Chi Square

1
Chi Square
Classifying yourself as studious or not.
Yes No Total 58 42 100
Are they significantly different?
Studious
Yes No Total
12 18 30
46 24 70
58 42 100
Yes No Total
Read ahead
Does reading ahead make a difference?
Independence?
2
One variable
Choice of PSYA01 Section
L01 L02 L03 L30 Total 25 40 15 36 116
Is this more than a chance difference?
O the observed frequency in a category E the
expected frequency in that category
We may expect different categories to have the
same frequency if chance alone is at work.
.55 4.17 6.79 1.69
13.17
Is this significant? Go to the table.
df k - 1
3
Two Variable
Are the two variables independent of each other?
Contingency Table
Career Choice
Nat. Sci. Soc. Sci Totals
contingency is another word for possibility
37 16 53
47 62 109
84 78 162
Male Female Totals
So this is a table of possibilities
Marginal Totals
The key is determining the expected frequencies
of the four observed frequencies (the 4 colored
cells).
4
Two Variables Expected Frequencies
Testing the null hypothesis that the variables
are independent
We know that the probability of the joint
occurrence of two independent events is the
product of their separate probabilities.
e.g., (84/162) X (53/162) .1696 or 16.96 of
the observations are expected in the upper left
hand cell. But, N (162) times 27.48 (expected
frequency)
37 16 53
47 62 109
84 78 162
Expected Frequencies
Now we can use..
27.48 25.52
56.52 52.48
5
Expected Frequencies and Alternative Calculations
R the row total C the column total
3.30 3.55 1.60 1.78
10.18
Is the probability of this Chi-Square value (or
larger) less than .05?
6
Degrees of Freedom for Two Variables
df (R-1)(C-1) R the number of rows C the
number of columns
With our example df (2-1)(2-1) 1
Go to Chi-Square Table and you find that the
critical value is 3.84. Our Chi-Squared obtained
must be larger than 3.84 for us to reject the
null hypothesis. What was the null hypothesis?
7
Phi Coefficient
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 variable are related.
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 prefect relations. If you know one
variables value you, you can perfectly predict
the value of the other variable.