CONTENTS. 
9 
Illustration iii.: The weather and the crops—14. Corre- 
lation between the movements of two variables: (a) 
Non-periodic movements: Illustration iv.: changes in 
infantile and general mortality—15-17. (b) Quasi-periodic 
movements : Illustration v.: the marriage-rate and foreign 
trade—18. Elementary methods of dealing with cases of 
non-linear regression—19. Certain rough methods ofapproxi- 
mating to the correlation-coefficient—20-22, The correla- 
tion-ratio . . : . . 191-209 
CHAPTER XI. 
MISCELLANEOUS THEOREMS INVOLVING THE USE OF 
THE CORRELATION-COEFFICIENT. 
1. Introductory—2. Standard-deviation of a sum or difference— 
3-5. Influence of errors of observation and of grouping on the 
standard-deviation—6-7. Influence of errors of observation 
on the correlation-coefficient (Spearman’s theorems) — 8. 
Mean and standard-deviation of an index-—9. Correlation 
between indices—10. Correlation-coefficient for a two x two- 
fold table—11. Correlation-coefficient for all possible pairs of 
NN values of a variable—12. Correlation due to heterogeneity 
of material —18. Reduction of correlation due to mingling 
of uncorrelated with correlated material — 14-17. The 
weighted mean—18-19. Application of weighting to the 
correction of death-rates, etc., for varying sex and age- 
distributions—20. The weighting of forms of average other 
than the arithmetic mean . . 210-228 
CHAPTER XII. 
PARTIAL CORRELATION. 
1-2. Introductory explanation—3. Direct deduction of the formule 
for two variables —4. Special notation for the general 
case : generalised regressions—5. Generalised correlations— 
6. Generalised deviations and standard - deviations — 
7-8. Theorems concerning the generalised product-sums— 
9. Direct interpretation of the generalised regressions— 
10-11. Reduction of the generalised standard-deviation— 
12. Reduction of the generalised regression—13. Reduction 
of the generalised correlation-coefficient—14. Arithmetical 
work : Example i. ; Example ii.—15. Geometrical repre- 
sentation of correlation between three variables by means of 
a model —16. The coefficient of n-fold correlation—17. Ex- 
pression of regressions and correlations of lower in terms of 
those of higher order—18. Limiting inequalities between 
the values of correlation-coefficients necessary for consist- 
ence—19. Fallacies . . . 229-253 
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