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Location, dispersion and distributional effects of various transformations on semen analysis variables

	Semen Volume	Sperm Density	Total Sperm	Motile Sperm Density	Total Motile Sperm	Normal Sperm Density	Total Normal Sperm

Optimal k	0.30	0.25	0.20	0.25	0.20	0.20	0.15
Location
Median	3.0	74.0	208	46.8	132	41.7	125
Arithmetic mean	3.2	89.7	293	58.0	188	56.1	182
Geometric mean	2.8	69.9	198	42.2	120	39.1	112
Power mean^*	2.9	74.9	216	46.3	137	42.4	122
Dispersion ${dagger}$
Empirical	0.8, 7.4	6.0, 280	13.0, 1120	3.5, 176	7.7, 699	3.4, 203	8.6, 611
Natural scale	-0.1, 6.6	-34.7, 214	-275, 861	-29.3, 145	-186, 562	7.9, 104	-17, 381
Log scale	1.1, 8.7	15.8, 309	30.4, 1291	7.4, 242	15.0, 959	6.5, 236	13.7, 917
Power scale	0.8, 7.5	13.0, 251	23.7, 996	5.9, 179	10.0, 654	5.1, 187	11.0, 711
Distribution
Skewness ${ddagger}$
Natural scale	8.69	13.51	26.43	12.79	24.21	14.97	27.16
Log scale	-5.61	-5.79	-6.09	-8.59	-7.69	-4.51	-4.93
Power scale	-0.76	-0.07	0.72	-1.09	-0.32	-0.13	-0.48
Kurtosis ${ddagger}$
Natural scale	5.96	13.01	61.90	11.07	52.23	18.18	71.67
Log scale	3.66	4.33	6.82	10.14	8.62	1.64	3.37
Power scale	-0.22	0.70	2.52	0.44	1.65	-0.45	0.79
W
Natural scale	0.926	0.866	0.739	0.867	0.754	0.829	0.713
Log scale	0.965	0.962	0.969	0.952	0.958	0.967	0.971
Power scale	0.981	0.982	0.988	0.985	0.987	0.983	0.987

^*Determined by backtransformation of mean of power scale distribution.
${dagger}$ 95% confidence limits determined from empirical or natural scale distribution or by backtransformation from log or power scales.
${ddagger}$ Expressed as standardized normal deviates.