1way

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1-way 2-way Chi Square (Crosstabs)
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When to use 1-Way Chi Square (c2)Goodness of
fit

• Analysis of frequency distributions to test
  whether distribution of responses fits
  presupposed proportions in population
• Univariate, the variable is categorical (nominal
  or ordinal), i.e, check only one type questions
  
• What did you like best about your dining
  experience today?

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The Statistical Question

• There will likely be differences in responses to
  the different categories.
• For example What did you like best about us
  today?
• 43 said quality of food
• 34 said fast, friendly service
• 23 said restaurant atmosphere
• But are these differences statistically
  significant? In other words, do these
  differences reflect attitudes of the population,
  or just this particular sample?

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Example 1-way Chi Square

• Research question Are Dominos, Pizza Hut, and
  Papa Johns pizza equally preferred among UNM
  students?
• Questionnaire question Which of the following
  do you prefer, Dominos, Pizza Hut, or Papa
  Johns? (check one)
• You sample 105 UNM students

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Hypothesis Testing

• Ho pd pph ppj
• (i.e., if preferences equal, expected value
  should be 35/105 or 33.3 for each)
• Ha pd ? pph ? ppj
• Assume an alpha of .05

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SPSS for 1-way Chi Square

• Analyzenonparametric testschi square
• Move your variable to the test variable list and
  hit OK
• There is a difference in how many people actually
  said they preferred each and how many were
  expected (35)
• The test statistic, c2 2.46, df 2
• Is this a big enough difference to make an
  inference, or could differences be due to random
  sampling error?

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Conclusion

• For c2 2.46, df 2, and a .05, the pvalue
  would need to be equal to or less than .05 to be
  significant.
• p .293, Our conclusion here?
• Retain the null. There is a slight difference in
  preferences but it is not a statistically
  significant difference and could be due to random
  sampling error.

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When to use2-way Chi Square (c2)

• For compare group research questions
• Involving 2 variables, the grouping variable and
  whatever variable you wish to compare the
  subgroups on (bivariate)
• When both variables are categorical, i.e.,
  nominal or ordinal

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Example 2-way Chi Square

• Research question Are Dominos, Pizza Hut, and
  Papa Johns pizza equally preferred by male and
  female UNM students?
• Questionnaire question Which of the following
  do you prefer, Dominos Pizza Hut, or Papa
  Johns? (check one)
• AND Gender Male Female
• You sample 105 UNM students

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Significant Test for 2-way Chi Sq

• Ho Males and females have equal preferences for
  Dominos, Pizza Hut, and Papa Johns pizza.
• Ha Males and females do not have not equal
  preferences for Dominos, Pizza Hut, and Papa
  Johns pizza.
• Set alpha for testing here, a .01

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AnalyzeDescriptive StatsCrosstabs

• Put one variable in Row and the other in Column
• Request observed expected counts, row, column
  percentages (dont need total) so you will have
  all the information you need to interpret each
  cell

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Interpretation

• Look at the overall test statistic (c2 14.01, p
  .001)
• Conclusion
• Do you reject the null or accept the null at a
  .01?
• Reject null. There is a significant difference
  between males females in terms of their pizza
  preferences.
• Now, interpret further by looking at the cells.
  Decide which way you are reading (down or across
  doesnt matter) and use the frequency
  percentages to describe what is different between
  the groups (NOT within a group!). Look at cells
  with big difference between observed and expected
  values.

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Interpreting Percentages for 2-way Chi square

• Always start with of the.. and insert either
  your row or column title. If you are reading
  rows, read across within the row variable. If
  you are reading columns, read down within the
  column variable
• Conclusion It appears males prefer Dominos and
  Papa Johns and females prefer Pizza Hut.
  Reading down columns Of those preferring
  Dominos, 75 are male and 25 are female. Of
  those preferring Pizza Hut, 34.1 are male and
  65.9 are female. Or read across rows Of the
  males, 45.8 prefer Dominos as opposed to only
  19.6 of females. Of the females, 58.7 prefer
  Pizza Hut as opposed to only 23.7 of males.