QUIZ#3
REVIEW
ChiSquare
Nonparametrics tests
o
No assumptions about the shape of the population (Binomial, X², Sign Test)
o
Nominal & Ordinal Data
ChiSquare Tests
o
Hypothesis testing procedure for nominal variables (group people into categories; i.e.
hair color, gender, political parties)
o
Compare how well an observed distribution fits an expected distribution. The
expected distribution can be based on theory, prior results, and assumption of equal
distribution across categories
o
When do we use ChiSquare? Data in the form of frequency counts in different
categories. Nominal categories (still categories although it is changed to
frequencies…no rank or order (nominal data)
o
Two types of Chisquare tests: Goodness of Fit and Test of Association /
Independence
1.
Goodness of Fit
a.
Single nominal variable
b.
Dichotomous (only two choices: yes/no; male/female; correct/incorrect
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
c.
Can use either the binomial X²GoF
d.
Degrees of Freedom = number of categories – 1
i.
Example: Hair color is the variable and the categories are red, blonde, black,
brown, other. Df = 51=4
e.
Formula:
X² = Σ (OE) ^2 / E
Where O = observed frequencies and E= expected frequencies for each category
f.
For all chisquare tests the formula is the same, what changes is the formula for
getting the expected frequencies and df.
g.
Obtaining the Expected Frequencies: you figure out the expected frequencies by
multiplying the proportion in the population to which you are comparing times the #
in your sample. If a population is not known, then in some cases you compare
observed to an equal number of people in each category.
h.
X² Distribution
i.
Df = # categories – 1
ii.
Use table to get critical value according to alpha and df (cut off values)
iii.
Shape varies as df changes
iv.
Only positive X² critical values since you square each value
v.
Compare obtained X² value to critical X² value
vi.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 Dicorcia
 Statistical hypothesis testing, Statistical significance, Statistical power, Nominal Data, yr olds

Click to edit the document details