Statistics II for Dummies

by Rumsey, Deborah J.

• ISBN13: 9780470466469
• ISBN10: 0470466464
• Edition: 1st
• Format: Paperback
• Copyright: 2009-08-31
• Publisher: For Dummies

Summary

The ideal supplement and study guide for students preparing for advanced statisticsPacked with fresh and practical examples appropriate for a range of degree-seeking students, Statistics II For Dummies helps any reader succeed in an upper-level statistics course. It picks up with data analysis where Statistics For Dummies left off, featuring new and updated examples, real-world applications, and test-taking strategies for success. This easy-to-understand guide covers such key topics as sorting and testing models, using regression to make predictions, performing variance analysis (ANOVA), drawing test conclusions with chi-squares, and making comparisons with the Rank Sum Test.Deborah Rumsey, PhD, is a Statistics Education Specialist and Auxiliary Faculty Member in the Department of Statistics at The Ohio State University. She is the author of Statistics For Dummies (978-0-7645-5423-0), Statistics Workbook For Dummies (978-0-7645-8466-4), and Probability For Dummies (978-0-471-75141-0).

Author Biography

Deborah Rumsey, PhD, is a Statistics Education Specialist and Auxiliary Faculty Member in the Department of Statistics at Ohio State University. She is also a Fellow of the American Statistical Association and has received the Presidential Teaching Award from Kansas State University. Dr. Rumsey has published numerous papers and given many professional presentations on the subject of statistics education.

Table of Contents

Introduction	p. 1
About This Book	p. 1
Conventions Used in This Book	p. 2
What You're Not to Read	p. 3
Foolish Assumptions	p. 3
How This Book Is Organized	p. 3
Tackling Data Analysis and Model-Building Basics	p. 4
Using Different Types of Regression to Make Predictions	p. 4
Analyzing Variance with ANOVA	p. 4
Building Strong Connections with Chi-Square Tests	p. 5
Nonparametric Statistics: Rebels without a Distribution	p. 5
The Part of Tens	p. 5
Icons Used in This Book	p. 5
Where to Go from Here	p. 6
Tackling Data Analysis and Model-Building Basics	p. 7
Beyond Number Crunching: The Art and Science of Data Analysis	p. 9
Data Analysis: Looking before You Crunch	p. 9
Nothing (not even a Straight line) lasts forever	p. 11
Data snooping isn't cool	p. 11
No (data) fishing allowed	p. 12
Getting the Big Picture: An Overview of Stats II	p. 13
Population parameter	p. 13
Sample statistic	p. 14
Confidence interval	p. 14
Hypothesis test	p. 15
Analysis of variance (ANOVA)	p. 15
Multiple comparisons	p. 16
Interaction effects	p. 16
Correlation	p. 17
Linear regression	p. 18
Chi-square tests	p. 19
Nonparametrics	p. 20
Finding the Right Analysis for the Job	p. 21
Categorical versus Quantitative Variables	p. 22
Statistics for Categorical Variables	p. 23
Estimating a proportion	p. 23
Comparing proportions	p. 24
Looking for relationships between categorical variables	p. 25
Building models to make predictions	p. 26
Statistics for Quantitative Variables	p. 27
Making estimates	p. 27
Making comparisons	p. 28
Exploring relationships	p. 28
Predicting y using x	p. 30
Avoiding Bias	p. 31
Measuring Precision with Margin of Error	p. 33
Knowing Your Limitations	p. 34
Reviewing Confidence Intervals and Hypothesis Tests	p. 37
Estimating Parameters by Using Confidence Intervals	p. 38
Getting the basics: The general form of a confidence interval	p. 38
Finding the confidence interval for a population mean	p. 39
What changes the margin of error?	p. 40
Interpreting a confidence interval	p. 43
What's the Hype about Hypothesis Tests?	p. 44
What Ho and Ha really represent	p. 44
Gathering your evidence into a test statistic	p. 45
Determining strength of evidence with a p-value	p. 45
False alarms and missed opportunities: Type I and II errors	p. 46
The power of a hypothesis test	p. 48
Using Different Types of Regression to Make Predictions	p. 53
Getting in Line with Simple Linear Regression	p. 55
Exploring Relationships with Scatterplots and Correlations	p. 56
Using scatterplots to explore relationships	p. 57
Collating the information by using the correlation coefficient	p. 58
Building a Simple Linear Regression Model	p. 60
Finding the best-fitting line to model your data	p. 60
The y-intercept of the regression line	p. 61
The slope of the regression line	p. 62
Making point estimates by using the regression line	p. 63
No Conclusion Left Behind: Tests and Confidence Intervals for Regression	p. 63
Scrutinizing the slope	p. 64
Inspecting the y-intercept	p. 66
Building confidence intervals for the average response	p. 68
Making the band with prediction intervals	p. 69
Checking the Model's Fit (The Data, Not the Clothes!)	p. 71
Defining the conditions	p. 71
Finding and exploring the residuals	p. 73
Using r2 to measure model fit	p. 76
Scoping for outliers	p. 77
Knowing the Limitations of Your Regression Analysis	p. 79
Avoiding slipping into cause-and-effect mode	p. 79
Extrapolation: The ultimate no-no	p. 80
Sometimes you need more than one variable	p. 81
Multiple Regression with Two X Variables	p. 83
Getting to Know the Multiple Regression Model	p. 83
Discovering the uses of multiple regression	p. 84
Looking at the general form of the multiple regression model	p. 84
Stepping through the analysis	p. 85
Looking at x's and y's	p. 85
Collecting the Data	p. 86
Pinpointing Possible Relationships	p. 88
Making scatterplots	p. 88
Correlations: Examining the bond	p. 89
Checking for Multicolinearity	p. 91
Finding the Best-Fitting Model for Two x Variables	p. 92
Getting the multiple regression coefficients	p. 93
Interpreting the coefficients	p. 94
Testing the coefficients	p. 95
Predicting y by Using the x Variables	p. 97
Checking the Fit of the Multiple Regression Model	p. 98
Noting the conditions	p. 98
Plotting a plan to check the conditions	p. 98
Checking the three conditions	p. 100
How Can I Miss You If You Won't Leave? Regression Model Selection	p. 103
Getting a Kick out of Estimating Punt Distance	p. 104
Brainstorming variables and collecting data	p. 104
Examining scatterplots and correlations	p. 106
Just Like Buying Shoes: The Model Looks Nice, But Does It Fit?	p. 109
Assessing the fit of multiple regression models	p. 110
Model selection procedures	p. 111
Getting Ahead of the Learning Curve with Nonlinear Regression	p. 115
Anticipating Nonlinear Regression	p. 116
Starting Out with Scatterplots	p. 117
Handling Curves in the Road with Polynomials	p. 119
Bringing back Polynomials	p. 119
Searching for the best polynomial model	p. 122
Using a second-degree polynomial to pass the quiz	p. 123
Assessing the fit of a polynomial model	p. 126
Making predictions	p. 129
Going Up? Going Down? Go Exponential!	p. 130
Recollecting exponential models	p. 130
Searching for the best exponential model	p. 131
Spreading secrets at an exponential rate	p. 133
Yes, No, Maybe So: Making Predictions by Using Logistic Regression	p. 137
Understanding a Logistic Regression Model	p. 138
How is logistic regression different from other regressions?	p. 138
Using an S-curve to estimate probabilities	p. 139
Interpreting the coefficients of the logistic regression model	p. 140
The logistic regression model in action	p. 141
Carrying Out a Logistic Regression Analysis	p. 142
Running the analysis in Minitab	p. 142
Finding the coefficients and making the model	p. 144
Estimating p	p. 145
Checking the fit of the model	p. 146
Fitting the Movie Model	p. 147
Analyzing Variance with Anova	p. 151
Testing Lots of Means? Come On Over to Anova!	p. 153
Comparing Two Means with a t-Test	p. 154
Evaluating More Means with Anova	p. 155
Spitting seeds: A situation just waiting for Anova	p. 155
Walking through the steps of Anova	p. 156
Checking the Conditions	p. 157
Verifying independence	p. 157
Looking for what's normal	p. 158
Taking note of spread	p. 159
Setting Up the Hypotheses	p. 162
Doing the F-Test	p. 162
Running Anova in Minitab	p. 163
Breaking down the variance into sums of squares	p. 164
Locating those mean sums of squares	p. 165
Figuring the F-statistic	p. 166
Making conclusions from Anova	p. 168
What's next?	p. 169
Checking the Fit of the Anova Model	p. 170
Sorting Out the Means with Multiple Comparisons	p. 173
Following Up after Anova	p. 174
Comparing cellphone minutes: An example	p. 174
Setting the Stage for multiple comparison procedures	p. 176
Pinpointing Differing Means with Fisher and Tukey	p. 177
Fishing for differences with Fisher's LSD	p. 178
Using Fisher's new and improved LSD	p. 179
Separating the turkeys with Tukey's test	p. 182
Examining the Output to Determine the Analysis	p. 183
So Many Other Procedures, So Little Time!	p. 184
Controlling for baloney with the Bonferroni adjustment	p. 185
Comparing combinations by using Scheffe's method	p. 186
Finding out whodunit with Dunnett's test	p. 186
Staying cool with Student Newman-Keuls	p. 187
Duncan's multiple range test	p. 187
Going nonparametric with the Kruskal-Wallis test	p. 188
Finding Your Way through Two-Way Anova	p. 191
Setting Up the Two-Way Anova Model	p. 192
Determining the treatments	p. 192
Stepping through the sums of squares	p. 193
Understanding Interaction Effects	p. 194
What is interaction, anyway?	p. 195
Interacting with interaction plots	p. 195
Testing the Terms in Two-Way Anova	p. 198
Running the Two-Way Anova Table	p. 199
Interpreting the results: Numbers and graphs	p. 200
Are Whites Whiter in Hot Water? Two-Way Anova Investigates	p. 202
Regression and Anova: Surprise Relatives!	p. 207
Seeing Regression through the Eyes of Variation	p. 208
Spotting variability and finding an ""x-planation""	p. 208
Getting results with regression	p. 209
Assessing the fit of the regression model	p. 211
Regression and Anova: A Meeting of the Models	p. 212
Comparing sums of squares	p. 212
Dividing up the degrees of freedom	p. 214
Bringing regression to the Anova table	p. 215
Relating the F-and t-statistics: The final frontier	p. 216
Building Strong Connections with Chi-Square Tests	p. 219
Forming Associations with Two-Way Tables	p. 221
Breaking Down a Two-Way Table	p. 222
Organizing data into a two-way table	p. 222
Filling in the cell counts	p. 223
Making marginal totals	p. 224
Breaking Down the Probabilities	p. 225
Marginal probabilities	p. 226
Joint probabilities	p. 227
Conditional probabilities	p. 228
Trying To Be Independent	p. 233
Checking for independence between two categories	p. 233
Checking for independence between two variables	p. 235
Demystifying Simpson's Paradox	p. 236
Experiencing Simpson's Paradox	p. 236
Figuring out why Simpson's Paradox occurs	p. 239
Keeping one eye open for Simpson's Paradox	p. 240
Being Independent Enough for the Chi-Square Test	p. 241
The Chi-square Test for Independence	p. 242
Collecting and organizing the data	p. 243
Determining the hypotheses	p. 245
Figuring expected cell counts	p. 245
Checking the conditions for the test	p. 246
Calculating the Chi-square test statistic	p. 247
Finding your results on the Chi-square table	p. 249
Drawing your conclusions	p. 253
Putting the Chi-square to the test	p. 255
Comparing Two Tests for Comparing Two Proportions	p. 257
Getting reacquainted with the Z-test for two population proportions	p. 257
Equating Chi-square tests and Z-tests for a two-by-two table	p. 258
Using Chi-Square Tests for Goodness-of-Fit (Your Data, Not Your Jeans)	p. 263
Finding the Goodness-of-Fit Statistic	p. 264
What's observed versus what's expected	p. 264
Calculating the goodness-of-fit statistic	p. 266
Interpreting the Goodness-of-Fit Statistic Using a Chi-Square	p. 268
Checking the conditions before you start	p. 270
The steps of the Chi-square goodness-of-fit test	p. 270
Nonparametric Statistics: Rebels without a Distribution	p. 273
Going Nonparametric	p. 275
Arguing for Nonparametric Statistics	p. 275
No need to fret if conditions aren't met	p. 276
The median's in the spotlight for a change	p. 277
So, what's the catch?	p. 279
Mastering the Basics of Nonparametric Statistics	p. 280
Sign	p. 280
Rank	p. 282
Signed rank	p. 283
Rank sum	p. 284
All Signs Point to the Sign test and Signed Rank Test	p. 287
Reading the Signs: The Sign Test	p. 288
Testing the median	p. 290
Estimating the median	p. 292
Testing matched pairs	p. 294
Going a Step Further with the Signed Rank Test	p. 296
A limitation of the sign test	p. 296
Stepping through the signed rank test	p. 297
Losing weight with signed ranks	p. 298
Pulling Rank with the Rank Sum Test	p. 303
Conducting the Rank Sum Test	p. 303
Checking the conditions	p. 303
Stepping through the test	p. 304
Stepping up the sample size	p. 306
Performing a Rank Sum Test: Which Real Estate Agent Sells Homes Faster?	p. 307
Checking the conditions for this test	p. 307
Testing the hypotheses	p. 309
Do the Kruskal-Wallis and Rank the Sums with the Wilcoxon	p. 313
Doing the Kruskal-Wallis Test to Compare More than Two Populations	p. 313
Checking the conditions	p. 315
Setting up the test	p. 317
Conducting the test step by step	p. 317
Pinpointing the Differences: The Wilcoxon Rank Sum Test	p. 320
Pairing off with pariwise comparisons	p. 320
Carrying out comparison tests to see who's different	p. 321
Examining the medians to see how they're different	p. 323
Pointing Out Correlations with Spearman's Rank	p. 325
Pickin' On Pearson and His Precious Conditions	p. 326
Scoring with Spearman's Rank Correlation	p. 327
Figuring Spearman's rank correlation	p. 328
Watching Spearman at work: Relating aptitude to performance	p. 329
The Part of Tens	p. 333
Ten Common Errors in Statistical Conclusions	p. 335
Ten Ways to Get Ahead by Knowing Statistics	p. 347
Ten Cool Jobs That Use Statistics	p. 357
Appendix: Reference Tables	p. 367
Index	p. 379
Table of Contents provided by Ingram. All Rights Reserved.