Chi Square & Correlation - University of Texas at El Paso

Chi Square & Correlation

Nonparametric Test of Chi2

Used when too many assumptions are violated in T-Tests:

Sample size too small to reflect population Data are not continuous and thus not appropriate

for parametric tests based on normal distributions.

2 is another way of showing that some pattern in data is not created randomly by chance.

X2 can be one or two dimensional. X2 deals with the question of whether what

we observed is different from what is expected

Calculating X2

What would a contingency table look

like if no relationship exists between

gender and voting for Bush? (i.e.

statistical independence)

Male

Female

Voted for Bush Voted for Kerry

25

25 50

25

25 50

50

50

100

NOTE: INDEPENDENT VARIABLES ON COLUMS AND DEPENDENT ON ROWS

Calculating X2

What would a contingency table look like if a perfect relationship exists between gender and voting for Bush?

Male

Female

Voted for Bush Voted for Kerry

50

0

0

50

Calculating the expected value

^

f ij

=

( f i )( N

f j)

^

f= ij

The expected frequency of the cell in the ith row and jth column

Fi = The total in the ith row marginal Fj = The total in the jth column marginal

N = The grand total, or sample size for the entire table

Expected Voted for Bush = 50x50 / 100 = 25

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