Page 14 - Statistics II for Dummies

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Statistics II For Dummies
Part IV: Building Strong Connections
with Chi-Square Tests ............................................... 219

Chapter 13: Forming Associations with Two-Way Tables . . . . . . . . .221
Breaking Down a Two-Way Table ..............................................................222
Organizing data into a two-way table ..............................................222
Filling in the cell counts ....................................................................223
Making marginal totals ......................................................................224
Breaking Down the Probabilities ...............................................................225
Marginal probabilities .......................................................................226
Joint probabilities ..............................................................................227
Conditional probabilities ..................................................................228
Trying To Be Independent ..........................................................................233
Checking for independence between two categories ...................233
Checking for independence between two variables......................235
Demystifying Simpson’s Paradox ..............................................................236
Experiencing Simpson’s Paradox .....................................................236
Figuring out why Simpson’s Paradox occurs .................................239
Keeping one eye open for Simpson’s Paradox ...............................240

Chapter 14: Being Independent Enough for the Chi-Square Test . . .241
The Chi-square Test for Independence ....................................................242
Collecting and organizing the data ..................................................243
Determining the hypotheses ............................................................245
Figuring expected cell counts ..........................................................245
Checking the conditions for the test ...............................................246
Calculating the Chi-square test statistic .........................................247
Finding your results on the Chi-square table .................................249
Drawing your conclusions ................................................................253
Putting the Chi-square to the test ....................................................255
Comparing Two Tests for Comparing Two Proportions ........................257
Getting reacquainted with the Z-test for
two population proportions .........................................................257
Equating Chi-square tests and Z-tests for a two-by-two table .....258

Chapter 15: Using Chi-Square Tests for Goodness-of-Fit
(Your Data, Not Your Jeans). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .263
Finding the Goodness-of-Fit Statistic ........................................................264
What’s observed versus what’s expected ......................................264
Calculating the goodness-of-fi t statistic ..........................................266
Interpreting the Goodness-of-Fit Statistic Using a Chi-Square ...............268
Checking the conditions before you start ......................................270
The steps of the Chi-square goodness-of-fi t test ...........................270

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