Synergetics coordinates

In probability theory and statistics, Goodman & Kruskal's lambda ($\lambda$) is a measure of proportional reduction in error in cross tabulation analysis. For any sample with a nominal independent variable and dependent variable (or ones that can be treated nominally), it indicates the extent to which the modal categories and frequencies for each value of the independent variable differ from the overall modal category and frequency, i.e. for all values of the independent variable together. $\lambda$ can be calculated with the equation

$\lambda =\frac{{\epsilon }_1-{\epsilon }_2}{{\epsilon }_1}.$

where

${\epsilon }_1$ is the overall non-modal frequency, and

${\epsilon }_2$ is the sum of the non-modal frequencies for each value of the independent variable.

Values for lambda range from zero (no association between independent and dependent variables) to one (perfect association).

Weaknesses

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Relationship Status and Blood Pressure (fictitious)

		Relationship Status		Total
		Unmarried	Married
Blood Pressure	Normal	80% (120)	51% (102)	63.4% (222)
	High	20% (30)	49% (98)	36.6% (128)
Total		42.9% (150)	57.1% (200)	100% (350)

For this sample,

$\lambda =\frac{128-(30+98)}{128}=0$

even though the data demonstrate a pronounced relationship between the independent and dependent variables.

See also

• Proportional reduction in loss

References

• Goodman, L.A., Kruskal, W.H. (1954) "Measures of association for cross classifications". Part I. Journal of the American Statistical Association, 49, 732–764. Template:Jstor
• Goodman, L.A., Kruskal, W.H. (1959) "Measures of Association for Cross Classifications. II: Further Discussion and References". Journal of the American Statistical Association, 52, 123–163. Template:Jstor
• Goodman, L.A., Kruskal, W.H. (1963) "Measures of Association for Cross Classifications III: Approximate Sampling Theory", Journal of the American Statistical Association, 58, 310–364. Template:Jstor Electronic Instrument Positions Staff (Standard ) Cameron from Clarence Creek, usually spends time with hobbies and interests which include knotting, property developers in singapore apartment For sale and boomerangs. Has enrolled in a world contiki journey. Is extremely thrilled specifically about visiting .