A First Course Mathematical Statistics

Front Cover
CUP Archive, Jan 2, 1949 - Mathematics - 271 pages
This book provides the mathematical foundations of statistics. Its aim is to explain the principles, to prove the formulae to give validity to the methods employed in the interpretation of statistical data. Many examples are included but, since the primary emphasis is on the underlying theory, it is of interest to students of a wide variety of subjects: biology, psychology, agriculture, economics, physics, chemistry, and (of course) mathematics.
 

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Contents

Change of origin and unit
4
Grouped distribution
10
The Normal Distribution
16
PROBABILITY AND PROBABILITY DISTRIBUTIONS
19
Expected value of a sum or a product of two variates
26
Theorems of Tohebychef and Bernoulli
32
Cumulative function of a distribution
39
SOME STANDARD DISTRIBUTIONS
46
Standard errors in moments about a fixed value
133
Covariance of moments of different orders about a fixed value
135
Standard errors of the variance and the standard deviation of a large sample
136
Comparison of the standard deviations of two large samples
137
Sampling covariance of the means of the variables pcu re
140
Relation between the two functions
147
Beta distribution of the first kind 168
153
Linear constraints Degrees of freedom
166

Derivation from the binomial distribution page
50
Some properties of the normal distribution
51
Probabilities and relative frequencies for various intervals
55
Distribution of a sum of independent normal variates
57
Examples III
58
Mathematical Notes
63
Chapter IV
67
Continuous distributions
68
Lines of regression
69
Coefficient of correlation Standard error of estimate
72
Estimates from the regression equation
74
Change of units
75
Numerical illustration
76
Correlation of ranks
79
Bivariate probability distributions
80
Variance of a sum of variates
82
Examples IV
83
FURTHER CORRELATION THEORY CURVED REGRESSION LINES 33 Arrays Linear regression
87
Correlation ratios
89
Calculation of correlation ratios
91
Other relations
92
Continuous distributions
93
Bivariate normal distribution
95
Intraclass correlation
97
Polynomial regression Normal equations page
99
Index of correlation
102
Some related regressions
104
Examples V
105
Chapter VI
109
Large samples Test of significance
111
Comparison of large samples
112
Poissonian and Lexian sampling Samples of varying size
114
Sampling of Values of a Variable 48 Random and simple sampling
116
Sampling distributions Standard errors
117
Sampling distribution of the mean
119
Normal population Fiducial limits for unknown mean
121
Comparison of the means of two large samples
122
Standard error of a partition value
124
Examples VI
126
Chapter VII
130
Standard errors of class frequencies
131
Covariance of the frequencies in different classes
132
Test of goodness of fit
173
Distribution of regression coefficients and correlation ratios
179
FURTHER TESTS OF SIGNIFICANCE SMALL SAMPLES 84 Small samples page
185
Students Distribution 85 The statistic t and its distribution
186
Test for an assumed population mean
189
Comparison of the means of two samples
190
Significance of an observed correlation
192
Significance of an observed regression coefficient
194
Distribution of the range of a sample
195
Distribution of the Variance Ratio 92 Ratio of independent estimates of the population variance
196
Fishers distribution Table of F
198
Fishers Transformation of the Correlation Coefficient 94 Distribution of r Fishers transformation
200
Comparison of correlations in independent samples
202
Combination of estimates of a correlation coefficient
203
Examples X
205
Chapter XI
209
Homogeneous population One oriterion of classification
210
Calculation of the sums of squares
212
Two criteria of classification
214
The Latin square Three oriteria of classification
217
Significance of an observed correlation ratio
221
Significance of a regression funotion
223
Test for nonlinearity of regression
224
Resolution of the sum of products One criterion of classification page
226
Calculation of the sums of products
228
Examination and elimination of the effect of regression
229
Two criteria of classification
233
Examples XI
236
MULTIVARIATE DISTRIBUTIONS PARTIAL AND MULTIPLE CORRELATIONS 100 Introductory Yules notation
242
Distribution of three or more variables
244
Determination of the coefficients of regression
246
Multiple correlation
249
Partial correlation
250
Reduction formula for the order of a standard deviation
253
Reduction formula for the order of a regression coefficient
254
Normal distribution
255
Significance of an observed partial correlation
256
Significance of an observed multiple correlation
257
Examples XII
260
Literature for Reference
263
Index
273
Table of I 188
277

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