Basic Statistical Analysis

Transcription

1 indexerrt.qxd 8/21/2002 9:47 AM Page 1 Corrected index pages for Sprinthall Basic Statistical Analysis Seventh Edition

2 indexerrt.qxd 8/21/2002 9:47 AM Page 656 Index Abscissa, 24 AB-STAT, vii ADD-OR rule, and probability, 126 After-only design, Alpha level, confidence levels and, increasing, 256 levels of, Alternative hypothesis (Ha), 156, 242 one-tail, 249 for t test, 242 Analysis of variance (ANOVA) advantages of, applications, between-group variability, 332 experimental research, 330 factorial ANOVA, 331 Friedman ANOVA by ranks, null hypothesis and, 315 one-way F ratio, post-facto research, 331 significant interaction, 332 sum of squares, Tukey s HSD, , 444 two-way ANOVA, , A priori hypothesis, 357 Association research, 270 Association (See Correlation) Averages, law of, 120 Bar graphs, Before-after (B/A) design (See also Repeated Measures) and paired t ratio and within-subjects F ratio, experimental research, 199, problems of, Beta coefficient, 396 Beta level, power of statistical test, 254 Between-group variability, 332 Between-Subjects Experimental Design, Bias political polling, sampling, 141 Bimodal distributions, Binomial distribution compared to normal distributions, 560 continuous distributions, 559 discrete distributions, 559 Binomial probability, 557 Binomial proportions, 564 z test and, 564 Bivariate scatter plot, regression equation, regression line, Bonferroni test, 315 Canonical correlation, 416 Categorical Data (See also nominal data), 195 Cause and effect cause, problems isolating, 271 correlation and, 273, 277 as trap in research, Ceiling effect, 209 Census, 136 Central limit theorem, 151 Central tendency, measures of mean, median, mode, Chance defying chance, 174 frequency expected due to, 355 laws of, Chance hypothesis (See Null hypothesis) Chi square and proportions, 567 coefficient of contingency, dependent samples and, locating differences and, 364 McNemar test, by k Chi square (goodness of fit), 356 percentages and, 367 requirements for, in research simulations, , 538, 551, 552 r k chi square, chi square, 362, 365, 367 z score and, 368 Coefficient of contingency, limitations, 373 nominal data, 371 Coefficient of determination, 287 Collinearity, 411 Combination research, 215 Combinations and probability, Computers bugs in software, 521 caution, words of, 524 common problems, computer literacy, logic checkpoints, 524 types of statistical programs, 518 Concurrent validity, 491 Conditional probability, 118 Confidence intervals, , for differences between independent samples, 245 for paired differences, 434 long run and, 182 precision and, 180 single sample t and, 183 standard error of estimate and, two-sample t and, 245 Confidence levels, alpha and, Confounding variables, 217 Constants, nature of, Construct validity, 495 Continuous distributions, 559 Control Groups repeated-measures design, 205 change in, experimental research, 199, failure to use, examples, inadequate group, examples, paired t, Correlated samples problems of, 436 Correlation (See also Regression analysis) cause and effect, , 278 coefficient of, , 300 decision about choosing/using tests, interclass and intraclass,

3 indexerrt.qxd 8/21/2002 9:47 AM Page 657 Index 657 interpreting values, 276 negative correlations, 274, 277, 279 Pearson r, 273 positive correlations, 274, 277, 278 scatter plots and, significance, Spearman, 293 Spearman-Brown, 481 zero correlations, 274, 277 Correlation matrix, 291 Correlation strength (See also Test reliability) determination of, 287 Covariate, 412 Cox, Gertrude, Criterion referencing, 489 and reliability, 477 Cronbach s alpha, 487 Cyril Hoyt reliability method, 488 Curve (See also Distributions; Normal curve) leptokurtic, 58 mesokurtic, 58 platykurtic, 58 Data categorical data, 195 interval data, measurement data, nominal data, ordinal data, 196 ranked data, 196 ratio data, 197 Deciles, 48 Degrees of freedom chi square, 356, k chi square (goodness of fit), 356 paired t ratio, r k chi square (r by k), 358 sum of squares, 322 t ratio, , Dependent (correlated) selection, 427 Dependent samples, chi square and, Dependent Variables, Descriptive statistics, Deviation method, standard deviation, Deviation score, 50 Difference chi square and, 364 distribution of differences, Difference, hypothesis of alpha and confidence levels, 245 estimated standard error of, 233 experimental research and, 214 post-facto research and, 214 power, 254 sample groups, independent vs. correlated, significance, 239 t ratio, , 242, 244 Discrete distributions, 559 Discriminant analysis, 343 Dispersion (See Variability) Distribution free tests (See Nonparametric tests) Distribution of differences, mean of, null hypothesis, standard deviation of, two populations, 232 Distributions bimodal distributions, binomial distributions, of differences, frequency distributions, skewed distributions, 33 36, unimodal distribution, 38 Double-blind research, Effect Size, 222 chi square, 374 factorial ANOVA, 331 one-way ANOVA, 327 paired t, single-sample t, 178 two-sample t, 255 within subjects ANOVA, 444 Error, meaning in statistics, (See also Specific types of errors) Estimated standard deviation, calculation of, Estimated standard error of difference, paired t ratio, corrected equation for, 429 Estimated standard error of the mean, Eta square, 327, 338, 339 Exit polling, 145 Experimental research, 190, 199, 202 between-subjects, analysis of variance (ANOVA), repeated-measures design, combination research, control groups, , 210 dependent selection, double-blind research, equivalent groups, creating, 202 experimental group, hypothesis of difference and, 229 matched-group design, 211 matched-subjects design, , quasi-experimental design, 212 randomized assignments, 203 random samples, repeated measures design, 429 representative sampling, 138 research simulations, validity, external/internal, 202 External Validity, 202 Face validity, 490 Factor, nature of, 332 Factorial ANOVA, 331 between-group variability, 332 calculations, compared to within-subjects F ratio, graphs and, in research simulations, 541 theory of, 331 Fisher, Sir Ronald, 316 Floor effect, 210 F ratio requirements, 327 in research simulations, 538, 541, 552, 553 sum of squares, within-subjects F ratio, Frequency distribution curve, 66 Frequency of distributions, Frequency of Error, Law of, Frequency polygons, Friedman ANOVA by ranks, calculations, in research simulations, 542 sample size, 156, 467 Frustration-regression hypothesis, research design, F table, one-way F ratio, 327 Gallup poll, 144 Galton, Sir Francis, 151, 276, Gambler s fallacy, Gauss, Karl Friedrich, 70 Goodness of fit (See 1 k chi square) Gossett, William Sealy, 16, 240 Grade-equivalent scores (GEs), 108 Graphs correlations and, 277 factorial ANOVA, 331 frequency distributions, frequency polygons, histograms, scatter plot, variability and, zero as base of ordinate, Grouped-data techniques, Guilford, J.P., 287 Halo effect, Hawthorne effect, 207 Histograms, Homogeneity of variance, 327 Homoscedasticity, 292 Honestly Significant Difference test (See Tukey s HSD) Hypothesis, types for statistical testing, 531 Independent variables, Inferential statistics, 18 (See also Parameter estimates) key concepts in, Informed consent, 215 Interaction effects, 332 Interdecile range, 50 Interval data, Interval estimate, , confidence interval, , Interval scale,

4 indexerrt.qxd 8/21/2002 9:47 AM Page Index Item analysis, 496 item difficulty, item discrimination, 497 Kruskal-Wallis H test, calculation, sample size, 462 Kuder-Richardson (K-R 21) reliability, 483 Kurtosis, /6 rule, 59 standard deviation/range relationship, Law of averages, 120 Law of Frequency of Error, Laws of chance, 120 Leptokurtic curve, 58 Levene s test for equality of variances, 631 Linearity, 404 Literary Digest poll, Long-run relative frequency, 115, 118 Lovelace, Ada, 520 McNemar test, dependent samples, matched-subjects design, 370 in research simulations, 540 Yates correction, 371 Manipulated independent variable, MANOVA, 343 Mann-Whitney U, calculations, interpretation, 460 in research simulations, 543 sample size, 460 Matched-subjects (M/S) design (See also Paired t ratio; Withinsubjects F ratio) experimental research, McNemar test, paired t ratio, problems of, Maximum correlation (test and criterion), Mean, calculation, confidence interval, distribution of differences, of distribution of means, formula, interpretation, 31 skewed distribution, standard error of, from z score, Mean square, sum of squares, 322 Measurement, nature of, Measurement data, Measurement scaling, interval scale, nominal scale, ordinal scale, 196 ratio scale, 197 Measurement theory, 194 Median (Mdn), calculation, 35 skewed distributions, 36 Mere presence phenomenon, 364 Mesokurtic curve, 58 Meta-analysis, Minimum difference for t ratio, 248 Mode (Mo), bimodal distributions, finding modes, interpretation, unimodal distributions, 38 MULT-AND rule and probability, Multiple R, components of, equation for, 406 multiple regression, in research simulations, 546 Negative correlations, 274, 277, 279 Nominal data, (See also Chi square) coefficient of contingency, Nominal scale, Nonparametric tests (See also Chi square) advantages/disadvantages of, 467 Friedman ANOVA by ranks, Kruskal-Wallis H test, Mann-Whitney U, ordinal data and, Wilcoxon T test, Normal curve areas of, equation, features of, 66 68, 85 as frequency distribution curve, normal curve equivalents (NCEs), Norm referencing, 474 Null hypothesis, 156, 172, analysis of variance (ANOVA) and, 315 distribution of differences, 243 nature of, 241 for t test, 242 Pearson r, 283 Odds, 120 Oh boy! graph, 29 1 k chi square (goodness of fit), 355 calculation, 355 degrees of freedom, interpretation, 356 testing a priori hypothesis, 357 One-tail t table, , 578 advantages/disadvantages of, 251 alternative hypothesis and, 242, 249 negative t ratio, 251 sign of, 251 One-tail t test, 249 alternative hypothesis, 242, 249 One-way ANOVA (See F ratio) One-way F ratio, calculation between subjects, 325 F table, 327 requirements of, 327 summary of results, 326 Ordinal data scale, 196 (See also nonparametric tests) Spearman and, 293 Ordinate, Outliers, 141, 286 Paired t ratio, advantages of, 430 before-after design, 436 cautions about, 436 control group changes and, degrees of freedom, and matched control group, 439 power and, 435 in research simulations, 550 standard error of difference, corrected equation for 429 Parameter estimates alpha level, as hypothesis, interval estimates, point estimates, of population standard deviation, of standard error of the mean, t ratio, z scores, Parameters nature of, 137 sampling distributions, Partial correlation, 412 equation, variable or covariate identification, 412 Pascal, Blaise, 16, Path analysis, Pearson, Karl, 275, 400 Pearson r, coefficient of determination, 287 interpretation of, 287 limitations, 293 null hypothesis and, 283 Pearson r table, 283, 579 reliability, 477 requirements for, 292 restricted range, significance, , z score method, 280 Percentages chi square and, converted to probability statements, Percentile ranks, Percentiles, to raw scores, table, 91, 576 from z scores, 82 to z scores, 91 Permutations and probability, Platykurtic curve, 58 Point biserial, 498

5 indexerrt.qxd 8/21/2002 9:47 AM Page 659 Index 659 Point estimate of population mean, 168 Political polling, bias, Gallup poll, 144 Literary Digest poll, Population nature of, 139 standard deviation, Positive correlations, 274, 277, 278 Post-facto research, 190, analysis of variance (ANOVA), 331 combination research, 215 ethical issues, 214 hypothesis of association and, 270 hypothesis of difference and, 229 nature of, post-hoc fallacy, 213 research simulations, Post-hoc fallacy, 213 Power, 254, 435 paired t ratio and, 435 Power of statistical tests, 254 beta level, 254 Predictive validity, 477 Probability ADD-OR rule, 126 binomial probability, 557 combining probabilities, conditional probability, 118 gambler s fallacy, independent events and, 115 long run relative frequency, 115, 118 MULT-AND rule, versus odds, 120 percentage areas of normal curve and, percentages converted to probability statements, z scores, Proportions binomial proportions, chi square and, difference, testing, Qualitative research, 216 Quartile deviation, Quartiles, Quasi-experimental design, 212 Quota (stratified) sampling, 140 Randomized assignment, 203 Random sampling, Range (R), interdecile range, 50 interquartile range, 49 percentiles, relationship to standard deviation, restricted range, Ranked data, 196 (See also Ordinal data) Ratio data, 197 Raw scores from percentiles, from T scores, from z scores, to T scores, to z scores, Regression analysis beta coefficient, 396 bivariate scatter plot, 389 confidence interval equation, multiple R, regression equation, standard error of estimate, theory of regression, 398 Regression line, extent of scatter around, slope of, 393 Y intercept of, 392 Reliability (See Test reliability) Repeated measures design, 208 Representative sampling, 138 Research, 199 (See also Experimental research; Post-facto research) burden of proof and, 555 cause and effect trap, combination research, 215 dependent variables, experimental research, 190, 199, 202 fitting statistical test to, 256 independent variables, key characteristics, 554 post-facto research, 190, 199, qualitative, 216 simulations, variables/constants in, Research errors, case examples, confounding variables, 217 control group related, 217 halo effect, Hawthorne effect, 207 Research simulations checklist questions for, critical decision points, 532 examples of, 532 methodology, Restricted range, r k chi square (r by k), 358 calculation, contingency table, degrees of freedom, interpretation, 360 variations of, 361 Robustness, 331 Rulon formula, 503 Sample, nature of, 137 Sample size, Sample Standard deviation, calculation, Sampling bias, 141 outliers, 141 political polling, random sampling, representative sample, 138 sampling distributions, sampling error, stratified (quota) sampling, 140 Sampling distributions central limit theorem, 151 of difference, 230 infinite vs. finite sampling, mean of distribution of means, parameters, importance of, standard error of the mean, , 153 Scatter plot, 277 bivariate scatter plot, configurations, Secondary variance, 217 Significance correlation, 284 hypothesis of difference and, , 239, 242 nature of, 173 Pearson r and, , t ratio, 172 two samples, evaluating, Significant interaction, 341 Single-sample t ratio, confidence intervals and, 183 t comparison, Skewed distributions mean, 33 median, 36 skewness assessing, 42, 570 working with, 39 Spearman, Charles, 293 Spearman r, calculating for non-normal distributions of interval data, 297 calculating with interval data, 295 calculating with ordinal data, requirements for, 299 in research simulations, 537 Spearman-Brown prophecy formula, 481 Split-half reliability, 482 Squares (See Sum of squares) SPSS (statistical Analysis Package for the Social Scientist, , 586 Standard deviation, computational method, deviation method, estimated standard deviation, outliers, 141 relationship to range, sample standard deviation, unbiased estimator, 163 from z scores to, Standard error, meaning in statistics, 151 Standard error of difference, 233 Standard error of estimate, calculation, 402 confidence interval, Standard error of measurement, 500 Standard error of the mean, , 153 estimated standard error of the mean,

6 indexerrt.qxd 8/21/2002 9:47 AM Page Index Stanines, normal curve, table, z scores, Statistics nature of, 17, common stumbling blocks related to, 4 12 descriptive statistics, history of, inferential statistics, 18 Stepwise regression, 416 Stevens, S.S., 195 Stochastic model, 277 Stratified (quota) sampling, 140 Subject independent variables, 191 Sum of squares, 317, 322 components of variability, 318 computational method, converting to variance estimates, degrees of freedom, 324 F ratio, interpretation of, 321 mean square, 325 Test bias, 476 Test reliability, 477 Alternate or parallel form, 480 Correlation strength, determination of, Internal consistency, Spearman-Brown prophecy, 481 Split-half method, 482 Techniques for increasing reliability, 488 Test-retest method, 478 Test Validity, 477 Concurrent, 491 Construct, 495 Content, 491 Face, 490 Predictive, t ratio, calculation, 236 degrees of freedom, , 243, 247 equal size samples, 236 for independent samples, , 243 limitations, negative, 251 one-tail t test, 249, 251 paired t ratio, requirements for, 254 significance, 173, 239 sign of, 172, 244, 251 single-sample t ratio, 170 t comparison, 244 two samples, value of, 253 two-tail t table, 170, 243, 577 two-tail t test, 243 unequal size samples, z score and, T score applications, calculations, from raw scores, to raw scores, t table decisions about using tables, one-tail t table, , 578 two-tail t table, 170, 577 t test alternative hypothesis for, 242, 249 vs. correlation coefficient, 300 null hypothesis for, in research simulations, 536, 543 successive, drawbacks of, two-tail t test, 243 True experiment, 202, 204 Tukey s HSD, , 444 applications, calculation, , 444 interpretation, 329 within-subjects F ratio, chi square, 362, 365, 367 Yates correction, 362, 366 Two-tail t table, 170, 243, 577 sign of t ratio, 172 t comparison, 173 Two-tail t test, 243 Two-way ANOVA, , Type 1 error, , 254 (See also Alpha level) Type 2 error, 254, 435 (See also Beta level) Unbiased estimate, 163 Unimodal distributions, U test (See Mann-Whitney U test) Validity (See Test validity) Variability, measures of graphs and, 57 kurtosis, 58 range, standard deviation, variance, 54 zero, value in, Variables, confounding variables, 217 dependent variables, independent variables, Variance, 54 (See also Analysis of variance) calculation, homogeneity of variance, 327 Variance estimates, sum of squares converted to, Wilcoxon T test, procedure, in research simulations, 549 sample size, 464 Wilks Lambda, 637 Within-subjects design, 205, 441 Within-subjects F ratio, calculation, correlation within subjects, importance of, 445 compared to factorial ANOVA, 446 interpretation, 446 in research simulations, 532 Tukey s HSD, 444 Wow! graph, Yates correction, 362 McNemar test, chi square, 362 Zero correlations, 274, 277 z scores, applications, areas of normal curve, chi square and, 368 equation, to mean, parameter estimates and, Pearson r, 280 percentage rules, 86 from percentiles, to percentiles, z test,