Alternate Forms of the One-Way ANOVA F and Kruskal–Wallis Test Statistics

Figures & data

Fig. 1 Child blood lead levels by parent lead exposure level.

Table 1 Child blood lead levels by parent exposure level.

Exposure level	Child blood lead levels (micrograms per deciliter)	Average	Standard deviation
Low	10, 15, 16, 17, 21, 23, 27, 36	20.62500	8.12294
Medium	20, 22, 29, 31, 34, 35, 39	30.00000	6.92820
High	13, 14, 18, 23, 24, 25, 34, 35, 37, 38, 39, 41, 43, 44, 45, 48, 49, 62, 73	37.10526	15.53453

Table 2 Contributions to the F statistic by pairs of samples.

Pairs of exposure levels	$n_i{n}_j{({\overline{x}}_i-{\overline{x}}_j)}^2$	Contribution to the F statistic
Low-medium	4921.875	9.3%
Low-high	41,283.059	78.0%
Medium-high	6714.474	12.7%
Total:	52,919.408