than the r-squared, I have included the Pearson coefficients and the two-sided p-values for The Spirit Level Delusion graphs below for anybody who should want to compare them.

The first number is the correlation coefficient (the strength of the correlation). The figure in brackets is the p-value (the confidence that the correlation has not been caused by chance). Both numbers go from 0.00 to 1.00. For the first figure, the higher the number, the stronger the correlation. For the latter, lower numbers represent stronger associations. Statistical significance is usually represented by a p-value of at least 0.05, with 0.01 or less being preferred.

Life expectancy (UN 2004): -0.4515 (0.03)

Life expectancy (UN 2006): 0.16 (0.42)

Life expectancy (UN 2009): 0.22 (0.27)

Obesity: 0.01 (0.96)

Smoking: -0.31 (0.11)

Alcohol: -0.25 (0.21)

Infant mortality: 0.13 (0.51)

Trust: -0.29 (0.13)

Teen births: 0.32 (0.10)

Happiness: 0.05 (0.81)

Homicide: 0.30 (0.12)

Recycling/suicide: 0.64 (0.04)

Prison: 0.59 (<0.01)

Crime: -0.15 (0.45)

Victim of crime: -0.344 (0.21)

Recycling: -0.739 (<0.01)

Charity: 0.40 (0.25)

Foreign aid: 0.527 (0.01)

Single parents: -0.06 (0.285)

Suicide: -0.475 (0.01)

Unemployment: 0.033 (0.88)

Community life: 0.54 (0.03)

Alcohol/divorce: 0.35 (0.12)

Education: -0.154 (0.44)

Quality of life: 0.13 (0.51)

Homicide/suicide: -0.03 (0.86)

% GDP in tax/inequality: -0.65 (<0.01)

Happiness/income: 0.62 (<0.01)

Trust/income: 0.56 (<0.01)

#### 1 comment:

Ross Burkhart said...

Mr. Snowdon,

These are interesting correlations in their strength and weakness...does each correlation correspond to a page number in the hardback version of the book, and does each correlation correspond to inequality being correlated with each variable on your list?

Thanks,
Ross