CONTENTS.
9
Illustration iii.: The weather and the crops—14. Correlation
 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 ofapproximating
 to the correlation-coefficient—20-22, The correlation-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 twofold
 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 agedistributions—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 representation
 of correlation between three variables by means of
a model —16. The coefficient of n-fold correlation—17. Expression
 of regressions and correlations of lower in terms of
those of higher order—18. Limiting inequalities between
the values of correlation-coefficients necessary for consistence—19.
 Fallacies . . . 229-253

X1i
PAGE