example.md

Example 4: Simulate the standard error for the mean

Contents

• Overview
  • Standard error for the mean
• Import files
• The main function
• Results
• Source Code

Overview

Standard error for the mean

Import files

package examples.stats.example4;

import org.apache.commons.math3.stat.descriptive.DescriptiveStatistics;
import utils.ListMaths;
import utils.ListUtils;

import java.util.ArrayList;
import java.util.List;
import java.util.Random;

The main function

public class Example4 {

    public static List<Double> getNormalSample(double mu, double sd, int n){

        List<Double> sample = new ArrayList<>(n);

        Random rnd = new Random();
        for(int i=0; i<n; ++i){
            double value = rnd.nextGaussian()*sd + mu;
            sample.add(value);
        }

        return sample;
    }

    public static void main(String[] args){


        final double N_SIM = 1000;
        final int N = 10;
        final  double MU = 0.0;
        final double SIGMA = 1.0;

        List<Double> means = new ArrayList<Double>();

        for( int itr=0; itr < N_SIM; ++itr){
            List<Double> sample = Example4.getNormalSample(MU, SIGMA, N);

            double mean = ListMaths.sum(sample)/((double)sample.size());
            //System.out.println(mean);
            means.add(mean);
        }

        double[] vals = ListUtils.toDoubleArray(means);
        DescriptiveStatistics stats = new DescriptiveStatistics(vals );

        System.out.println("Standard deviation  of means is: "+stats.getStandardDeviation());
        System.out.println("sigma/sqrt(N) is: " + SIGMA/Math.sqrt(N));
    }
}

Results

Standard deviation  of means is: 0.3081356365887988
sigma/sqrt(N) is: 0.31622776601683794

Source Code

Example4.java