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Intermediate Statistics For Dummies
Part IV: Building Strong Connections with
Chi-Square Tests .......................................................207
Chapter 13: Forming Associations with Two-Way Tables . . . . . . . . .209
Breaking Down a Two-Way Table ...............................................................210
Organizing data into a two-way table ..............................................210
Filling in the cell counts.....................................................................211
Making marginal totals ......................................................................212
Breaking Down the Probabilities................................................................213
Marginal probabilities........................................................................213
Joint probabilities ..............................................................................215
Conditional probabilities...................................................................215
Trying to be Independent ...........................................................................221
Checking for independence between two categories....................221
Checking for independence between two variables......................222
Demystifying Simpson’s Paradox...............................................................223
Experiencing Simpson’s Paradox .....................................................224
Asking why: Simpson’s Paradox.......................................................226
Keeping one eye open for Simpson’s Paradox................................228
Chapter 14: Being Independent Enough for the Chi-Square Test . . . . .229
A Hypothesis Test for Independence ........................................................230
Collecting and organizing the data...................................................232
Determining the hypotheses.............................................................232
Figuring expected cell counts...........................................................233
Checking the conditions for the test ...............................................235
Calculating the Chi-square test statistic..........................................236
Finding your results on the Chi-square table .................................238
Drawing your conclusions.................................................................241
Comparing Two Tests for Comparing Two Proportions .........................243
Getting reacquainted with the Z-test for two population
proportions .....................................................................................244
Equating Chi-square tests and Z-tests for a two-by-two table......245
Chapter 15: Using Chi-Square Tests for Goodness-of-Fit
(Your Data, Not Your Jeans) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .249
Finding the Goodness-of-Fit Statistic.........................................................249
What’s observed versus what’s expected.......................................250
Calculating the goodness-of-fit statistic ..........................................252
Interpreting the Goodness-of-Fit Statistic By Using Chi-Square.............254
Checking the conditions before you start.......................................255
The steps of the Chi-square goodness-of-fit test............................256