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How to calculate confidence interval for means with unknown standard deviation using the Student t distribution. Needs Apache Commons Math library.
import org.apache.commons.math3.distribution.TDistribution;
import org.apache.commons.math3.exception.MathIllegalArgumentException;
import org.apache.commons.math3.stat.descriptive.SummaryStatistics;
public class ConfidenceIntervalApp {
public static void main(String args[]) {
// data we want to evaluate: average height of 30 one year old male and female toddlers
// interestingly, at this age height is not bimodal yet
double data[] = new double[] { 63.5, 81.3, 88.9, 63.5, 76.2, 67.3, 66.0, 64.8, 74.9, 81.3, 76.2, 72.4, 76.2, 81.3, 71.1, 80.0, 73.7, 74.9, 76.2, 86.4, 73.7, 81.3, 68.6, 71.1, 83.8, 71.1, 68.6, 81.3, 73.7, 74.9 };
// Build summary statistics of the dataset "data"
SummaryStatistics stats = new SummaryStatistics();
for (double val : data) {
stats.addValue(val);
}
// Calculate 95% confidence interval
double ci = calcMeanCI(stats, 0.95);
System.out.println(String.format("Mean: %f", stats.getMean()));
double lower = stats.getMean() - ci;
double upper = stats.getMean() + ci;
System.out.println(String.format("Confidence Interval 95%%: %f, %f", lower, upper));
}
private static double calcMeanCI(SummaryStatistics stats, double level) {
try {
// Create T Distribution with N-1 degrees of freedom
TDistribution tDist = new TDistribution(stats.getN() - 1);
// Calculate critical value
double critVal = tDist.inverseCumulativeProbability(1.0 - (1 - level) / 2);
// Calculate confidence interval
return critVal * stats.getStandardDeviation() / Math.sqrt(stats.getN());
} catch (MathIllegalArgumentException e) {
return Double.NaN;
}
}
}
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