java-statistical-inference

This package is a java implementation of an opinionated statistical inference engine with fluent api to make it easier for conducting statistical inference with little or no knowledge of statistical inference principles involved

Features

• Confidence Interval for numerical variable and proportions (one group or two groups)

• Hypothesis Testing for Single Numerical Variable

• Hypothesis Testing for Single Categorical Variable (Proportion)

• Hypothesis Testing for Two Group Numerical Variable

• Hypothesis Testing for Two Group Categorical Variable (Proportion)

• ANOVA: Independence Test between a Numerical Variable and a Categorical Variable

• Chi-Square Test: Independence Test between a Categorical Variable and another Categorical Variable

• ANOVA for Regression: Independence Test between a Numerical Variable and another Numerical Variable

• Automatic change of sampling distribution based on sample size:

  • Normal distribution for large sample on categorical variable (one or two groups)
  • Bootstrap simulation for small sample on categorical variable (one or two groups)
  • Normal distribution for large sample on numerical variable (one or two groups)
  • Student-T distribution for small sample on numerical variable (one or two groups)

• Central Limit Theorem Conditions Check

Install

Add the following dependency into your POM file:

<dependency>
<groupId>com.github.chen0040</groupId>
<artifactId>java-statistical-inference</artifactId>
<version>1.0.4</version>
</dependency>

Usage

Single Numerical Variable

The code below shows how to declare a single numerical variable kie (knowledge inference engine):

Variablevariable = newVariable("Amount");
NumericalSampleKiekie = variable.numericalSample();

The code below shows how to load observed data about the variable "Amount" into the kie:

kie.addObservations(newdouble[] { 0.2, 0.4, 0.6, 0.12, 0.9, 0.13, -0.12, -0.55, 0.5});

Alternatively the observed data can be loaded from a data frame (please refer to here for more example on how to create a data frame)

DataFramedataFrame = DataQuery.csv().from(newFileInputStream("amount.csv"))
.selectColumn(0).asNumeric().asInput("Amount").build();
kie.addObservations(dataFrame);

The code below shows the various statistics that can be obtained from the kie about the variable "Amount":

Meanmean = kie.mean();
doubleconfidenceLevel = 0.95;
ConfidenceIntervalconfidenceInterval = mean.confidenceInterval(confidenceLevel);
System.out.println("sample.mean: " + kie.getSampleMean());
System.out.println("sample.sd: " + kie.getSampleSd());
System.out.println("sample.size: " + kie.getSampleSize());
System.out.println("sample.median: " + kie.getSampleMedian());
System.out.println("sample.max: " + kie.getSampleMax());
System.out.println("sample.min: " + kie.getSampleMin());
System.out.println("sample.1st.quartile: " + kie.getSampleFirstQuartile());
System.out.println("sample.3rd.quartile: " + kie.getSampleThirdQuartile());
System.out.println("sampling distribution: " + kie.getSamplingDistribution());
System.out.println("confidence interval for Amount: " + confidenceInterval);

The kie also provides user friendly statement for the confidence interval:

System.out.println(kie.mean().confidenceInterval(0.95).getSummary());

The code belows shows how to test the null hypothesis that "The population mean of Amount is 0.5", with significance level of 0.05:

doubleexpected_mean = 0.5;
TestingOnValuetest = kie.test4MeanEqualTo(expected_mean);
System.out.println("sampling distribution: " + test.getDistributionFamily());
System.out.println("test statistic: " + test.getTestStatistic());
System.out.println("p-value (one-tail): " + test.getPValueOneTail());
System.out.println("p-value (two-tails): " + test.getPValueTwoTails());

The kie also provides user friendly statement for the null hypothesis test:

TestingOnValuetest = kie.test4MeanEqualTo(0.5);
System.out.println(test.getSummary());

Single Categorical Variable

The code below shows how to declare a single categorical variable kie (knowledge inference engine):

Variablevariable = newVariable("Type");
NumericalSampleKiekie = variable.categoricalSample();

The code below shows how to load observed data about the variable "Type" into the kie:

kie.addObservations(newString[] { "Asset", "Liability", "Equity", "Revenue", "Expense", "Liability", "Equity", "Revenue", "Asset", "Liability", "Equity" });

Alternatively the observed data can be loaded from a data frame

InputStreaminputStream = newFileInputStream("iris.data");
DataFramedataFrame = DataQuery.csv(",").from(inputStream)
.selectColumn(4).asCategory().asInput("Type").build();
kie.addObservations(dataFrame);

The code below shows the various statistics that can be obtained from the kie about the variable "Amount":

Proportionproportion = kie.proportion("Liability");
doubleconfidenceLevel = 0.95;
ConfidenceIntervalconfidenceInterval = proportion.confidenceInterval(confidenceLevel);
System.out.println("sample.mean: " + kie.getSampleMean("Liability"));
System.out.println("sample.proportion: " + kie.getSampleProportion("Liability"));
System.out.println("sample.sd: " + kie.getSampleSd("Liability"));
System.out.println("sample.size: " + kie.getSampleSize());
System.out.println("sampling distribution: " + kie.getSamplingDistribution());
System.out.println("confidence interval for Type == Liability: " + confidenceInterval);

The kie also provides user friendly statement for the confidence interval:

System.out.println(kie.proportion("Liability").confidenceInterval(0.95).getSummary());

The code belows shows how to test the null hypothesis that "The population proportion of Type==Liability is 0.5", with significance level of 0.05:

doubleexpected_proportion = 0.5;
TestingOnValuetest = kie.test4MeanEqualTo(expected_proportion);
System.out.println("sampling distribution: " + test.getDistributionFamily());
System.out.println("test statistic: " + test.getTestStatistic());
System.out.println("p-value (one-tail): " + test.getPValueOneTail());
System.out.println("p-value (two-tails): " + test.getPValueTwoTails());

The kie also provides user friendly statement for the null hypothesis test:

TestingOnValuetest = kie.test4ProportionEqualTo(0.5);
System.out.println(test.getSummary());

Paired Sample for a Numerical Variable

The sample code below shows how to run statistical inference on the sample from a paired observations (e.g. before, after) for a numerical variable:

Variablevariable1 = newVariable("Begin");
Variablevariable2 = newVariable("End");
InputStreaminputStream = newFileInputStream("calcium-paired.dat");
DataFramedataFrame = DataQuery.csv().from(inputStream)
.selectColumn(1).asNumeric().asInput("Begin")
.selectColumn(2).asNumeric().asInput("End")
.build();
PairedSampleKiekie = variable2.pair(variable1).numericalSample();
kie.addObservations(dataFrame);
Meanmean = kie.difference();
ConfidenceIntervalconfidenceInterval = mean.confidenceInterval(0.95);
TestingOnValuetest = kie.testDifferenceEqualTo(0.5);
System.out.println("sample.difference-mean: " + kie.getSampleDifferenceMean());
System.out.println("sample.difference-sd: " + kie.getSampleDifferenceSd());
System.out.println("sample.size: " + kie.getSampleSize());
System.out.println("sample.median: " + kie.getSampleMedian());
System.out.println("sample.max: " + kie.getSampleMax());
System.out.println("sample.min: " + kie.getSampleMin());
System.out.println("sample.1st.quartile: " + kie.getSampleFirstQuartile());
System.out.println("sample.3rd.quartile: " + kie.getSampleThirdQuartile());
System.out.println("sampling distribution (difference): " + kie.getSamplingDistribution());
System.out.println("95% confidence interval: " + confidenceInterval);
System.out.println("========================================================");
System.out.println(confidenceInterval.getSummary());
System.out.println(test.getSummary());

In the above codes, the "calcium-paired.dat" contains results of a randomized comparative experiment to investigate the effect of calcium on blood pressure in African-American men. A treatment group of 10 men received a calcium supplement for 12 weeks. All subjects had their blood pressure tested before and after the 12-week period.

Compare Two Groups for a Numerical Variable

The sample below shows the statistical inference on samples from two different groups (e.g., from two different experiment setup) for a numerical variable:

Variablevariable = newVariable("Decrease");
TwoGroupNumericalSampleKiekie = variable.twoGroupNumericalSample(newVariable("Treatment"), "Calcium", "Placebo");
InputStreaminputStream = newFileInputStream("calcium.dat");
DataFramedataFrame = DataQuery.csv().from(inputStream)
.skipRows(33)
.selectColumn(0).asCategory().asInput("Treatment")
.selectColumn(3).asNumeric().asInput("Decrease")
.build();
kie.addObservations(dataFrame);
MeanDifferencedifference = kie.difference();
ConfidenceIntervalconfidenceInterval = difference.confidenceInterval(0.95);
TestingOnValueDifferencetest = kie.test4GroupDifference();
System.out.println("sample1.mean: " + kie.getGroup1SampleMean());
System.out.println("sample1.sd: " + kie.getGroup1SampleSd());
System.out.println("sample1.size: " + kie.getGroup1SampleSize());
System.out.println("sample1.median: " + kie.getGroup1SampleMedian());
System.out.println("sample1.max: " + kie.getGroup1SampleMax());
System.out.println("sample1.min: " + kie.getGroup1SampleMin());
System.out.println("sample1.1st.quartile: " + kie.getGroup1SampleFirstQuartile());
System.out.println("sample1.3rd.quartile: " + kie.getGroup1SampleThirdQuartile());
System.out.println("sample2.mean: " + kie.getGroup2SampleMean());
System.out.println("sample2.sd: " + kie.getGroup2SampleSd());
System.out.println("sample2.size: " + kie.getGroup2SampleSize());
System.out.println("sample2.median: " + kie.getGroup2SampleMedian());
System.out.println("sample2.max: " + kie.getGroup2SampleMax());
System.out.println("sample2.min: " + kie.getGroup2SampleMin());
System.out.println("sample2.2st.quartile: " + kie.getGroup2SampleFirstQuartile());
System.out.println("sample2.3rd.quartile: " + kie.getGroup2SampleThirdQuartile());
System.out.println("sampling distribution: " + kie.getSamplingDistribution());
System.out.println("95% confidence interval: " + confidenceInterval);
System.out.println("========================================================");
System.out.println(confidenceInterval.getSummary());
System.out.println(test.getSummary());

In the above codes, the "calcium.dat" contains results of a randomized comparative experiment to investigate the effect of calcium on blood pressure in African-American men. A treatment group of 10 men received a calcium supplement for 12 weeks, and a control group of 11 men received a placebo during the same period. All subjects had their blood pressure tested before and after the 12-week period.

The "kie.test4GroupDifference()" can be used to test whether the numerical variable is independent of another categorical variable which has two levels (i.e. the "group" variable)

Compare Two Groups for a Categorical Variable

The sample below shows the statistical inference on samples from two different groups (e.g., from two different experiment setup) for a categorical variable:

Variablevariable_use = newVariable("UseContraceptive");
Variablevariable_urban = newVariable("IsUrban");
InputStreaminputStream = newFileInputStream("contraception.csv");
DataFramedataFrame = DataQuery.csv(",")
.from(inputStream)
.selectColumn(3).asCategory().asInput("UseContraceptive")
.selectColumn(6).asCategory().asInput("IsUrban")
.build();
TwoGroupCategoricalSampleKiekie = variable_use.twoGroupCategoricalSampleKie(variable_urban, "Y", "N");
kie.addObservations(dataFrame);
ProportionDifferencedifference = kie.proportionDifference("Y");
ConfidenceIntervalconfidenceInterval = difference.confidenceInterval(0.95);
TestingOnProportionDifferencetest = kie.test4GroupDifference("Y");
System.out.println("sample1.mean: " + kie.getGroup1SampleMean("Y"));
System.out.println("sample1.proportion: " + kie.getGroup1SampleProportion("Y"));
System.out.println("sample1.sd: " + kie.getGroup1SampleSd("Y"));
System.out.println("sample1.size: " + kie.getGroup1SampleSize());
System.out.println("sample2.mean: " + kie.getGroup2SampleMean("Y"));
System.out.println("sample2.proportion: " + kie.getGroup2SampleProportion("Y"));
System.out.println("sample2.sd: " + kie.getGroup2SampleSd("Y"));
System.out.println("sample2.size: " + kie.getGroup2SampleSize());
System.out.println("sampling distribution: " + kie.getSamplingDistribution("Y"));
System.out.println("95% confidence interval: " + confidenceInterval);
System.out.println("========================================================");
System.out.println(confidenceInterval.getSummary());
System.out.println(test.getSummary());

In the above codes, the "contraception.csv" contains results of whether a person is from urban area and whether he/she uses contraception.

The "kie.test4GroupDifference('Y')" can be used to test whether the categorical variable is independent of another categorical variable which has two levels (i.e. the "group" variable)

ANOVA: Independence Test for a Numerical variable and a Categorical Variable

The sample code belows show to test for the independence between a categorical variable (explanatory variable) a numerical variable (response variable):

Variablevariable1 = newVariable("Age");
Variablevariable2 = newVariable("LiveChannel");
CategoricalToNumericalSampleKiekie = variable1.multipleGroupNumericalSample(variable2);
InputStreaminputStream = FileUtils.getResource("contraception.csv");
DataFramedataFrame = DataQuery.csv(",")
.from(inputStream)
.skipRows(1)
.selectColumn(5).asNumeric().asInput("Age")
.selectColumn(4).asCategory().asInput("LiveChannel")
.build();
kie.addObservations(dataFrame);
Anovatest = kie.test4Independence();
System.out.println(test.getSummary());

In the above codes, the "contraception.csv" contains results of which channel the person watch (categorical) and what is his/her age (numeric).

Chi-Square: Independence Test for two Categorical Variables

The sample code belows show to test for the independence between two categorical variables

Variablevariable1 = newVariable("UseContraceptive");
Variablevariable2 = newVariable("LiveChannel");
CategoricalToCategoricalSampleKiekie = variable1.multipleGroupCategoricalSample(variable2);
InputStreaminputStream = newFileInputStream("contraception.csv");
DataFramedataFrame = DataQuery.csv(",")
.from(inputStream)
.skipRows(1)
.selectColumn(3).transform(text -> text.equals("Y") ? "Use" : "DontUse").asInput("UseContraceptive")
.selectColumn(4).asCategory().asInput("LiveChannel")
.build();
kie.addObservations(dataFrame);
ChiSquareTesttest = kie.test4Independence();
ContingencyTablecontingencyTable = kie.getOrCreateContingencyTable();
System.out.println(contingencyTable.getSummary());
System.out.println(test.getSummary());

In the above codes, the "contraception.csv" contains results of whether a person watch which live channel (categorical variable) and whether he/she uses contraception (another categorical variable).

Linear dependency between two numerical variables X and Y

The sample code between shows how to analyze the linear dependency between two numerical variable X and Y:

finalRandomrandom = newRandom(System.currentTimeMillis());
// regression: y is strongly correlated to x by y = 25 + 5 * xSampler.DataSampleBuilderbuilder = newSampler().forColumn("x").generate((name, index) -> (double)index)
.forColumn("y").generate((name, index) -> 25 + (index + random.nextDouble()) * 5 + random.nextDouble())
.end();
DataFramedataFrame = DataQuery.blank()
.newInput("x")
.newOutput("y")
.end().build();
dataFrame = builder.sample(dataFrame, 100);
System.out.println(dataFrame.head(10));
Variablex = newVariable("x");
XYSampleKiekie = x.regression(newVariable("y"));
kie.addObservations(dataFrame);
SampleLinearRegressionmodel = kie.model();
System.out.println("correlation between x and y: " + model.getCorrelation());
System.out.println("y-intercept: " + model.getIntercept());
System.out.println("slope: " + model.getSlope());
System.out.println("R^2: " + model.getR2()); // explained variabilitySystem.out.println("SD(X): " + model.getSX());
System.out.println("SD(Y): " + model.getSY());
System.out.println("Mean(X): " + model.getXBar());
System.out.println("Mean(Y): " + model.getYBar());
Anova4Regressionanova = kie.test4Independence();
System.out.println(anova.getSummary());