Inference for TwoWay Tables

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Inference for Two-Way Tables

• Presented by Antonio Carranza

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Inference for Two-Way Tables

• Two-Way Tables
• Relationship between Categorical Variables
• Chi-Square Test for two-way tables

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Statistically Significant

• Analyze the kind of contingency tables by using
  the Chi-Square Test.
• Main goal Is to decide if the data shows a
  statistical significance relationship by
  performing a Significance Test.

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Two-Way Tables (Categorical Variable)

• Two-way tables let us compare the distribution of
  a categorical variable (Factor B) by (yes or no)
  responses to a question between different
  populations (Factor A).
• Table size Rows x Columns
• Ex.
• 2 x 2
  3 x 2

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Relationship between Categorical Variables

• First step To determine if there is a
  significant difference in (Factor B). State the
  null hypothesis and the alternative hypothesis.
• Ho the row and column variables are independent
  (ex. there is no relationship between the two).
• Ha the row and the column variables are
  dependent.

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Expected Cell Count

• Then In doing inferences for a table is to
  figure out what the results would look like if
  the distribution of the categorical variable
  (Factor B) where the same in both populations
  (Factor A).
• Inferences procedures work in count.
• Then Calculate the expected counts for each
  population in the table
• .

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Observed and Expected Counts

• The test will be based on a measure of how far
  the observed table is from the expected table.
• If the observed count is far different from the
  expected count then we can suspect that the null
  hypothesis is false.
• Example observed expected

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Factor B (Categorical Variable)
Factor A (Two different populations)
Total of observations (Table count) A1 A2
or B1 B2
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Chi-Square Statistic

• To do the comparing and to measure how far the
  expected table is from the observed table, we use
  the Chi-square test statistic
• Chi-square statistic is used to measure how far
  the observed count is deviated from the expected
  count smaller the closer the fit of the data.
• Chi-square of zero means the data exactly fit the
  predicted values.

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Chi-Square Distribution

• Comparing the value of the test statistic with
  the critical value for its distribution.
• Unlike the Normal or t distributions, the
• distribution takes values in

0 5 10 15 20 30 40 50
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p-Value for the Chi-Square Test

• If the observed and expected counts are very
  different, will be large, indicating evidence
  against Ho.
• Thus, the p-value is always based on the right-
  hand tail of the distribution.