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[project @ 2007-10-31 01:08:14 by jwe]
author jwe
date Wed, 31 Oct 2007 01:09:28 +0000
parents fd42779a8428
children 0220da981c2a
comparison
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7080:7e465260a48f 7081:503001863427
144 @section Tests 144 @section Tests
145 145
146 Octave can perform several different statistical tests. The following 146 Octave can perform several different statistical tests. The following
147 table summarizes the available tests. 147 table summarizes the available tests.
148 148
149 @iftex
150 @tex
151 \vskip 6pt
152 {\hbox to \hsize {\hfill\vbox{\offinterlineskip \tabskip=0pt
153 \halign{
154 \vrule height2.0ex depth1.ex width 0.6pt #\tabskip=0.3em &
155 # \hfil & \vrule # & # \hfil & # \vrule width 0.6pt \tabskip=0pt\cr
156 \noalign{\hrule height 0.6pt}
157 & @strong{Hypothesis} && {\bf Test Functions} &\cr
158 \noalign{\hrule}
159 & Equal mean values && anova, hotelling\_test2, t\_test\_2, &\cr
160 & && welch\_test, wilcoxon\_test, z\_test\_2 &\cr
161 & Equal medians && kruskal\_wallis\_test, sign\_test &\cr
162 & Equal variances && bartlett\_test, manova, var\_test &\cr
163 & Equal distributions && chisquare\_test\_homogeneity, &\cr
164 & && kolmogorov\_smirnov\_test\_2, u\_test &\cr
165 & Equal marginal frequencies && mcnemar\_test &\cr
166 & Equal success probabilities && prop\_test\_2 &\cr
167 & Independent observations && chisquare\_test\_independence, &\cr
168 & && run\_test &\cr
169 & Uncorrelated observations && cor\_test &\cr
170 & Given mean value && hotelling\_test, t\_test, z\_test &\cr
171 & Observations from distribution && kolmogorov\_smirnov\_test &\cr
172 & Regression && f\_test\_regression, t\_test\_regression &\cr
173 \noalign{\hrule height 0.6pt}
174 }}\hfill}}
175 @end tex
176 @end iftex
177 @ifnottex
149 @multitable @columnfractions .4 .5 178 @multitable @columnfractions .4 .5
150 @item @strong{Hypothesis} 179 @item @strong{Hypothesis}
151 @tab @strong{Test Functions} 180 @tab @strong{Test Functions}
152 @item Equal mean values 181 @item Equal mean values
153 @tab @code{anova}, @code{hotelling_test2}, @code{t_test_2}, 182 @tab @code{anova}, @code{hotelling_test2}, @code{t_test_2},
172 @item Observations from given distribution 201 @item Observations from given distribution
173 @tab @code{kolmogorov_smirnov_test} 202 @tab @code{kolmogorov_smirnov_test}
174 @item Regression 203 @item Regression
175 @tab @code{f_test_regression}, @code{t_test_regression} 204 @tab @code{f_test_regression}, @code{t_test_regression}
176 @end multitable 205 @end multitable
206 @end ifnottex
177 207
178 The tests return a p-value that describes the outcome of the test. 208 The tests return a p-value that describes the outcome of the test.
179 Assuming that the test hypothesis is true, the p-value is the probability 209 Assuming that the test hypothesis is true, the p-value is the probability
180 of obtaining a worse result than the observed one. So large p-values 210 of obtaining a worse result than the observed one. So large p-values
181 corresponds to a successful test. Usually a test hypothesis is accepted 211 corresponds to a successful test. Usually a test hypothesis is accepted
244 (the inverse of the CDF) of a large number of distributions. 274 (the inverse of the CDF) of a large number of distributions.
245 275
246 The following table summarizes the supported distributions (in 276 The following table summarizes the supported distributions (in
247 alphabetical order). 277 alphabetical order).
248 278
249 @multitable @columnfractions .4 .2 .2 .2 279 @c Do the table explicitly in TeX if possible to get a better layout.
280 @iftex
281 @tex
282 \vskip 6pt
283 {\hbox to \hsize {\hfill\vbox{\offinterlineskip \tabskip=0pt
284 \halign{
285 \vrule height2.0ex depth1.ex width 0.6pt #\tabskip=0.3em &
286 # \hfil & \vrule # & # \hfil & \vrule # & # \hfil & \vrule # & # \hfil &
287 # \vrule width 0.6pt \tabskip=0pt\cr
288 \noalign{\hrule height 0.6pt}
289 & {\bf Distribution} && {\bf PDF} && {\bf CDF} && {\bf Quantile}&\cr
290 \noalign{\hrule}
291 &Beta && betapdf && betacdf && betainv&\cr
292 &Binomial && binopdf && binocdf && binoinv&\cr
293 &Cauchy && cauchy\_pdf && cauchy\_cdf && cauchy\_inv&\cr
294 &Chi-Square && chi2pdf && chi2cdf && chi2inv&\cr
295 &Univariate Discrete && discrete\_pdf && discrete\_cdf && discrete\_inv&\cr
296 &Empirical && empirical\_pdf && empirical\_cdf && empirical\_inv&\cr
297 &Exponential && exppdf && expcdf && expinv&\cr
298 &F && fpdf && fcdf && finv&\cr
299 &Gamma && gampdf && gamcdf && gaminv&\cr
300 &Geometric && geopdf && geocdf && geoinv&\cr
301 &Hypergeometric && hygepdf && hygecdf && hygeinv&\cr
302 &Kolmogorov Smirnov && {\it Not Available} && kolmogorov\_&& {\it Not Available}&\cr
303 & && && smirnov\_cdf &&&\cr
304 &Laplace && laplace\_pdf && laplace\_cdf && laplace\_inv&\cr
305 &Logistic && logistic\_pdf && logistic\_cdf && logistic\_inv&\cr
306 &Log-Normal && lognpdf && logncdf && logninv&\cr
307 &Pascal && nbinpdf && nbincdf && nbininv&\cr
308 &Univariate Normal && normpdf && normcdf && norminv&\cr
309 &Poisson && poisspdf && poisscdf && poissinv&\cr
310 &t (Student) && tpdf && tcdf && tinv&\cr
311 &Univariate Discrete && unidpdf && unidcdf && unidinv&\cr
312 &Uniform && unifpdf && unifcdf && unifinv&\cr
313 &Weibull && wblpdf && wblcdf && wblinv&\cr
314 \noalign{\hrule height 0.6pt}
315 }}\hfill}}
316 @end tex
317 @end iftex
318 @ifnottex
319 @multitable @columnfractions .31 .23 .23 .23
250 @item @strong{Distribution} 320 @item @strong{Distribution}
251 @tab @strong{PDF} 321 @tab @strong{PDF}
252 @tab @strong{CDF} 322 @tab @strong{CDF}
253 @tab @strong{Quantile} 323 @tab @strong{Quantile}
254 @item Beta Distribution 324 @item Beta Distribution
325 @tab @code{poissinv} 395 @tab @code{poissinv}
326 @item t (Student) Distribution 396 @item t (Student) Distribution
327 @tab @code{tpdf} 397 @tab @code{tpdf}
328 @tab @code{tcdf} 398 @tab @code{tcdf}
329 @tab @code{tinv} 399 @tab @code{tinv}
330 @item Univariate Discrete Distribution 400 @item Univariate Discrete Distribution
331 @tab @code{unidpdf} 401 @tab @code{unidpdf}
332 @tab @code{unidcdf} 402 @tab @code{unidcdf}
333 @tab @code{unidinv} 403 @tab @code{unidinv}
334 @item Uniform Distribution 404 @item Uniform Distribution
335 @tab @code{unifpdf} 405 @tab @code{unifpdf}
338 @item Weibull Distribution 408 @item Weibull Distribution
339 @tab @code{wblpdf} 409 @tab @code{wblpdf}
340 @tab @code{wblcdf} 410 @tab @code{wblcdf}
341 @tab @code{wblinv} 411 @tab @code{wblinv}
342 @end multitable 412 @end multitable
413 @end ifnottex
343 414
344 @DOCSTRING(betacdf) 415 @DOCSTRING(betacdf)
345 416
346 @DOCSTRING(betainv) 417 @DOCSTRING(betainv)
347 418
478 @c Should rand, randn, rande, randp, and randg be moved to here? 549 @c Should rand, randn, rande, randp, and randg be moved to here?
479 550
480 The following table summarizes the available random number generators 551 The following table summarizes the available random number generators
481 (in alphabetical order). 552 (in alphabetical order).
482 553
554 @iftex
555 @tex
556 \vskip 6pt
557 {\hbox to \hsize {\hfill\vbox{\offinterlineskip \tabskip=0pt
558 \halign{
559 \vrule height2.0ex depth1.ex width 0.6pt #\tabskip=0.3em &
560 # \hfil & \vrule # & # \hfil & # \vrule width 0.6pt \tabskip=0pt\cr
561 \noalign{\hrule height 0.6pt}
562 & {\bf Distribution} && {\bf Function} &\cr
563 \noalign{\hrule}
564 & Beta Distribution && betarnd &\cr
565 & Binomial Distribution && binornd &\cr
566 & Cauchy Distribution && cauchy\_rnd &\cr
567 & Chi-Square Distribution && chi2rnd &\cr
568 & Univariate Discrete Distribution && discrete\_rnd &\cr
569 & Empirical Distribution && empirical\_rnd &\cr
570 & Exponential Distribution && exprnd &\cr
571 & F Distribution && frnd &\cr
572 & Gamma Distribution && gamrnd &\cr
573 & Geometric Distribution && geornd &\cr
574 & Hypergeometric Distribution && hygernd &\cr
575 & Laplace Distribution && laplace\_rnd &\cr
576 & Logistic Distribution && logistic\_rnd &\cr
577 & Log-Normal Distribution && lognrnd &\cr
578 & Pascal Distribution && nbinrnd &\cr
579 & Univariate Normal Distribution && normrnd &\cr
580 & Poisson Distribution && poissrnd &\cr
581 & t (Student) Distribution && trnd &\cr
582 & Univariate Discrete Distribution && unidrnd &\cr
583 & Uniform Distribution && unifrnd &\cr
584 & Weibull Distribution && wblrnd &\cr
585 & Wiener Process && wienrnd &\cr
586 \noalign{\hrule height 0.6pt}
587 }}\hfill}}
588 @end tex
589 @end iftex
590 @ifnottex
483 @multitable @columnfractions .4 .3 591 @multitable @columnfractions .4 .3
484 @item @strong{Distribution} @tab @strong{Function} 592 @item @strong{Distribution} @tab @strong{Function}
485 @item Beta Distribution @tab @code{betarnd} 593 @item Beta Distribution @tab @code{betarnd}
486 @item Binomial Distribution @tab @code{binornd} 594 @item Binomial Distribution @tab @code{binornd}
487 @item Cauchy Distribution @tab @code{cauchy_rnd} 595 @item Cauchy Distribution @tab @code{cauchy_rnd}
503 @item Univariate Discrete Distribution @tab @code{unidrnd} 611 @item Univariate Discrete Distribution @tab @code{unidrnd}
504 @item Uniform Distribution @tab @code{unifrnd} 612 @item Uniform Distribution @tab @code{unifrnd}
505 @item Weibull Distribution @tab @code{wblrnd} 613 @item Weibull Distribution @tab @code{wblrnd}
506 @item Wiener Process @tab @code{wienrnd} 614 @item Wiener Process @tab @code{wienrnd}
507 @end multitable 615 @end multitable
616 @end ifnottex
508 617
509 @DOCSTRING(betarnd) 618 @DOCSTRING(betarnd)
510 619
511 @DOCSTRING(binornd) 620 @DOCSTRING(binornd)
512 621