Statistics manual: with examples taken from ordnance development
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Dover Publ.
1960
|
| Edition: | Republ. |
| Series: | Dover Books on advanced mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 288 S. Ill. |
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| 100 | 1 | |a Crow, Edwin L. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Statistics manual |b with examples taken from ordnance development |c by Edwin L. Crow ; Frances A. Davis ; Margaret W. Maxfield |
| 250 | |a Republ. | ||
| 264 | 1 | |a New York |b Dover Publ. |c 1960 | |
| 300 | |a XVII, 288 S. |b Ill. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Dover Books on advanced mathematics | |
| 650 | 7 | |a Schätztheorie |2 swd | |
| 650 | 7 | |a Testtheorie |2 swd | |
| 700 | 1 | |a Davis, Frances A. |e Verfasser |4 aut | |
| 700 | 1 | |a Maxfield, Margaret W. |e Verfasser |4 aut | |
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Record in the Search Index
| _version_ | 1804116359019233280 |
|---|---|
| adam_text | CONTENTS
Foreword iii
Introduction v
Acknowledgment viii
Chapter 1. DEFINITIONS AND DISTRIBUTIONS
1.1. Definitions 3
1.1.1. Population and Sample 3
1.1.2. Distribution 4
1.1.3. Measures of Central Location 10
a. Mean 10
b. Median 11
c. Mode 12
d. Midrange 12
1.1.4. Measures of Dispersion 12
a. Standard Deviation 12
b. Range 13
c. Mean Deviation 13
d. Various Percentile Estimates 13
e. Probable Error . . , 13
1.1.5. Coding 14
1.1.6. Sampling Distribution 14
1.1.7. Test of a Statistical Hypothesis 15
1.1.8. Level of Significance a and Types of Error . . . . 16
1.1.9. Operating Characteristic Curve 17
1.1.10. Confidence Intervals 18
1.1.11. Tolerance Intervals 18
1.1.12. Degrees of Freedom 19
1.2. Particular Distributions 19
1.2.1. Normal Distribution 19
1.2.2. Binomial Distribution 30
1.2.3. Poisson Distribution 32
Bibliography 35
xi
CONTENTS
Chapter 2. TESTS AND CONFIDENCE INTERVALS
FOR MEANS
2.0. Introduction 37
2.1. Test for Mean [i, When Standard Deviation r Is Known ... 38
2.1.1. Assumptions 38
2.1.2. Normal Test 38
a. Determination of Sample Size 40
2.1.3. Confidence Intervals 43
a. Determination of Sample Size 43
2.2. Test for /a When a Is Unknown 44
2.2.1. The I* Test 44
2.2.2. The t Test 45
a. Determination of Sample Size 46
2.2.3. Confidence Intervals 47
a. Determination of Sample Size 48
2.3. Test for Proportion p 48
2.3 1. Assumptions 49
2.3.2. Test 49
a. Test for a Sample of Size n 150 49
b. Test for a Sample of Size n 5/p0 50
I c. Determination of Sample Size 51
2.3.3. Confidence Intervals 51
a. Graphical and Tabular Solutions 51
b. Numerical Solution 52
2.4. Test for ^ — fi,2 When r1 and r2 Are Known 52
2.4.1. Test Conditions and Assumptions 52
2.4.2. Normal Test 53
a. Test for Paired Observations 53
b. Test for Two Independent Samples 53
c. Determination of Size of
Independent Samples 54
2.4.3. Confidence Intervals 55
a. Determination of Size of
Independent Samples 55
2.5. Test for ^ — /t2 When ax and r2 Are Unknown 55
2.5.1. Assumptions and Design of Experiment 55
2.5.2. Test for Paired Observations 56
a. Sign Test 56
b. The t Test on Differences 57
2.5.3. Test for Two Independent Samples When tx = r2 . . 57
a. The rd Test 57
b. The t Test 57
xii
CONTENTS
2.5.4. Test of /ij — /t2 = 0 for Two Independent Samples
When a± =£ r2 60
2.6. Test for a Difference Between Proportions, p± — p2 .... 62
2.7. Test for Differences Among Several Means 62
2.8. Detection of a Trend in a Set of Means, Standard Deviations
Unknown but Assumed Equal . . . 62
2.8.1. Assumptions 62
2.8.2. Method 63
Bibliography 64
Chapter 3. TESTS AND CONFIDENCE INTERVALS FOR
STANDARD DEVIATIONS
3.0. Introduction 67
3.1. Computation of s 68
3.2. x2 Test for o ina Normal Distribution 70
3.2.1. Assumptions 70
3.2.2. Test 70
a. Determination of Sample Size 72
3.2.3. Confidence Intervals 73
a. Determination of Sample Size 73
3.3. F Test for o^/er., for Normal Distributions 74
3.3.1. Assumptions 74
3.3.2. Test 74
a. Determination of Sample Size 77
3.3 3. Confidence Intervals 77
a. Determination of Sample Size 78
3.4. M Test for Homogeneity of Variances 78
3.4.1. Assumptions 78
3.4.2. Test 78
Bibliography 81
Chapter 4. TESTS OF DISTRIBUTIONS AS A WHOLE
AND ALLIED PROBLEMS
4.0. Introduction 83
4.1. Run Test for Randomness 83
4.2. The x2 Test for Goodness of Fit 85
4.3. Testing the Fit of a Normal Distribution 87
4.3.1. Transformations To Obtain Normality 88
4.4. Confidence Band for Cumulative Distribution 90
4.5. Sensitivity Testing 91
4.5.1. Up and Down Method 93
xiii
CONTENTS
4.6. Test for Independence in Contingency Tables 97
4.7. Consistency of Several Samples 100
4.7.1. The x2 Test 100
4.7.2. Run Test for Comparing Two Samples 101
4.8. Gross Errors 1°2
4.9. Tolerance Intervals 104
Bibliography 106
Chapter 5. PLANNING OF EXPERIMENTS AND ANALYSIS
OF VARIANCE
5.0. Introduction 109
5.1. Common Designs for Experiments Ill
5.1.1. Complete Factorial Design for Treatments 114
5.1.2. Complete Randomization for Background Conditions . 115
5.1.3. Randomized Block Design for Background Conditions . 116
5.1.4. Latin Square Design for Background Conditions . . .116
5.1.5. Other Designs 117
5.2. Types of Analysis of Variance 118
5.2.1. Type I Problems 118
5.2.2. Type II Problems 118
5.3. Assumptions of Analysis of Variance 119
5.4. One Factor Analysis 120
5.4.1. Assumptions 120
5.4.2. Analysis 122
5.5. Two Factor Analysis 127
5.5.1. Two Factor Analysis Without Replication 127
5.5.2. Two Factor Analysis With Replication 133
5.6. Multiple Factor Analysis 139
Bibliography 144
Chapter 6. FITTING A FUNCTION OF ONE OR
MORE VARIABLES
6.0. Introduction 147
6.1. Linear Regression (Two Variables) 152
6.1.1. Regression Line 152
6.1.2. Variation About the Regression Line 156
6.1.3 Fraction of y Variance Accounted for by
Regression—Correlation Coefficient r 157
xiv
CONTENTS
6.1.4. Reliability of Regression Measures .158
a. Significance of Sample Correlation Coefficient r . .159
b. Confidence Interval for Population
Correlation Coefficient p 159
c. Significance Test and Confidence Interval for the
Slope b of the Regression Line 160
d. Significance of the Difference Between the
Regression Coefficients b± and b2 of
Two Separate Equations 161
e. Confidence Interval for an Ordinate to the
True Regression Line 162
f. Prediction Interval for Individual Value of y . . .163
6.1.5. Summary of Computations for Two Variable
Linear Regression 164
6.1.6. Test for Linearity of Regression 165
6.2. Multiple Linear Regression 168
6. 2.1. Multiple Linear Equation 169
6.2.2. Determination of Partial Regression Coefficients . . . 170
6.2.3. Variation About the Regression Plane 174
6.2.4. Relative Variation (Type II Problem) 175
a. Multiple Correlation Coefficient 175
b. Partial Correlation Coefficients 176
6.2.5. Reliability of Multiple Regression Measures .... 177
a. Significance of Regression as a Whole 177
b. Significance of Multiple Correlation Coefficient . .178
c. Significance of Partial Correlation Coefficients . . .178
d. Confidence Intervals for Partial
Correlation Coefficients 179
e. Significance Tests and Confidence Intervals for
Partial Regression Coefficients 179
f. Confidence Interval for Ordinate to the
True Regression Plane 181
g. Prediction Interval for Individual Value of y . . . 182
6.3. Non Linear Regression 183
6.3.1. Polynomial Equations 185
6.3.2. Orthogonal Polynomials, When x is Equally Spaced . . 186
6.4. Planning the Experiment for Fitting a Function 191
Bibliography 193
Chapter 7. QUALITY CONTROL CHARTS
7.0. Introduction 195
7.1. Charts Using Attributes 199
xv
CONTENTS
7.2. Charts Using Variables 202
Bibliography 205
Chapter 8. ACCEPTANCE SAMPLING
8.0. Introduction 209
8.1. Attributes or Variables 210
8.2. Choice of Plan 211
8.2.1. Acceptable Quality Level (AQL) 211
8.2.2. Single, Double, or Multiple Sampling 212
8.2.3. Inspection Level 213
8.2.4. Sample Size and Severity of Inspection 214
8.2.5. Plans for Normal Inspection 215
a. Attributes 215
b. Variables 216
8.3. Operating Characteristic (OC) Curve and Its Use in
Designing Plans 217
8.4. Sequential Plans 220
8.4.1. Sequential Plan for Proportion Defective p 221
8.4.2. Sequential Plan for Standard Deviation o 224
Bibliography 225
Appendix Tables:
1. Cumulative Normal Distribution 229
2. Percentiles of the Normal Distribution 230
3. Upper Percentage Points of the / Distribution . . . .231
4. Upper Percentage Points of the x2 Distribution .... 232
5. Critical Values for the F Distribution 234
6. Critical Values for the M Distribution at the
5% Significance Level 240
7. Critical Absolute Values of Correlation Coefficient r . . 241
8. Factors for Determining Confidence Limits for
Population Standard Deviation a 242
9. Critical Values for the Sign Test 243
10. Critical Values for Runs 244
11. Half Widths da for Construction of Confidence Bands
for Cumulative Distributions 248
12. Factor k for Estimating Normal Standard Deviation
From the Range w as kw 248
xvi
CONTENTS
13. Critical Values for Tests Using the Range w 249
(a) Critical Values for Tl = 249
(b) Critical Values for rd = ¦ * ~ *2 249
w1 + w2
14. Critical Values for S2/s2 250
15. Orthogonal Polynomials 251
1(5. Critical Values for Test Ratios for Gross Errors . . . .252
17. Tolerance Factors K for Population Proportion P
of Normal Distributions 253
18. Factors for Computing Control Chart Lines 254
19. Constants for a Sampling Plan With OC Curve
Through (plt 0.95) and (p2, 0.05) 255
(a) Single Sampling Plan 255
b) Double Sampling Plan 255
20. Table of a = log10 1 ~ ^ and b = log10 * ~ ° . . . . 256
21. Confidence Limits for a Proportion 257
(a) Two Sided Limits 257
(b) One Sided Limits 262
Appendix Charts:
I. Rectangular Normal Probability Chart 269
II. 90% Confidence Belts for Proportions 270
III. 95% Confidence Belts for Proportions 271
IV. 99% Confidence Belts for Proportions 272
V. OC Curves for Testing the Hypothesis fi = a by the
Equal Tails Normal Test 273
VI. OC Curves for Testing the Hypothesis jit = a by the
Equal Tails / Test 274
VII. OC Curves for Testing the Hypothesis a ~ aa
Against a — r, o ,, by the 2 Test 275
VIII. OC Curves for Testing the Hypothesis r, = a..
Against o , ov, by the F Test . . . . 276
IX. Number of Degrees of Freedom Required To Estimate the
Standard Deviation Within p% of Its True Value,
With Prescribed Confidence 277
X. Number of Degrees of Freedom in Each Sample Required
To Estimate ax/a2 Within p% of Its True Value,
With Prescribed Confidence 278
XL 95% Confidence Belts for Correlation Coefficient .... 279
Index 281
xvii
|
| any_adam_object | 1 |
| author | Crow, Edwin L. Davis, Frances A. Maxfield, Margaret W. |
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| author_sort | Crow, Edwin L. |
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| bvnumber | BV001920655 |
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| edition | Republ. |
| format | Book |
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| indexdate | 2024-07-09T15:37:15Z |
| institution | BVB |
| language | English |
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| physical | XVII, 288 S. Ill. |
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| publisher | Dover Publ. |
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| series2 | Dover Books on advanced mathematics |
| spelling | Crow, Edwin L. Verfasser aut Statistics manual with examples taken from ordnance development by Edwin L. Crow ; Frances A. Davis ; Margaret W. Maxfield Republ. New York Dover Publ. 1960 XVII, 288 S. Ill. txt rdacontent n rdamedia nc rdacarrier Dover Books on advanced mathematics Schätztheorie swd Testtheorie swd Davis, Frances A. Verfasser aut Maxfield, Margaret W. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001251761&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Crow, Edwin L. Davis, Frances A. Maxfield, Margaret W. Statistics manual with examples taken from ordnance development Schätztheorie swd Testtheorie swd |
| title | Statistics manual with examples taken from ordnance development |
| title_auth | Statistics manual with examples taken from ordnance development |
| title_exact_search | Statistics manual with examples taken from ordnance development |
| title_full | Statistics manual with examples taken from ordnance development by Edwin L. Crow ; Frances A. Davis ; Margaret W. Maxfield |
| title_fullStr | Statistics manual with examples taken from ordnance development by Edwin L. Crow ; Frances A. Davis ; Margaret W. Maxfield |
| title_full_unstemmed | Statistics manual with examples taken from ordnance development by Edwin L. Crow ; Frances A. Davis ; Margaret W. Maxfield |
| title_short | Statistics manual |
| title_sort | statistics manual with examples taken from ordnance development |
| title_sub | with examples taken from ordnance development |
| topic | Schätztheorie swd Testtheorie swd |
| topic_facet | Schätztheorie Testtheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001251761&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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