Chisquare analysis

1
Chi-square analysis

• K300 Class 22
• April 2, 2009

2
Overview

• Test for goodness of fit
• Test for independence
• SPSS computer output for test for independence

3
Chi-square tests

• To types of hypothesis tests using Chi-square
  distribution and testing whether frequency
  distribution is as expected
• Test for goodness of fit
• Test for independence

4
Test for goodness of fit

• Have an observed frequency distribution
• Ask whether observed distribution is different
  from some given, expected frequency distribution
• Null hypothesis, no difference
• Alternative hypothesis, difference

5
Chi-square test for goodness of fit

• Formula for test valuedegrees of freedom
  equal to number of categories minus 1
• O observed frequency
• E expected frequency
• Expected frequency for each category must be 5 or
  more

6
Goodness of fit test example

• Raincoat manufacturer selects sample of 50
  raincoats sold and determines color
• Is there a color preference for raincoats?
• Level of significance 0.10

7
Step 1 state hypotheses

• Null hypothesisH0 No preference for color of
  raincoat
• Alternative hypothesisH1 Preference for color
  of raincoat

8
Step 2 critical value

• Degrees of freedom 4 1 3
• Level of significance alpha 0.10
• Critical value Chi-square 6.251

9
Step 3 test value

• Expected values
• Test value

10
Step 4 make decision

• Test value of 3.28 less than critical value of
  6.251
• Cannot reject null hypothesis

11
Step 5 summarize the results

• Cannot say that consumers show a preference for
  the color of the raincoat

12
Test for independence

• Have sample with cases classified by two nominal
  variables
• Means of travel to library
• Whether checked out book
• Does the distribution of cases on one variable
  depend on category in which cases falls on other
  variable?
• Does whether book checked out depend on means of
  travel to library?

13
Test for independence

• If the variables are independent (null
  hypothesis), the distributions across one
  variable would be expected to be the same for all
  categories of the other
• If the variables are not independent (alternative
  hypothesis), the distribution across the one
  variable would be different for and would depend
  upon the category of the other

14
Chi-square test for independence

• Formula for test valuedegrees of freedom
  equal to (rows 1) times (columns 1)
• O observed frequency
• E expected frequency
• Expected frequency for each category must be 5 or
  more

15
Test for independence example

• Survey of patrons leaving Central Library
• Obtain information for these questions
• Means of travel to librarywalk, auto, bus
• Whether or not checked out book
• Do patrons differ in whether they checked out
  book based on their means of travel to the
  library?
• Level of significance 0.05

16
Test for independence example contingency table
17
Step 1 state hypotheses

• Null hypothesisMeans of travel to library and
  whether or not checked out book are independent
• Alternative hypothesisWhether or not checked out
  book depends upon means of travel to library

18
Step 2 critical value

• Degrees of freedom (rows 1) x (cols 1) (2
  1) x (3 1) 2
• Level of significance alpha 0.05
• Critical value chi-square 5.991

19
Step 3 test value

• Steps in process
• Compute expected values
• Compute chi-square test value

20
Expected values
21
Formula for test value
22
Computing chi-square

• Computation of chi-square
• with (2-1)(3-1) 2 degrees of freedom

23
Step 4 making the decision

• Test value chi square 4.13 is less than
  critical value 5.991
• Cannot reject the null hypothesis

24
Step 5 summarize the results

• Cannot conclude that whether or not a library
  patron checks out a book depends upon the means
  of travel to the library

25
SPSS crosstabs and chi-square test for
independence

• SPSS procedure Statistics, Summarize, Crosstabs
• Row(s) is one variable dividing cases into groups
  (sometimes the one thought to be dependent upon
  the other)
• Column(s) is a second variable dividing cases
  into groups (sometimes the one on which first is
  dependent)
• Select Statistics and check Chi-square to get the
  chi-square statistics

26
SPSS crosstabs and chi-square test output