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## Chi Square

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**1. **Chi Square

**2. **Two chi square tests Goodness of fit
One variable
Determines how well the sample proportions match a pre-specified distribution
Independence
Two variables
Determines whether there is a relationship between two variables

**3. **Test for independence Each person is classified on two separate variables
Examples
(1) littering condition and (2) littering behavior
(1) gender and (2) hair color
(1) gender and (2) facial expression

**4. **Steps in hypothesis testing State the hypotheses
null
research
Select an alpha level and determine the critical value
Compute the test statistic
Make a decision

**5. **Test for independence Null hypothesis
There is no difference between population proportions
The distribution of proportions for one group/condition does not differ from the distribution of proportions of another group/condition
There is no relationship between two variables

**6. **Test for independence Null hypothesis (H0):
There is no relationship between two variables.
The distribution of proportions for one group/condition does not differ from the distribution of proportions of another group/condition.
Research hypothesis (H1):
There is a relationship between the two variables.
The distribution of proportions for one group does differ from the distribution of another group.

**7. **Example littering (Cialdini et al., 1990).

**8. **Littering study Null hypothesis
There is no relationship between the amount of existing litter and littering behavior.
The proportion of people littering will not differ across the three litter conditions.
Research hypothesis
(Nondirectional) There is a relationship between the amount of existing litter and littering behavior.
(Nondirectional) The proportion of people littering will differ across the three litter conditions.
(Directional) The proportion of people littering will increase as the amount of existing litter increases.

**9. **Test for independence Degrees of freedom (df)
df = (R 1)(C 1)
R = the number of rows
C = the number of columns

**11. **Test for independence Degrees of freedom (df)
df = (R 1)(C 1)
R = the number of rows
C = the number of columns
Rows = 2
Columns = 3
df = (2 1)(3 1) = 2

**12. **Critical values for chi square distribution