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Lab Stuff

Questions about Chi-Square?

Intro to Analysis of Variance (ANOVA)

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Final lab will be distributed onThursday Very similar to lab 3, but with different

dataYou will be expected to find appropriate

variables for three major tests

(correlation, t-test, chi-square test ofindependence)

You will be expected to interpret thefindings from each test (one short

paragraph per test). 3

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4

Student Not Student Total

Males 46(40.97)

71(76.02)

117

Females 37(42.03) 83 (77.97) 120

Total 83 154 237 Observed

Expected

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In its simplest form, it is used tocompare means for three or morecategories. Example:

Income (metric) and Marital Status (many

categories)

Relies on the F-distributionJust like the t-distribution and chi-square

distribution, there are several sampling 6

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If we have a categorical variable with 3+categories and a metric/scale variable, wecould just run 3 t-tests.

One problem is that the 3 tests would not beindependent of each other (i.e., all of theinformation is known).

As number of comparisons grow, likelihood ofsome differences are expected but do not

necessarily indicate an overall difference.

A better approach: compare the variabilitybetween groups (treatment variance + error)

to the variability within the groups (error) 7

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MS = mean square bg = between groups wg = within groups

The numerator anddenominator have their own

degrees of freedom df = of cate ories 1 k-1

wg

bg

MS

MSF =

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Generally, an f-ratio is a measure of

how different the means are relativeto the variability within each sample

Larger values greater likelihoodthat the difference between meansare not just due to chance alone

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If there is no difference between themeans, then the between-group sum of

squares should = the within-group sum ofsquares.

wg

bg

MS

MSF =

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A right-skewed distribution

It is a ratio of two chi-squaredistributions

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F-test for ANOVA is a one-tailed test.

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http://tinyurl.com/271ANOVA

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http://tinyurl.com/271ANOVAhttp://tinyurl.com/271ANOVA

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How do we know where the differences exist oncewe know that we have an overall differencebetween groups?

t-tests become important after an ANOVA so thatwe can find out which pairs are significantlydifferent (post-hoc tests).

Certain corrections can be applied to such post-

hoc t-tests so that we account for multiplecomparisons (e.g., Bonferroni correction, whichdivides p-value by the number of comparisonsbeing made)

There are many means comparisons test available(Tukey, Sidak, Bonferroni, etc). All are basically 14

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Conceptual Intro to ANOVA

Class Example: anova.do

GSS96_small.dta

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http://faculty.vassar.edu/lowry/ch13pt1.htmlhttp://faculty.vassar.edu/lowry/ch13pt1.html