Chi SquareFr Chris - St Francis High School

March 2006

Two Applications

• Goodness of Fit (one way)

Two-Way (Contingency) Table

1-Way(Univariate) Data

• Observed frequencies are from a RANDOM SAMPLE

Large Sample size (expect at least 5 in each category)

Stolen Cars by Color

Null Hypothesis: Color makes no difference

San Luis Obispo Telegram-Tribune 9/2/96

Alternative Hypothesis: Color makes a difference

15% white, 15% blue, 35% red, 30% black, 5% other

white blue red black other

Observed 140 100 270 230 90Expected 124.5 124.5 290.5 249.5 41.5

white blue red black other

Observed 140 100 270 230 90Expected 124.5 124.5 290.5 249.5 41.5

SRS, and All EXPECTED cells >5 so large enough sample

Since P(Chi-sq, df=4 > 18.46) < .001so we reject the null hypothesis,

and conclude certain colors are more likely to be stolen

Now you try: According to SLO Trib, 12/15/99,

SRS of 200 purchases of California Lotto tix:

Age 18-34 35-64 65+played 36 130 34

California in 1999 had 35% 18-34, 51% 35-64, 14% over 65

Try a Chi-Sq Goodness of Fit Test

2 way Chi-Square is even more Fun!According to Research Quarterly for Exercise and Sport, (1990) p 315-320, SRS of 1200 looked at

hours of TV and a cardiovascular test

Hrs of TV Fit Unfit

0 35 147

1-2 101 629

3-4 28 222

5+ 4 34

But we compute df=(r-1)(c-1)

and the expected frequencies are

computed with by the marginal totals

Hrs of TV Fit Unfit Totals

0 35 147 1821-2 101 629 730

3-4 28 222 250

5+ 4 34 38168 1032 1200

Hrs of TV Fit Unfit Totals

0 25.5 156.5 1821-2 102.2 627.8 730

3-4 35.0 215.0 250

5+ 5.3 32.7 38168 1032 1200

Expected Frequency = (Row)(Col)/total

df=(4-1)(2-1)=3, So we reject the Null Hypothesis at the .05 level for any

Chi Square over 12.83

less than 12.83, so there is not enough evidence to reject the null hypothesis at the .05 level, so there is little evidence here that would suggest that the hours watching TV is associated with

one’s cardiovascular fittness.

sex died lived

men 630 168women 136 323

class died lived

high 117 187

middle 163 112

low 536 192Would you rather be rich or a woman if you were on the Titanic?

Actually the Chi-Square statistic tests against the null hypothesis (no difference according to category)...

you need to look at the numbers to see what’s going on...