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## Chi Square

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**1. **Chi Square

**2. **Chi square test A chi square test is an inferential statistic
Analyzes proportions/frequency data
Uses proportions/distributions from a sample to test hypotheses about proportions/ distributions in the population
Two tests
Chi square test for goodness of fit
Chi square test for independence

**3. **Example littering (Cialdini et al., 1990). Research question:
Does the amount of existing litter influence littering behavior?
IV:
Amount of existing litter
Levels (conditions):
0 or 1 piece
2 or 4 pieces
8 or 16 pieces
DV:
Littering behavior (littered or didnt litter)
What scale/level of measurement is this?

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

**5. **Descriptive statistics Descriptive statistics for nominal data
Mode
Frequencies/proportions

**6. **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

**7. **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

**8. **Test for goodness of fit Forms of the null hypothesis
No preference
There is no difference in proportions among the categories
Participants do not prefer one category over another
Example: Pepsi: 50%, Coke 50%
No difference from a comparison population
There is no difference between the sample distribution and a known (population) distribution
Example: ND: 20% Bl, 75% Br, 5% R
US: 20% Bl, 75% Br, 5% R

**9. **Test for goodness of fit Null hypothesis
Specifies a distribution of proportions
Research hypothesis
Specifies that the distribution will be different than that indicated in the null hypothesis

**10. **Calculating the test statistic Observed frequencies
the number of individuals from the sample who are classified in a particular category
fo
Expected frequencies
the number of individuals from the sample who are expected to be classified in a particular category
fe

**11. **Calculating the test statistic