Statistical methods:
Gespeichert in:
1. Verfasser: | |
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Format: | Buch |
Sprache: | English |
Veröffentlicht: |
New York
Holt, Rinehart & Winston
1967
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Ausgabe: | 2. ed. |
Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | XVI, 462 S. Abb. |
Internformat
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100 | 1 | |a Edwards, Allen L. |e Verfasser |4 aut | |
245 | 1 | 0 | |a Statistical methods |
250 | |a 2. ed. | ||
264 | 1 | |a New York |b Holt, Rinehart & Winston |c 1967 | |
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Datensatz im Suchindex
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adam_text | IMAGE 1
CONTENTS
PREFACE VII
1. MEASURES OF CENTRAL TENDENCY AND VARIABILITY 1
1.1 INTRODUCTION 1
1.2 A PROBLEM IN LEARNING 1
1.3 A LEARNING EXPERIMENT 2
1.4 THE RANGE AS A MEASURE OF VARIABILITY 3
1.5 THE ARITHMETIC MEAN AND THE DIFFERENCE BETWEEN TWO MEANS 5
1.6 THE AVERAGE DEVIATION AS A MEASURE OF VARIABILITY 7 1.7 THE VARIANCE
AND STANDARD DEVIATION AS MEASURES OF VARIABILITY 8
1.8 THE MEDIAN AS A MEASURE OF CENTRAL TENDENCY 10 1.9 THE
SEMI-INTERQUARTILE RANGE 13
1.10 OTHER MEASURES OF CENTRAL TENDENCY AND VARIABILITY 14 1.11 SAMPLES
AND STATISTICS 15
1.12 A PROOF CONCERNING THE SUM OF SQUARED DEVIATIONS FROM THE MEAN 16
1.13 A NOTE TO THE STUDENT 16
EXAMPLES 17
2. SIMPLIFYING STATISTICAL COMPUTATIONS 21
2.1 INTRODUCTION 21
2.2 THE APPROXIMATE NATURE OF MEASUREMENTS 21
2.3 SIGNIFICANT FIGURES 22
2.4 ROUNDING NUMBERS 23
2.5 RAW SCORE FORMULA FOR THE SUM OF SQUARES 24
2.6 SUBTRACTION OF A CONSTANT 25
2.7 DIVIDING BY A CONSTANT 26
2.8 GROUPING MEASURES INTO CLASSES OR INTERVALS 28
2.9 NUMBER OF CLASSES OR INTERVALS 29
IMAGE 2
2.10 SIZE OF THE CLASS INTERVAL 29
2.11 LIMITS OF THE INTERVALS 29
2.12 TALLYING THE SCORES 30
2.13 ASSUMPTIONS CONCERNING GROUPED MEASURES 31
2.14 CODING THE MID-POINTS 31
2.15 CALCULATION OF THE MEAN 32
2.16 CALCULATION OF THE STANDARD DEVIATION 33
2.17 SUBTRACTING A CONSTANT OTHER THAN THE MID-POINT OF THE LOWEST
INTERVAL 34
2.18 THE CHARLIER CHECKS 34
2.19 CALCULATION OF THE MEDIAN 35
2.20 SUMMARY OF STEPS IN CODING A FREQUENCY DISTRIBUTION 36 EXAMPLES 37
3. GRAPHICAL REPRESENTATION OF FREQUENCY DISTRIBUTIONS 41 3.1
INTRODUCTION 41
3.2 THE HISTOGRAM 41
3.3 THE FREQUENCY POLYGON 44
3.4 THE CUMULATIVE-PROPORTION GRAPH 46
3.5 SKEWED DISTRIBUTIONS 48
3.6 OBTAINING CENTILES FROM A CUMULATIVE-PROPORTION GRAPH 49 3.7 THE
NORMAL DISTRIBUTION 50
3.8 COMPARING DIFFERENT DISTRIBUTIONS GRAPHICALLY 53
EXAMPLES 57
4. STANDARD SCORES AND NORMALIZING DISTRIBUTIONS 60
4.1 STANDARD SCORES 60
4.2 COMBINING SCORES FROM DIFFERENT TESTS 62
4.3 TRANSFORMED STANDARD SCORES 64
4.4 NORMALIZING A DISTRIBUTION OF SCORES 65
4.5 T SCORES 69
4.6 NORMALIZING RANKED DATA 70
EXAMPLES 71
5. LINEAR REGRESSION 74
5.1 INTRODUCTION 74
5.2 EQUATION OF A STRAIGHT LINE 74
5.3 THE GRAPH OF Y = A + BX 76
5.4 THE SLOPE AND INTERCEPT OF THE LINE 77
5.5 POSITIVE AND NEGATIVE RELATIONSHIPS 77
5.6 FINDING A LINE OF BEST FIT 78
5.7 METHOD OF LEAST SQUARES 80
5.8 THE SUM OF PRODUCTS 81
IMAGE 3
5.9 THE RESIDUAL SUM OF SQUARES 82
5.10 THE RESIDUAL VARIANCE AND STANDARD ERROR OF ESTIMATE 84 5.11 THE
POWER CURVE 85
5.12 THE EXPONENTIAL CURVE 88
5.13 THE LOGARITHMIC CURVE 91
EXAMPLES 93
6. THE PRODUCT-MOMENT CORRELATION COEFFICIENT 97
6.1 INTRODUCTION 97
6.2 THE CORRELATION COEFFICIENT 98
6.3 FORMULAS FOR THE CORRELATION COEFFICIENT 101
6.4 THE REGRESSION OF Y ON X 103
6.5 THE STANDARD ERROR OF ESTIMATE: S Y . X 104
6.6 THE REGRESSION OF X ON Y 106
6.7 CORRELATION AND REGRESSION COEFFICIENTS 107
6.8 THE RESIDUAL SUM OF SQUARES 109
6.9 COEFFICIENTS OF DETERMINATION AND NONDETERMINATION 110 6.10 THE
DIFFERENCE FORMULA FOR R 111
6.11 CALCULATION OF R WHEN N IS LARGE 112
EXAMPLES 116
7. POINT COEFFICIENTS AND OTHER MEASURES OF ASSOCIATION 1 22 7.1
INTRODUCTION 122
7.2 THE POINT BISERIAL COEFFICIENT OF CORRELATION: R PB 123
7.3 THE PHI COEFFICIENT: ^ 126
7.4 THE BISERIAL COEFFICIENT OF CORRELATION :R B 128
7.5 THE TETRACHORIC CORRELATION COEFFICIENT: R, 131
7.6 THE RANK CORRELATION COEFFICIENT: R 133
7.7 THE CORRELATION RATIO: R YX 136
7.8 PROPERTIES OF THE CORRELATION RATIO 139
7.9 THE CORRELATION RATIO AND CORRELATION COEFFICIENT 141 EXAMPLES 142
8. SETS, SAMPLE SPACES, AND RANDOM VARIABLES 149
8.1 INTRODUCTION 149
8.2 SETS AND OPERATIONS ON SETS 151
8.3 SAMPLE SPACES, PROBABILITY, AND EVENTS 153
8.4 THE PROBABILITY OF E X U E 2 WHEN , N 2 = P 155
8.5 THE PROBABILITY OF E X U E 2 WHEN , N 2 I I^ 155
8.6 INDEPENDENT EVENTS 156
8.7 NONINDEPENDENT EVENTS: CONDITIONAL PROBABILITIES 157 8.8
BAYES THEOREM 159
8.9 MEAN AND VARIANCE OF A DISCRETE RANDOM VARIABLE 160
IMAGE 4
8.10 INDEPENDENT RANDOM VARIABLES 162
8.11 THE COVARIANCE 164
8.12 THE SUM OF N RANDOM VARIABLES 165
8.13 THE DIFFERENCE BETWEEN TWO RANDOM VARIABLES 167 8.14 THE MEAN OF N
RANDOM VARIABLES 168
EXAMPLES 171
9. THE BINOMIAL PROBABILITY DISTRIBUTION 175
9.1 INTRODUCTION 175
9.2 THE NATURE OF BINOMIAL EXPERIMENTS 176
9.3 THE NUMBER OF PERMUTATIONS OF N OBJECTS TAKEN N AT A TIME 179
9.4 THE NUMBER OF PERMUTATIONS OF N OBJECTS TAKEN R AT A TIME 179
9.5 THE NUMBER OF PERMUTATIONS OF N OBJECTS WHEN SOME OF THE OBJECTS ARE
ALIKE 180
9.6 THE NUMBER OF COMBINATIONS OF N OBJECTS TAKEN R AT A TIME 182
9.7 A BINOMIAL EXPERIMENT WITH N = 10 TRIALS AND WITH P = 1/2 183
9.8 TYPE I AND TYPE II ERRORS AND THE POWER OF A TEST 184
9.9 THE BINOMIAL EXPANSION 187
9.10 THE STANDARD NORMAL CURVE 189
9.11 CONTINUOUS VARIABLES AND PROBABILITIES 191
9.12 THE MEAN AND VARIANCE OF THE BINOMIAL DISTRIBUTION AND OF T 192
9.13 THE NORMAL APPROXIMATION OF THE PROBABILITY DISTRIBU- TION OF T 193
EXAMPLES 196
1 0. THE T TEST FOR MEANS 200
10.1 SELECTING A RANDOM SAMPLE 200
10.2 THE STANDARD ERROR OF THE MEAN OF A RANDOM SAMPLE 202 10.3 UNBIASED
ESTIMATES OF YU. A 2 , AND 7JF 2 204
10.4 THE T DISTRIBUTION 206
10.5 CONFIDENCE INTERVAL FOR THE MEAN 207
10.6 THE T TEST FOR THE DIFFERENCE BETWEEN TWO MEANS 209
10.7 CONFIDENCE INTERVAL FOR THE DIFFERENCE BETWEEN TWO MEANS 212
10.8 FAILURE TO REJECT A GIVEN NULL HYPOTHESIS 212
10.9 HOMOGENEITY OF TWO VARIANCES 213
IMAGE 5
CONTENTS XIII
10.10 VIOLATIONS OF ASSUMPTIONS OF THE T TEST 214
10.11 THE T TEST FOR PAIRED OBSERVATIONS 215
EXAMPLES 220
11. ONE-SIDED AND TWO-SIDED TESTS AND THE POWER OF TESTS 226 11.1 THE
TWO-SIDED TEST: /I 1 = N 2 226
11.2 ONE-SIDED TESTS: ^ I 2 AND HI ^ HI 227
11.3 THE POWER OF THE TWO-SIDED TEST: ^ = /I 2 229
11.4 POWER OF THE ONE-SIDED TEST OF N L I 2 232
11.5 POWER OF THE ONE-SIDED TEST OF M HZ 235
11.6 A COMPARISON OF A ONE- AND A TWO-SIDED TEST WHEN H I FI 2 236
11.7 ONE- AND TWO-SIDED TESTS: GENERAL CONSIDERATIONS 238 11.8
ESTIMATING THE NUMBER OF OBSERVATIONS NEEDED IN AN EX- PERIMENT 239
EXAMPLES 243
1 2. SIGNIFICANCE TESTS FOR CORRELATION AND REGRESSION COEFFICIENTS 245
12.1 INTRODUCTION 245
12.2 TESTING THE NULL HYPOTHESIS THAT P = 0 246
12.3 THE Z TRANSFORMATION FOR R 248
12.4 THE SIGNIFICANCE OF THE DIFFERENCE BETWEEN TWO R S 250 12.5 TESTING
THE NULL HYPOTHESIS THAT J3 Y = 0 252
12.6 THE SIGNIFICANCE OF THE DIFFERENCE BETWEEN TWO REGRESSION
COEFFICIENTS 253
EXAMPLES 255
13. THE ANALYSIS OF VARIANCE: RANDOMIZED GROUP DESIGN 257 13.1
INTRODUCTION 257
13.2 SUMS OF SQUARES AND MEAN SQUARES 258
13.3 EXPECTED VALUE OF MS T WITH NO TREATMENT EFFECTS 262 13.4 EXPECTED
VALUE OF MS T WITH TREATMENT EFFECTS 263 13.5 THE TEST OF SIGNIFICANCE
264
13.6 THE S -METHOD FOR TESTING THE DIFFERENCE BETWEEN ANY TWO MEANS 265
13.7 COMPARISONS ON A SET OF & MEANS 267
13.8 THE STANDARD ERROR OF A COMPARISON 268
13.9 THE CASE OF K = 2 TREATMENTS 269
13.10 VIOLATIONS OF THE ASSUMPTIONS OF THE FTEST 270 EXAMPLES 271
IMAGE 6
14. TWO-FACTOR EXPERIMENTS 274
14.1 INTRODUCTION 274
14.2 NOTATION FOR A TWO-FACTOR EXPERIMENT 275
14.3 THE ANALYSIS OF VARIANCE FOR A TWO-FACTOR EXPERIMENT 277 14.4
COMPARISONS ON THE TREATMENT SUMS 278
14.5 ORTHOGONAL COMPARISONS 281
14.6 COMPARISONS ON THE TREATMENT MEANS 281
14.7 PROOF THAT T 2 = F 282
14.8 THE MEANING OF A TWO-FACTOR INTERACTION EFFECT 282 14.9 ORTHOGONAL
COMPARISONS: A SPECIFIC EXAMPLE 284 14.10 ADDITIONAL SETS OF MUTUALLY
ORTHOGONAL COMPARISONS 284 14.11 GENERAL EQUATIONS FOR THE SUMS OF
SQUARES IN A TWO-
FACTOR EXPERIMENT 286
EXAMPLES 290
1 5. EXPERIMENTS CONCERNED WITH CHANGE IN PERFORMANCE OVER TRIALS 293
15.1 INTRODUCTION 293
15.2 THE ANALYSIS OF VARIANCE WITH S = 5 SUBJECTS AND T = 3 TRIALS 293
15.3 SUMS OF SQUARES AND MEAN SQUARES IN THE ANALYSIS OF VARIANCE 296
15.4 ASSUMPTIONS INVOLVED IN THE TEST OF SIGNIFICANCE 300 15.5 LINEAR
AND QUADRATIC COMPONENTS OF THE TRIAL SUM OF SQUARES 301
15.6 SIGNIFICANCE OF THE LINEAR COMPONENT FOR THE DATA OF TABLE 15.1 302
15.7 AN EXAMPLE WITH S = 10 SUBJECTS AND T = 4 TRIALS 304
15.8 TEST OF SIGNIFICANCE OF DEVIATIONS FROM LINEAR REGRESSION 305 15.9
ANOTHER EXAMPLE WITH S = 10 SUBJECTS AND T = 4 TRIALS 306 15.10 AN
EXPERIMENT INVOLVING A TREATMENT FACTOR 308
15.11 THE SIGNIFICANCE OF THE LINEAR COMPONENT OF THE TRIAL SUM OF
SQUARES 313
15.12 THE TEST OF SIGNIFICANCE OF THE LINEAR COMPONENT OF THE A X T SUM
OF SQUARES 314
15.13 THE TEST OF SIGNIFICANCE OF THE QUADRATIC COMPONENT OF THE A X T
SUM OF SQUARES 316
15.14 VIOLATIONS OF ASSUMPTIONS AND CONSERVATIVE F TESTS 317 15.15 A
CONSERVATIVE TEST FOR CASE I 318
15.16 CONSERVATIVE F TESTS FOR CASE II 319
EXAMPLES 319
IMAGE 7
16. THE X TEST OF SIGNIFICANCE 323
16.1 INTRODUCTION 323
16.2 THE X 2 TEST WITH C = 2 CATEGORIES 324
16.3 THE RELATIONSHIP BETWEEN Z 2 AND % 2 WITH 1 DEGREE OF FREEDOM 325
16.4 THE DISTRIBUTION OF F 326
16.5 THE X 2 TEST WITH C = 3 CATEGORIES 327
16.6 THE X 2 TEST FOR A N R XC CONTINGENCY TABLE 328
16.7 THE X 2 TEST FOR THE CONTINGENCY COEFFICIENT: C 331
16.8 THE X 2 TEST FOR THE PHI COEFFICIENT: R^ 332
16.9 CORRECTION FOR DISCONTINUITY 333
16.10 SMALL EXPECTED NUMBERS 333
16.11 THE MEDIAN TEST 334
16.12 THE MEDIAN TEST AS A SUBSTITUTE FOR THE / AND F TESTS 337 EXAMPLES
337
17. RANK ORDER STATISTICS AND TESTS OF SIGNIFICANCE 342
17.1 SIGNIFICANCE OF THE RANK CORRELATION: R 342
17.2 KENDALL S COEFFICIENT OF CONCORDANCE: W 344
17.3 CALCULATION OF THE SUMS OF SQUARES FOR AN M X N TABLE OF RANKS 348
17.4 SIGNIFICANCE TEST OF W CORRECTED FOR DISCONTINUITY 350 17.5 THE F
TEST FOR W 351
17.6 THE X 2 TEST FOR W 351
17.7 THE AVERAGE VALUE OF THE M(M - 1) VALUES OF R 352
17.8 THE RELIABILITY OF THE AVERAGE RANKS ASSIGNED TO N OBJECTS 352
17.9 A RANK TEST FOR THE DIFFERENCE BETWEEN TWO GROUPS 353 17.10 SUMMARY
OF STEPS IN THE RANK TEST FOR THE DIFFERENCE BETWEEN TWO GROUPS 355
17.11 THE STANDARD NORMAL CURVE APPROXIMATION FOR THE RANK TEST 356
17.12 CORRECTION FOR DISCONTINUITY FOR THE RANK TEST 358
17.13 ACCURACY OF THE STANDARD NORMAL CURVE APPROXIMATION 359 17.14 THE
KRUSKAL-WALLIS H TEST FOR MORE THAN TWO GROUPS 359 17.15 THE
KRUSKAL-WALLIS TEST AND WHITE S TEST FOR K = 2 GROUPS 361
17.16 THE WILCOXON TEST FOR PAIRED OBSERVATIONS 362
17.17 CORRECTIONS FOR TIED RANKS 364
EXAMPLES 367
IMAGE 8
REFERENCES
375
GLOSSARY
APPENDIX A. A REVIEW OF SOME ELEMENTARY MATHEMATICAL RULES AND
PRINCIPLES
ORDER OF OPERATIONS AND SYMBOLS OF GROUPING OPERATIONS WITH ZERO
OPERATIONS WITH RADICALS EXPONENTS LOGARITHMS SUMMATION
EQUATIONS
TABLES TABLE OF RANDOM NUMBERS TABLE OF SQUARES, SQUARE ROOTS, AND
RECIPROCALS OF NUMBERS FROM 1 TO 1000
AREAS AND ORDINATES OF THE NORMAL CURVE IN TERMS OF XJA TABLE OF X 2
TABLE OF T
VALUES OF THE CORRELATION COEFFICIENT FOR VARIOUS LEVELS OF SIGNIFICANCE
TABLE OF Z VALUES FOR R , THE 5 AND 1 PERCENT POINTS FOR THE
DISTRIBUTION OF F
TABLE OF FOUR-PLACE LOGARITHMS VALUES OF ESTIMATED R, BASED UPON
PEARSON S COSINE BE
APPENDIX B. TABLE TABLE
TABLE
TABLE TABLE TABLE
TABLE TABLE TABLE TABLE
TABLE TABLE TABLE
TABLE TABLE
I. II.
III.
IV. V. VI.
VII. VIII IX.
X.
XI. XII. XIII
XIV XV.
METHOD, FOR VARIOUS VALUES OF AD
TABLE OF T SCORES T SCORES CORRESPONDING TO RANKS VALUES OF THE RANK
CORRELATION COEFFICIENT R AT SELECTED SIGNIFICANCE POINTS THE 5 AND 1
PERCENT POINTS FOR THE DISTRIBUTION OF W
VALUES OF T AND T , WHICHEVER IS THE SMALLER, SIG- NIFICANT AT THE 5 AND
1 PERCENT LEVELS
APPENDIX C. ANSWERS TO THE EXAMPLES
INDEX OF NAMES
SUBJECT INDEX
381
385
385 386 386 387 388 391
393
395
396
401
414 424 425
426 427 428 432
434
435 436
437 438
439
441
455
457
|
any_adam_object | 1 |
author | Edwards, Allen L. |
author_facet | Edwards, Allen L. |
author_role | aut |
author_sort | Edwards, Allen L. |
author_variant | a l e al ale |
building | Verbundindex |
bvnumber | BV002897815 |
callnumber-first | H - Social Science |
callnumber-label | HA29 |
callnumber-raw | HA29 |
callnumber-search | HA29 |
callnumber-sort | HA 229 |
callnumber-subject | HA - Statistics |
classification_rvk | CM 4000 MR 2100 QH 231 SK 840 |
ctrlnum | (OCoLC)312136 (DE-599)BVBBV002897815 |
dewey-full | 311 |
dewey-hundreds | 300 - Social sciences |
dewey-ones | 311 - [Unassigned] |
dewey-raw | 311 |
dewey-search | 311 |
dewey-sort | 3311 |
dewey-tens | 310 - Collections of general statistics |
discipline | Soziologie Psychologie Mathematik Wirtschaftswissenschaften |
edition | 2. ed. |
format | Book |
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genre | 1\p (DE-588)4151278-9 Einführung gnd-content |
genre_facet | Einführung |
id | DE-604.BV002897815 |
illustrated | Illustrated |
indexdate | 2024-07-09T15:50:31Z |
institution | BVB |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001814610 |
oclc_num | 312136 |
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psigel | TUB-nveb |
publishDate | 1967 |
publishDateSearch | 1967 |
publishDateSort | 1967 |
publisher | Holt, Rinehart & Winston |
record_format | marc |
spelling | Edwards, Allen L. Verfasser aut Statistical methods 2. ed. New York Holt, Rinehart & Winston 1967 XVI, 462 S. Abb. txt rdacontent n rdamedia nc rdacarrier Statistique Statistische methoden gtt Statistik Statistics Methode (DE-588)4038971-6 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Statistik (DE-588)4056995-0 s Methode (DE-588)4038971-6 s DE-604 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001814610&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
spellingShingle | Edwards, Allen L. Statistical methods Statistique Statistische methoden gtt Statistik Statistics Methode (DE-588)4038971-6 gnd Statistik (DE-588)4056995-0 gnd |
subject_GND | (DE-588)4038971-6 (DE-588)4056995-0 (DE-588)4151278-9 |
title | Statistical methods |
title_auth | Statistical methods |
title_exact_search | Statistical methods |
title_full | Statistical methods |
title_fullStr | Statistical methods |
title_full_unstemmed | Statistical methods |
title_short | Statistical methods |
title_sort | statistical methods |
topic | Statistique Statistische methoden gtt Statistik Statistics Methode (DE-588)4038971-6 gnd Statistik (DE-588)4056995-0 gnd |
topic_facet | Statistique Statistische methoden Statistik Statistics Methode Einführung |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001814610&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
work_keys_str_mv | AT edwardsallenl statisticalmethods |