ON THEORIES OF ASSOCIATION. 
By KARL PEARSON, F.R.S. and DAVID HERON, D.Sc. 
CONTENTS. 
PAGE 
1. Introductory . 159 
2. History of Subject 160 
3. On the Boas-Yulean "Theoretical Value" of the Correlation (Pearson's <p) . . 166 
4. On Association and the Boas-Yulean Coefficient 171 
5. On the Surface of Constant Association and on " Natural " Equalisation . . . 183 
6. On the Coefficient of Association and the Assumption of Discrete Variates . . . 189 
7. On the Idleness of Mr Yule's Coefficient of Association when applied to Continuous 
Variates ................ 193 
(a) The Need for either Knowledge or Hypothesis as to the Nature of the Frequency . 193 
(b) The Fallacy of Mr Yule's Principle of Selection in the case of Continuous Variates . 202 
8. On the Application of Mr Yule's Coefficients to Discrete Variates : Mendelism . . 206 
9. On the Limitation in Value of the Boas-Yulean (p ....... . 214 
10. On the Coefficient of Contingency : Pigmentation Data 216 
11. The Eye-Colour Data 237 
12. The Vaccination Data 249 
13. On the Stability of Coefficients of Association . . . . . . ... . 256 
14. General Protest against the Use of Mr Yule's Coefficient of Association . . . 283 
15. Further Criticisms of Mr Yule's Methods of Controversy ; (a) Partial Correlations . 287 
(6) Failure to distinguish between Criticism of Method and Criticism of Conclusion. 289 
(c) Fallacies involved in the use of Percentages. Coefficient of Colligation . . 291 
(d) Mr Yule's use of Pearson's "Transfer" (ab-cd)IN as a Measure of Association 294 
(e) Mr Yule's Assumption as to Absurdities wbich must arise if Normal Distribution 
be applied to the " Blind " .......... 296 
16. Summary of General Conclusions ........... 299 
Appendix I. On the Fallacy of asserting Perfect Association in the case of One Vacant 
Quadrant in a Fourfold Table . 302 
Appendix II. On the Test of Goodness of Fit of Observation to Theory in Mendelian 
Experiments 309 
Appendix III. On the Equation to the Surface of Constant Q . 314 
(1) Introductory. 
The recent paper by Mr Yule entitled " On the Methods of Measuring Associa- 
tion between Two Attributes*" calls for an early reply on two grounds, — first 
because its singularly acrimonious tone is to us wholly inexplicable, not to say 
unusual, and secondly because we believe that, if Mr Yule's views are accepted, 
irreparable damage will be done to the growth of modern statistical theory. 
* Journal of the Royal Statistical Society, Vol. lxxv, pp. 579 — 652. London, 1912. 
