What If Variables are Nominal

1
What If Variables are Nominal?

• ED 690Chi-Square Introduction
• Wang

2
Types of Statistical Tests

• When running a t test and ANOVA
• We compare
• Mean differences between groups
• We assume
• random sampling
• the groups are homogeneous
• distribution is normal
• samples are large enough to represent population
  (30)
• DV Data represented on an interval or ratio
  scale
• These are Parametric tests!

3
Types of Tests

• When the assumptions are violated
• Subjects were not randomly sampled
• DV Data
• Ordinal (ranked)
• Nominal (categorized brands of candy, types of
  car, levels of education, learning styles, Likert
  Scale)
• The scores are greatly skewed or we have no
  knowledge of the distribution
• We use tests that are equivalent to t test and
  ANOVA
• Non-Parametric Test!

4
Chi Square

• used when data are nominal (both IV and DV)
• Comparing frequencies of distributions occurring
  in different categories or groups
• Tests whether group distributions are different
• Shoppers preference for the taste of 3 brands of
  candy
• determines the association between IV and DV by
  counting the frequencies of distribution
• Gender relative to study preference (alone or in
  group)

5
Types of Chi Square

• A one-dimensional Chi Square (p. 503 table--Gay)
• Determine if the observed frequencies are
  significantly different from the expected
  frequencies
• X Y Z (3 brands of candy)
• 40 30 20 (90 shoppers)
• Null hypothesis there is no difference between
  graduate students study preference

6
Types of CHI-SQUARE

• A two-dimensional Chi Square (p. 504 table)
• Frequencies are categorized along more than one
  dimensions
• Gender relative to study preferences
• Gender relative to voting for school voucher

7

Chi Square (by formula)

• Hypothesis Ho
• Level of significance
• Testing frequencies of categories
• Computation of Chi square value
• Determination of critical value
• DF R-1 (R is the no. of the categories--DV)
• Check in Chi-square table
• Obtained value critical value
• Decision
• Reject null hypothesis

8

Chi Square (by software)

• Use Sample data
• Culture-Color data sales data
• Answer the questions
• Differences culture-color region-product color
• Follow the Chi-square handout
• If p value
• Decision
• Reject null hypothesis