Table Of Content

SigmaPlot Statistics 1 Using the Advisor Wizard 3 Select what you need to do . . . . . . . . . . . . . . . . . . . . . . . 4 How are the data measured? . . . . . . . . . . . . . . . . . . . . . . 5 Did you apply more than one treatment per subject? . . . . . . . . . . 7 How many groups or treatments are there? . . . . . . . . . . . . . . . 8 What kind of data do you have? . . . . . . . . . . . . . . . . . . . .11 What kind of prediction do you want to make? . . . . . . . . . . . .12 What kind of curve do you want to use? . . . . . . . . . . . . . . . 13 How do you want to specify the independent variables? . . . . . . . .14 How do you want SigmaPlot to select the independent variable?. . . 15 Using Statistical Procedures 17 Using SigmaPlot Procedures . . . . . . . . . . . . . . . . . . . . . .17 Running SigmaPlot Procedures . . . . . . . . . . . . . . . . . . . . .17 Choosing the Procedure to Use . . . . . . . . . . . . . . . . . . . . .22 Describing Your Data with Basic Statistics. . . . . . . . . . . . . . 23 Choosing the Group Comparison Test to Use . . . . . . . . . . . . .29 Choosing the Repeated Measures Test to Use . . . . . . . . . . . . .34 When to Compare Effects on Individuals After Multiple Treatments 36 Choosing the Rate and Proportion Comparison to Use . . . . . . . . .38 Choosing the Prediction or Correlation Method . . . . . . . . . . . .39 Choosing the Survival Analysis to Use . . . . . . . . . . . . . . . . .41 iii Testing Normality . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Determining Experimental Power and Sample Size . . . . . . . . . 47 How to Determine the Power of an Intended Test . . . . . . . . . . 48 How To Estimate the Sample Size Necessary to Achieve a Desired Power48 Comparing Two or More Groups 51 About Group Comparison Tests. . . . . . . . . . . . . . . . . . . . 51 Parametric and Nonparametric Tests . . . . . . . . . . . . . . . . . 51 Comparing Two Groups . . . . . . . . . . . . . . . . . . . . . . . 52 Comparing Many Groups . . . . . . . . . . . . . . . . . . . . . . . 52 Data Format for Group Comparison Tests . . . . . . . . . . . . . . 52 Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . 53 Arranging Data for t-tests and ANOVAs . . . . . . . . . . . . . . . 53 Unpaired t-Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 About the Unpaired t-test . . . . . . . . . . . . . . . . . . . . . . . 57 Performing an Unpaired t-Test . . . . . . . . . . . . . . . . . . . . 58 Arranging t-Test Data . . . . . . . . . . . . . . . . . . . . . . . . . 58 Setting t-Test Options . . . . . . . . . . . . . . . . . . . . . . . . . 59 Running a t-Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Interpreting t-Test Results . . . . . . . . . . . . . . . . . . . . . . . 65 t-Test Report Graphs . . . . . . . . . . . . . . . . . . . . . . . . . 68 Mann-Whitney Rank Sum Test . . . . . . . . . . . . . . . . . . . . 70 About the Mann-Whitney Rank Sum Test . . . . . . . . . . . . . . 71 Performing a Mann-Whitney Rank Sum Test . . . . . . . . . . . . 71 Arranging Rank Sum Data . . . . . . . . . . . . . . . . . . . . . . 72 Setting Mann-Whitney Rank Sum Test Options . . . . . . . . . . . 72 Running a Rank Sum Test . . . . . . . . . . . . . . . . . . . . . . 75 Interpreting Rank Sum Test Results . . . . . . . . . . . . . . . . . 76 iv Rank Sum Test Report Graphs . . . . . . . . . . . . . . . . . . . . .78 One Way Analysis of Variance (ANOVA) . . . . . . . . . . . . . . .80 Performing a One Way ANOVA . . . . . . . . . . . . . . . . . . . .81 Arranging One Way ANOVA Data . . . . . . . . . . . . . . . . . .82 Setting One Way ANOVA Options . . . . . . . . . . . . . . . . . .82 Running a One Way ANOVA . . . . . . . . . . . . . . . . . . . . .87 Multiple Comparison Options for a One Way ANOVA . . . . . . . .89 Interpreting One Way ANOVA Results . . . . . . . . . . . . . . . .90 One Way ANOVA Report Graphs . . . . . . . . . . . . . . . . . . .96 Two Way Analysis of Variance (ANOVA) . . . . . . . . . . . . . .98 About the Two Way ANOVA . . . . . . . . . . . . . . . . . . . . .99 Performing a Two Way ANOVA . . . . . . . . . . . . . . . . . . . .99 Arranging Two Way ANOVA Data . . . . . . . . . . . . . . . . . 100 Setting Two Way ANOVA Options . . . . . . . . . . . . . . . . . 105 Running a Two Way ANOVA . . . . . . . . . . . . . . . . . . . . 109 Multiple Comparison Options for a Two Way ANOVA . . . . . . . 111 Performing a One Way ANOVA on Two Way ANOVA Data . . . . 114 Interpreting Two Way ANOVA Results . . . . . . . . . . . . . . . 114 Two Way ANOVA Report Graphs . . . . . . . . . . . . . . . . . . 122 Three Way Analysis of Variance (ANOVA) . . . . . . . . . . . . . 123 About the Three Way ANOVA . . . . . . . . . . . . . . . . . . . . 124 Performing a Three Way ANOVA . . . . . . . . . . . . . . . . . . 124 Arranging Three Way ANOVA Data . . . . . . . . . . . . . . . . . 125 Setting Three Way ANOVA Options . . . . . . . . . . . . . . . . . 129 Running a Three Way ANOVA . . . . . . . . . . . . . . . . . . . 134 Multiple Comparison Options for a Three Way ANOVA . . . . . . 136 Interpreting Three Way ANOVA Results . . . . . . . . . . . . . . 139 Three Way ANOVA Report Graphs . . . . . . . . . . . . . . . . . 146 Kruskal-Wallis Analysis of Variance on Ranks . . . . . . . . . . . 147 About the Kruskal-Wallis ANOVA on Ranks . . . . . . . . . . . . 148 Performing an ANOVA on Ranks . . . . . . . . . . . . . . . . . . 148 v Arranging ANOVA on Ranks Data . . . . . . . . . . . . . . . . . .149 Setting the ANOVA on Ranks Options . . . . . . . . . . . . . . . .150 Running an ANOVA on Ranks . . . . . . . . . . . . . . . . . . . 154 Multiple Comparison Options for ANOVA on Ranks . . . . . . . .156 Interpreting ANOVA on Ranks Results . . . . . . . . . . . . . . .157 ANOVA on Ranks Report Graphs . . . . . . . . . . . . . . . . . .161 Performing a Multiple Comparison . . . . . . . . . . . . . . . . . .162 Holm-Sidak Test . . . . . . . . . . . . . . . . . . . . . . . . . . .163 Tukey Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .164 Student-Newman-Keuls (SNK) Test . . . . . . . . . . . . . . . . .164 Bonferroni t-Test . . . . . . . . . . . . . . . . . . . . . . . . . . .164 Fisher’s Least Significance Difference Test . . . . . . . . . . . . .165 Dunnett’s Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . .165 Dunn’s test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .165 Duncan’s Multiple Range . . . . . . . . . . . . . . . . . . . . . . .165 One Sample t-Test 167 About the One Sample t-Test . . . . . . . . . . . . . . . . . . . . .167 Performing a One Sample t-Test . . . . . . . . . . . . . . . . . . .167 Arranging One Sample t-Test Data . . . . . . . . . . . . . . . . . .168 Setting One Sample t-Test Data Options . . . . . . . . . . . . . . .168 Running a One Sample t-Test . . . . . . . . . . . . . . . . . . . . .171 Interpreting One Sample t-Test Results . . . . . . . . . . . . . . . .172 One Sample t-Test Report Graphs . . . . . . . . . . . . . . . . . .173 vi Comparing Repeated Measurements of the Same Individuals 175 About Repeated Measures Tests . . . . . . . . . . . . . . . . . . . 175 Parametric and Nonparametric Tests . . . . . . . . . . . . . . . . . 175 Comparing Individuals Before and After a Single Treatment . . . . 176 Comparing Individuals Before and After Multiple Treatments . . . 176 Data Format for Repeated Measures Tests . . . . . . . . . . . . . . 176 Raw Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 Indexed Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 Paired t-Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 Performing a Paired t-test . . . . . . . . . . . . . . . . . . . . . . . 178 Arranging Paired t-Test Data . . . . . . . . . . . . . . . . . . . . . 179 Setting Paired t-Test Options . . . . . . . . . . . . . . . . . . . . . 179 Running a Paired t-Test . . . . . . . . . . . . . . . . . . . . . . . . 183 Interpreting Paired t-Test Results . . . . . . . . . . . . . . . . . . . 185 Paired t-Test Report Graphs . . . . . . . . . . . . . . . . . . . . . 188 Wilcoxon Signed Rank Test . . . . . . . . . . . . . . . . . . . . . 190 About the Signed Rank Test . . . . . . . . . . . . . . . . . . . . . 191 Performing a Signed Rank Test . . . . . . . . . . . . . . . . . . . . 191 Arranging Signed Rank Data . . . . . . . . . . . . . . . . . . . . . 192 Setting Signed Rank Test Options . . . . . . . . . . . . . . . . . . 192 Running a Signed Rank Test . . . . . . . . . . . . . . . . . . . . . 195 Interpreting Signed Rank Test Results . . . . . . . . . . . . . . . . 196 Signed Rank Test Report Graphs . . . . . . . . . . . . . . . . . . . 198 One Way Repeated Measures Analysis of Variance (ANOVA) . . . 200 About the One Way Repeated Measures ANOVA . . . . . . . . . . 201 Performing a One Way Repeated Measures ANOVA . . . . . . . . 201 Arranging One Way Repeated Measures ANOVA Data . . . . . . . 202 Setting One Way Repeated Measures ANOVA Options . . . . . . . 203 vii Running a One Way Repeated Measures ANOVA . . . . . . . . . 206 Multiple Comparison Options (One Way RM ANOVA) . . . . . . .208 Interpreting One Way Repeated Measures ANOVA Results . . . . .209 One Way Repeated Measures ANOVA Report Graphs . . . . . . .216 Two Way Repeated Measures Analysis of Variance (ANOVA) . . .218 About the Two Way Repeated Measures ANOVA . . . . . . . . . .218 Performing a Two Way Repeated Measures ANOVA . . . . . . . .219 Arranging Two Way Repeated Measures ANOVA Data . . . . . . .219 Set Two Way Repeated Measures ANOVA Options . . . . . . . . .224 Running a Two Way Repeated Measures ANOVA . . . . . . . . . .227 Multiple Comparison Options (Two Way RM ANOVA) . . . . . .229 Interpreting Two Way Repeated Measures ANOVA Results . . . .230 Two way repeated measures ANOVA report graphs . . . . . . . . .238 Friedman Repeated Measures Analysis of Variance on Ranks . . . .239 About the Repeated Measures ANOVA on Ranks . . . . . . . . . .239 Performing a Repeated Measures ANOVA on Ranks . . . . . . . .239 Arranging Repeated Measures ANOVA on Ranks Data . . . . . . .240 Setting the Repeated Measures ANOVA on Ranks Options . . . . .240 Running a Repeated Measures ANOVA on Ranks . . . . . . . . . .243 Multiple Comparison Options (RM ANOVA on ranks) . . . . . . .244 Interpreting Repeated Measures ANOVA on Ranks Results . . . . .245 Repeated Measures ANOVA on Ranks Report Graphs . . . . . . . .249 Comparing Frequencies, Rates, and Proportions 251 About Rate and Proportion Tests . . . . . . . . . . . . . . . . . . 251 Contingency Tables . . . . . . . . . . . . . . . . . . . . . . . . . .251 Comparing the Proportions of Two Groups in One Category . . . .252 viii Comparing Proportions of Multiple Groups in Multiple Categories . 252 Comparing Proportions of the Same Group to Two Treatments . . . 252 Yates Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 Data Format for Rate and Proportion Tests . . . . . . . . . . . . . . 253 z-test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 Chi—Squared Analysis of Contingency Tables . . . . . . . . . . . 253 Fisher Exact Test . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 McNemar’s Test . . . . . . . . . . . . . . . . . . . . . . . . . . . 256 Comparing Proportions Using the z-Test . . . . . . . . . . . . . . . 258 About the z-test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 Performing a z-test . . . . . . . . . . . . . . . . . . . . . . . . . . 258 Arranging z-test Data . . . . . . . . . . . . . . . . . . . . . . . . . 259 Setting z-test Options . . . . . . . . . . . . . . . . . . . . . . . . . 259 Running a z-Test . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 Interpreting Proportion Comparison Results . . . . . . . . . . . . . 262 Chi-square Analysis of Contingency Tables . . . . . . . . . . . . . 265 About the Chi-Square Test . . . . . . . . . . . . . . . . . . . . . . 266 Performing a Chi-Square Test . . . . . . . . . . . . . . . . . . . . 266 Arranging Chi-Square Data . . . . . . . . . . . . . . . . . . . . . . 267 Setting Chi-Square Options . . . . . . . . . . . . . . . . . . . . . . 268 Running a Chi-Square Test . . . . . . . . . . . . . . . . . . . . . . 270 Interpreting Results of a Chi-Squared Analysis of Contingency tables 272 The Fisher Exact Test . . . . . . . . . . . . . . . . . . . . . . . . . 275 About the Fisher Exact Test . . . . . . . . . . . . . . . . . . . . . 275 Performing a Fisher Exact Test . . . . . . . . . . . . . . . . . . . . 276 Running a Fisher Exact Test . . . . . . . . . . . . . . . . . . . . . 277 Interpreting Results of a Fisher Exact Test . . . . . . . . . . . . . . 279 McNemar’s Test . . . . . . . . . . . . . . . . . . . . . . . . . . . 281 About McNemar’s Test . . . . . . . . . . . . . . . . . . . . . . . . 281 Performing McNemar’s Test . . . . . . . . . . . . . . . . . . . . . 282 Arranging McNemar Test Data . . . . . . . . . . . . . . . . . . . . 282 ix Setting McNemar’s Options . . . . . . . . . . . . . . . . . . . . .284 Running McNemar’s Test . . . . . . . . . . . . . . . . . . . . . . .285 Interpreting Results of McNemar’s Test . . . . . . . . . . . . . . .286 Relative Risk Test . . . . . . . . . . . . . . . . . . . . . . . . . . .288 About the Relative Risk Test . . . . . . . . . . . . . . . . . . . . .288 Performing the Relative Risk Test . . . . . . . . . . . . . . . . . .289 Arranging Relative Risk Test Data . . . . . . . . . . . . . . . . . .289 Setting Relative Risk Test Options . . . . . . . . . . . . . . . . . .290 Running the Relative Risk Test . . . . . . . . . . . . . . . . . . . .291 Interpreting Results of the Relative Risk Test . . . . . . . . . . . .293 Odds Ratio Test . . . . . . . . . . . . . . . . . . . . . . . . . . . .295 About the Odds Ratio Test . . . . . . . . . . . . . . . . . . . . . .295 Performing the Odds Ratio Test . . . . . . . . . . . . . . . . . . .296 Arranging Odds Ratio Test Data . . . . . . . . . . . . . . . . . . .296 Setting Odds Ratio Test Options . . . . . . . . . . . . . . . . . . .297 Running the Odds Ratio Test . . . . . . . . . . . . . . . . . . . . .298 Interpreting Results of the Odds Ratio Test . . . . . . . . . . . . . .300 Prediction and Correlation 303 About Regression . . . . . . . . . . . . . . . . . . . . . . . . . . .304 Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .305 Data Format for Regression and Correlation . . . . . . . . . . . . .305 Simple Linear Regression . . . . . . . . . . . . . . . . . . . . . . .306 About the Simple Linear Regression . . . . . . . . . . . . . . . . .306 Performing a Linear Regression . . . . . . . . . . . . . . . . . . .307 Arranging Linear Regression data . . . . . . . . . . . . . . . . . .307 Setting Linear Regression Options . . . . . . . . . . . . . . . . . .307 Running a Linear Regression . . . . . . . . . . . . . . . . . . . . .315 x Interpreting Simple Linear Regression Results . . . . . . . . . . . . 316 Simple Linear Regression Report Graphs . . . . . . . . . . . . . . 325 Multiple Linear Regression . . . . . . . . . . . . . . . . . . . . . . 325 About the Multiple Linear Regression . . . . . . . . . . . . . . . . 326 Performing a Multiple Linear Regression . . . . . . . . . . . . . . 327 Setting Multiple Linear Regression Options . . . . . . . . . . . . . 327 Running a Multiple Linear Regression . . . . . . . . . . . . . . . . 336 Interpreting Multiple Linear Regression Results . . . . . . . . . . . 338 Multiple Linear Regression Report Graphs . . . . . . . . . . . . . . 347 Multiple Logistic Regression . . . . . . . . . . . . . . . . . . . . . 348 About the Multiple Logistic Regression . . . . . . . . . . . . . . . 349 Performing a Multiple Logistic Regression . . . . . . . . . . . . . 349 Arranging Multiple Logistic Regression Data . . . . . . . . . . . . 350 Setting Multiple Logistic Regression Options . . . . . . . . . . . . 350 Running a Multiple Logistic Regression . . . . . . . . . . . . . . . 359 Interpreting Multiple Logistic Regression Results . . . . . . . . . . 360 Polynomial Regression . . . . . . . . . . . . . . . . . . . . . . . . 369 About the Polynomial Regression . . . . . . . . . . . . . . . . . . 369 Performing a Polynomial Regression . . . . . . . . . . . . . . . . . 370 Arranging Polynomial Regression Data . . . . . . . . . . . . . . . 370 Setting Polynomial Regression Options . . . . . . . . . . . . . . . 371 Running a Polynomial Regression . . . . . . . . . . . . . . . . . . 378 Interpreting Incremental Polynomial Regression Results . . . . . . 379 Interpreting Order Only Polynomial Regression Results . . . . . . . 382 Polynomial Regression Report Graphs . . . . . . . . . . . . . . . . 387 Stepwise Linear Regression . . . . . . . . . . . . . . . . . . . . . 387 About Stepwise Linear Regression . . . . . . . . . . . . . . . . . . 388 Performing a Stepwise Linear Regression . . . . . . . . . . . . . . 389 Arranging Stepwise Regression Data . . . . . . . . . . . . . . . . . 390 Setting Forward Stepwise Regression Options . . . . . . . . . . . . 390 Setting Backward Stepwise Regression Options . . . . . . . . . . . 401 xi Running a Stepwise Regression . . . . . . . . . . . . . . . . . . . .412 Interpreting Stepwise Regression Results . . . . . . . . . . . . . . .413 Stepwise Regression Report Graphs. . . . . . . . . . . . . . . . . 423 Best Subsets Regression . . . . . . . . . . . . . . . . . . . . . . .424 About Best Subset Regression . . . . . . . . . . . . . . . . . . . .424 "Best" Subsets Criteria . . . . . . . . . . . . . . . . . . . . . . . .425 Performing a Best Subset Regression . . . . . . . . . . . . . . . . .425 Arranging Best Subset Regression Data . . . . . . . . . . . . . . .426 Setting Best Subset Regression Options . . . . . . . . . . . . . . .426 Running a Best Subset Regression . . . . . . . . . . . . . . . . . .429 Interpreting Best Subset Regression Results . . . . . . . . . . . . .430 Pearson Product Moment Correlation . . . . . . . . . . . . . . . . .433 About the Pearson Product Moment Correlation Coefficient . . . . .434 Computing the Pearson Product Moment Correlation Coefficient . .434 Running a Pearson Product Moment Correlation . . . . . . . . . . .435 Interpreting Pearson Product Moment Correlation Results . . . . . .436 Pearson Product Moment Correlation Report Graph . . . . . . . . .437 Spearman Rank Order Correlation . . . . . . . . . . . . . . . . . .438 About the Spearman Rank Order Correlation Coefficient . . . . . .438 Computing the Spearman Rank Order Correlation Coefficient . . . .438 Arranging Spearman Rank Order Correlation Coefficient Data . . .439 Running a Spearman Rank Order Correlation . . . . . . . . . . . .439 Interpreting Spearman Rank Correlation Results . . . . . . . . . . .440 Spearman Rank Order Correlation Report Graph . . . . . . . . . . .441 Survival Analysis 443 Three Survival Tests. . . . . . . . . . . . . . . . . . . . . . . . . 443 Two Multiple Comparison Tests . . . . . . . . . . . . . . . . . . .444 xii

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SigmaPlot uses the Kolmogorov-Smirnov test (with Lilliefors’ correction) to test data for normality of the estimated underlying population.
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SigmaPlot uses the Kolmogorov-Smirnov test (with Lilliefors’ correction) to test data for normality of the estimated underlying population.

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