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# And count how many times the algorithm succeeds fails meet criterion 446 Appendix A—Statistics for Swarmers

This data set has 125 observations in it. From these simple frequen-cies we can calculate what the expected count in each condition should be. For instance, the first row contains 20 + 25 = 45 observations, and the first column contains 20 + 50 = 70 observations; thus we would ex-pect to find, in the first (Low-Fail) cell,

E T i × T j 45 × 70

252

ij = N = 125 =
Fail

Succeed

Low

20 25
50 30
Fail
25.2 19.8

High

44.8 35.2

where Ti is the total number of observations for the row, Tj is the total for the column, and N is the total number of observations. Thus we expect the cell to contain 25.2 observations. The same calculations can be done for all cells, resulting in the table of expected frequencies, shown in Table A.5.

2 ∑∑ ( O ij E ij ) 2
χ = E ij
i j
2 ( 20 25 2 . ) 2 ( 25 19 8 . ) 2 ( 50 44 8 . ) 2 ( 0 35 2 . ) 2 3 81
χ =
+

19 8

+

44 8

+
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