Chi-Square Test

Section 12.1

Categorical Variables

Based on observations

Univariate – single categorical variableExample: Sample 100 people & ask if they

agree or disagree with a question.

Bivariate – uses two categorical variablesExample: Sample 100 people & ask if they

are male/female and what political party they support.

One-Way Frequency Table - univariate

Democrat Democrat Democrat Independent

Republican Democrat Republican Independent

Republican Republican Republican Republican

  Democrat Republican Independent

Freq. 4 6 2

Data

Horizontal One-Way Table

  Freq.

Democrat 4

Republican 6

Independent 2

Vertical One-Way Table

Goodness of Fit Test

Used to measure the extent to which the observed counts differ from the expected counts.

K = # categories of a catagorical variable Df = k – 1 Test Statistic:

2

2

2 Observed Expected

Expected

Assumptions

Observed Values are based on random Samples

Sample size is large – each cell count is at least 5.

Hypotheses

Ho: State each proportion’s hypothesized value.

HA: At least 1 of the proportions differ from the hypothesized value.

It uses the Chi-Square Chart

Positively Skewed Uses d.f. On calculator!

Is there a preference in type of car?

  Freq. Expected

SUV 27 

Truck 25  

Sedan 29  

Sports 19  

P1=proportion who prefer a SUV

P2=proportion who prefer a truck

p3=proportion who prefer a sedan

P4=proportion who prefer a sports car

1 2 3 4:

: at least 1 prop. is differento

A

H p p p p

H

Assumptions: Random Samples & all cell counts are at least 5.

Use a Chi-Square goodness of fit Test

2

2 2 2 2

2

2

Observed - Predicted

Predicted

27 25 25 25 29 25 19 25

25 25 25 25

2.24

P-val = xcdf(2.24,∞, 3)=0.52

A researcher believes that the number of homicides crimes in CA by season is uniformly distributed. To test this claim, you randomly select 1200 homicides from a recent year and record the season when each

happened.

Season Freq

Spring 312

Summer 299

Fall 297

Winter 293

Results from a previous survey asking people who go to movies at least once a month are shown in the table below. To determine whether this distribution is still the same, you randomly select 1000 people who go to movies at least once a month and record the age of each. Are the

distributions the same?

Age Survey Freq

2 - 17 26.70% 240

18 - 24 19.80% 214

25 - 39 19.70% 183

40 - 49 14% 156

50+ 19.80% 207

Homework

Worksheet