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AFTER MIDTERM EXAM NOTES

PHI COEFFICIENT ( )φ

1. χ2 Will establish (at the .05 alpha level) whether two variables are

related. A significant Chi-Square means we reject the null hypothesis

(which assumes that the two variable are independent. We feel we have

evidence that the two variables are related.

2. φ Gives the numerical value to the relation. The value can range

from zero to one. Zero meaning no relation at all (independence) and

one indicating a perfect relation. If you know one variable’s value you,

you can perfectly predict the value of the other variable.

-perfect relation between row and column = 1

-significant χ2 relation does exist

- gives a numerical value to the solution (0 to +1)φ

Cramer’s Phi or V

Test of Proportions

Given: Total and % in cells convert to Os and use :

*Problem of small expected frequencies based on the assumption if

experiment repeated infinity times with some marginal frequencies, Os

(observed frequency) would be normally distributed around Es (expected

frequency)

-if E is too small, normality will not happen E must be greater than or

equal to 5

-when Es is less than 5, you can collapse into adjacent categories

- χ2 also assumes independent observations rows or columns totals

must be EQUAL to the number of subjects/observations

φχ

=

2

Ν

Standardized measure gives way of standardizing

relationship

N = sample size

K = # of rows or columns whichever is smaller

χ

2

2

=−

∑

( )O E

E