χ² Test, Distribution - Basic Statistics for Behavioral Sciences - Lecture Notes, Study notes of Statistics for Psychologists

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Basic Statistics for

The Behavioral Sciences

LECTURE NOTES

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Ch. 18. χ²-test I. Introduction A. χ²-distribution

1. has one parameter, df.
2. range 0 - ∞, positively skewed.
3. mean=df, variance=2df. B. Characteristic
4. Qualitative IV variable.
5. Dependent variable (DV) is frequency data.

II. Test for goodness-of-fit (χ²-test) A. Situation; interested in how well a population dist represented by given data fits a theoretical dist (uniform, normal, and etc.). B. Procedure

1. H 0 : distpop = distth H 1 : distpop ≠ distth
2. α: .05 or .01---> χ²crit, df=k-1, k=# of groups.
3. TS: χ²obs=
4. Decision: If χ²obs≥χ²crit, reject H 0. C. Assumption: Independence (mutually exclusive and exhaustive) of observations. D. Example

III. Tests for contingency tables (χ²-test) A. Situation; interested in the independence of two categorical variables. B. Procedure

1. H 0 : Two categories are independent. H 1 : Two categories are dependent.
2. α: .05 or .01--->χ²crit, df = (R-1)(C-1).
3. TS: χ²obs=

(row total)(column total)

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