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/*******************************************************************************
* Copyright (c) 2010-2020 Haifeng Li. All rights reserved.
*
* Smile is free software: you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as
* published by the Free Software Foundation, either version 3 of
* the License, or (at your option) any later version.
*
* Smile is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with Smile. If not, see .
******************************************************************************/
package smile.stat;
import smile.stat.distribution.Distribution;
import smile.stat.hypothesis.*;
/**
* Hypothesis test functions.
*
* @author Haifeng Li
*/
public interface Hypothesis {
/**
* Returns the significance code of p-value.
* Significance codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
*/
static String significance(double pvalue) {
if (pvalue < 0.001)
return "***";
else if (pvalue < 0.01)
return "**";
else if (pvalue < 0.05)
return "*";
else if (pvalue < 0.1)
return ".";
else
return "";
}
/** t-test. */
interface t {
/**
* Independent one-sample t-test whether the mean of a normally distributed
* population has a value specified in a null hypothesis. Small values of
* p-value indicate that the array has significantly different mean.
*/
static TTest test(double[] x, double mean) {
return TTest.test(x, mean);
}
/**
* Test if the arrays x and y have significantly different means. The data
* arrays are assumed to be drawn from populations with unequal variances.
* Small values of p-value indicate that the two arrays have significantly
* different means.
*/
static TTest test(double[] x, double[] y) {
return TTest.test(x, y, false);
}
/**
* Test if the arrays x and y have significantly different means. Small
* values of p-value indicate that the two arrays have significantly
* different means.
* @param option "equal.var" if the data arrays are assumed to be drawn
* from populations with the same true variance.
* "unequal.var if the data arrays are allowed to be drawn
* from populations with unequal variances.
* "paired" if x and y are two values (i.e., pair of values)
* for the same samples.
*/
static TTest test(double[] x, double[] y, String option) {
switch (option) {
case "unequal.var": return TTest.test(x, y, false);
case "equal.var": return TTest.test(x, y, true);
case "paired": return TTest.testPaired(x, y);
}
return TTest.testPaired(x, y);
}
/**
* Test whether the Pearson correlation coefficient, the slope of
* a regression line, differs significantly from 0. Small values of p-value
* indicate a significant correlation.
* @param r the Pearson correlation coefficient.
* @param df the degree of freedom. df = n - 2, where n is the number of samples
* used in the calculation of r.
*/
static TTest test(double r, int df) {
return TTest.test(r, df);
}
}
/** F-test. */
interface F {
/**
* Test if the arrays x and y have significantly different variances.
* Small values of p-value indicate that the two arrays have significantly
* different variances.
*/
static FTest test(double[] x, double[] y) {
return FTest.test(x, y);
}
}
/** The Kolmogorov-Smirnov test (K-S test). */
interface KS {
/**
* The one-sample KS test for the null hypothesis that the data set x
* is drawn from the given distribution. Small values of p-value show that
* the cumulative distribution function of x is significantly different from
* the given distribution. The array x is modified by being sorted into
* ascending order.
*/
static KSTest test(double[] x, Distribution dist) {
return KSTest.test(x, dist);
}
/**
* The two-sample KS test for the null hypothesis that the data sets
* are drawn from the same distribution. Small values of p-value show that
* the cumulative distribution function of x is significantly different from
* that of y. The arrays x and y are modified by being sorted into
* ascending order.
*/
static KSTest test(double[] x, double[] y) {
return KSTest.test(x, y);
}
}
/** Correlation test. */
interface cor {
/** Pearson correlation test. */
static CorTest test(double[] x, double[] y) {
return CorTest.pearson(x, y);
}
/**
* Correlation test. Supported methods include "pearson", "kendall", and "spearman".
*/
static CorTest test(double[] x, double[] y, String method) {
switch (method) {
case "pearson": return CorTest.pearson(x, y);
case "kendall": return CorTest.kendall(x, y);
case "spearman": return CorTest.spearman(x, y);
default: throw new IllegalArgumentException("Invalid correlation test method: " + method);
}
}
}
/** Chi-square test. */
interface chisq {
/**
* One-sample chisq test. Given the array bins containing the observed numbers of events,
* and an array prob containing the expected probabilities of events, and given
* one constraint, a small value of p-value indicates a significant
* difference between the distributions.
*/
static ChiSqTest test(int[] bins, double[] prob) {
return test(bins, prob, 1);
}
/**
* One-sample chisq test. Given the array bins containing the observed numbers of events,
* and an array prob containing the expected probabilities of events, and given
* the number of constraints (normally one), a small value of p-value
* indicates a significant difference between the distributions.
*/
static ChiSqTest test(int[] bins, double[] prob, int constraints) {
return ChiSqTest.test(bins, prob, constraints);
}
/**
* Two-sample chisq test. Given the arrays bins1 and bins2, containing two
* sets of binned data, and given one constraint, a small value of
* p-value indicates a significant difference between the distributions.
*/
static ChiSqTest test(int[] bins1, int[] bins2) {
return test(bins1, bins2, 1);
}
/**
* Two-sample chisq test. Given the arrays bins1 and bins2, containing two
* sets of binned data, and given the number of constraints (normally one),
* a small value of p-value indicates a significant difference between
* the distributions.
*/
static ChiSqTest test(int[] bins1, int[] bins2, int constraints) {
return ChiSqTest.test(bins1, bins2, constraints);
}
/**
* Given a two-dimensional contingency table in the form of an array of
* integers, returns Chi-square test for independence. The rows of contingency table
* are labels by the values of one nominal variable, the columns are labels
* by the values of the other nominal variable, and whose entries are
* nonnegative integers giving the number of observed events for each
* combination of row and column. Continuity correction
* will be applied when computing the test statistic for 2x2 tables: one half
* is subtracted from all |O-E| differences. The correlation coefficient is
* calculated as Cramer's V.
*/
static ChiSqTest test(int[][] table) {
return ChiSqTest.test(table);
}
}
}
