The Chi-Square Distribution and Test for Independence

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# The Chi-Square Distribution and Test for Independence - PowerPoint PPT Presentation

The Chi-Square Distribution and Test for Independence. Hypothesis testing between two or more categorical variables. Agenda. Wrapping up the t-test program example Chi-Square and Chi-Square test of independence. Chi-Square Distribution.

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### The Chi-Square Distribution and Test for Independence

Hypothesis testing between two or more categorical variables

Agenda
• Wrapping up the t-test program example
• Chi-Square and Chi-Square test of independence
Chi-Square Distribution
• The chi-square distribution results when independent variables with standard normal distributions are squared and summed.
Chi-square Degrees of freedom
• df = (r-1) (c-1)
• Where r = # of rows, c = # of columns
• Thus, in any 2x2 contingency table, the degrees of freedom = 1.
• As the degrees of freedom increase, the distribution shifts to the right and the critical values of chi-square become larger.
Using the Chi-Square Test
• Often used with contingency tables (i.e., crosstabulations)
• E.g., gender x student
• The chi-square test of independence tests whether the columns are contingent on the rows in the table.
• In this case, the null hypothesis is that there is no relationship between row and column frequencies.
• H0: The 2 variables are independent.
Requirements for Chi-Square test
• Must be a random sample from population
• Data must be in raw frequencies
• Variables must be independent
• Categories for each I.V. must be mutually exclusive and exhaustive
Special Cases
• Fisher’s Exact Test
• When you have a 2 x 2 table with expected frequencies less than 5.
• Strength of Association
• Some use Cramer’s V (for any two nominal variables) or Phi (for 2 x 2 tables) to give a value of association between the variables.
Practical Examples:
• chi2dist.do
• chisquare.do
• Auto.dta