Chi-Square
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Chi-Square Test: Parametric vs Nonparametric, Goodness of Fit and Independence, Slides of Statistics
An overview of the chi-square test, including its applications in parametric and nonparametric statistics, the chi-square test for goodness of fit, and the chi-square test for independence. It covers the null hypothesis, observed and expected frequencies, degrees of freedom, and interpretation of results.
Typology: Slides
2012/2013
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Chi-Square
Parametric vs Nonparametric
- Parametric DV: Interval/Ratio
- Nonparametric DV: nominal/ordinal
Null Hypothesis
- Population is evenly distributed the uniform distribution - Or - Some other distribution, such as the normal distribution - The sample distribution is not different from the theoretical distribution (such as the uniform distribution or the normal distribution)
Observed and expected frequency
- Observed: number of individuals from the sample who are classified in a particular category
- Expected frequency: the frequency for a particular category that is predicted from the null hypothesis
Degrees of Freedom
- df = C - 1
- where C is the number of categories
- The degrees of freedom are the number of categories that are free to vary
Interpretation
- If the null hypothesis is retained, the sample distribution is like that of the theoretical distribution
- If H 0 is rejected, distribution is different from what is expected
Report Writing: Discussion Section
- It appears as if the
is (or is not) distributed as expected. - Depends on the result
Example
- Concerned about health, neither concerned or not concerned, not concerned about health
- Could assume that a sample would be equally split among these three categories i.e., 120 subjects, 40 would say concerned, 40 neither, 40 not concerned (uniform distribution)
Chi square
- Chi square = 20
- D.f. = 2
- See p. 726
- Chi square = 20, p <.
- The distribution is significantly different from the expected distribution
Example
- Dr. Zelda, a correctional psychologist, is interested in determining whether the intelligence of delinquents enrolled in a state training school is normally distributed
Distribution of Intelligence in Dr.
Zelda’s School
Below 60 119
60-85 150
86-100 687
101-115 32
116-130 12
131+ 0
- Number of Samples: 1
- DV: IQ categories
- Target Population: delinquents enrolled in the state training school
H 1 : The distribution of frequencies of the IQ categories for the sample will be different from the population distribution of frequencies of the IQ categories
If the p-value of the obtained test statistic is less than .05, reject the null hypothesis
Calculations
O E O-E (O-E)^2 /E
119 23 96 9216 401
150 136 14 196 1
687 341 346 119716 351
32 341 309 95481 280
12 136 124 15376 113
0 23 23 529 23