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Lambda and Phi Coefficient

NOMINAL DATA: Association of a Bivariate Distribution

A. Association: Lambda

1. Symmetrical Lambda:=

fr + fc - (Fr + Fc)

2N - (Fr + Fc)

Where: N = total in sample

fr = largest number in each row

fc = largest number in each column

Fr = largest row total

Fc = largest column total

Example:

 MAJORS SOCIO-LOGY SOCIAL WORK CRIMINAL JUSTICE OTHERS MALE 1 0 15 7 23 FEMALE 14 7 7 15 43 15 7 22 22 66

Q1: What is the association between majors and sex?

A1:

2. Asymmetrical Lambda =

Where: N = total in sample

fi = largest number in a category of the independent variable

Fd = largest subtotal for a category of the dependent variable

Assumptions: The independent and dependent variables must be identified. The dependent variable is the variable being predicted.

Example: (Use the data table above.)

Q2: What is the association between majors and sex of student when trying to predict major from a knowledge of sex?

A2: Major is the dependent variable. Sex is the independent variable.

Example:

Q3: What is the association between majors and sex of student when trying to to predict sex from a knowledge of majors?

A3: Sex is the dependent variable.

Major is the independent variable.

Interpretation: Use scale below or convert to percent

Lambda symmetrical: "There is a ______ association between (variable 1) and (variable 2)" or convert to a percent and include in the statement, "There is a ____% improvement when trying to predict both variables simultaneously from the knowledge of each other".

Interpretations for

Lambda asymmetrical: "There is a_______association between (variable 1) and (variable 2)." or convert to a percent and include in the statement, "There is a ____% improvement when trying to predict (dependent variable) from the knowledge of (independent variable)."

Example:

Q1 = Small association between sex and major.

24% improvement when trying to predict both variables

simultaneously from a knowledge of each other.

Q2 = Small association between sex and major.

18% improvement when trying to predict major from a knowledge of sex.

Q3 = Moderately small association between sex and major.

35% improvement when trying to predict sex from a knowledge of major.

B. Phi coefficient (): =

Where:

 a b a+b c d c+d a+c b+d N

Assumptions:

dichotomous variables: each variable has exactly 2 categories (e.g. gender; yes, no).

discrete categories: a basic unit that cannot be subdivided (e.g. children, the number of children can only be whole numbers. There is no such thing as 1.5 children).

Example: Have you paid for or been paid for sex?

 MALE FEMALE YES 112 12 124 NO 505 822 1,327 617 834 1,451

Q: What is the association between commercialized sexual relations and gender?

A: = = .30

*These are the subtotals for rows and columns; it is not necessary to put them in any order.

Interpretation: Use scale. "There is a ______ association between (variable 1 category in upper left corner) and (variable 2 category in upper left corner)."

 a b *Remember! for the categories of cell "a" will be identical for the categories fo cell "d" and exactly opposite for the categories of cells "b" & "c". c d

For example above, +.30 is a moderately small positive relationship between being male and participating in sex for pay.

Tables may be set up in any order. Label them clearly and read the variables from the upper left hand corner.

Example: Have you paid for or been paid for sex?

 FEMALE MALE YES 12 112 124 NO 822 505 1,327 834 617 1,451

= -.30 is a moderately small negative relationship between being female and participating in sex for pay.

 MALE FEMALE NO 505 822 1,3274 YES 112 12 124 617 834 1,451

= -.30 is a moderately small negative relationship between being male and NOT participating in sex for pay.

 FEMALE MALE NO 822 505 1,327 YES 12 112 124 834 617 1,451

= +.30 is a moderately small positive relationship between being female and NOT participating in sex for pay.

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