SUPPLEMENTS—GOODNESS OF FIT.
TABLE A. — Theoretical Distribution of x2, calculated from Independence-values,
in Tables with 16 Compartments, compared with the Actual Distributions
given by 100 Experimental Tables. In the first case n’ must be taken as
10, 2n the second as 8. (Ref. 77.)
4 Rows, 4 Columns, 2 Rows, 8 Columns,
Expectation. Observation. Expectation. Observation.
0-5 16°6 17 34:0 295
5-10 484 44 47-1 565
10-15 260 32 153 10
15-20 7-3 8 30 3
20- 18 : 06 1
Total 100 1
For tables with 2 rows and 2 columns 350 experimental tables of
100 observations each were available. The observed distribution of
values of x2, calculated from the independence-frequencies, is shown
in Table B, together with the theoretical distribution obtained by
differencing the table on pp. 385-386. Testing goodness of fit on
Table B as it stands, »” is 10, x* works out at 7-53, and P is 0583.
TABLE B.-—Theoretical Distribution of x2 for a Table with 2 Rows and 2
Columns, when x* is calculated from the Independence-values, compared
with the Actual Results for 350 Experimental Tables. (Ref. 77.)
Number of Tables.
Value of x%
Expected. Observed.
0 -025 13402 122
025-050 48°15 54
050-075 32°56 41
0-75-1-00 24.21 24
1 -2 56:00 62
2 = 25°91 18
3 -4 13°22 13
4 -5 7:05
5 -6 3°86
6— 501
Tot=1 34 '~)

385
i 1001 100 avy 100
Ca «499 350