Binomial Test Algorithm
The Binomial Test Algorithm is a statistical method used to determine the probability of obtaining a specific number of successes in a fixed number of Bernoulli trials or binomial experiments. A Bernoulli trial is a random experiment with only two possible outcomes, typically labeled as "success" or "failure." These outcomes must be mutually exclusive and have a fixed probability of occurring in each trial. The Binomial Test is particularly useful in hypothesis testing to examine whether the observed proportion of successes differs significantly from an expected proportion or a null hypothesis. This algorithm is commonly applied in various fields, including medicine, psychology, and social science, to analyze the significance of experimental results or to verify if an observed phenomenon deviates from expected behavior.
The Binomial Test Algorithm computes the probability of obtaining a given number of successes using the binomial probability formula, which depends on the number of trials, the probability of success in a single trial, and the number of successes. The algorithm then calculates the cumulative probability of observing the given number of successes or any value more extreme, either higher or lower, depending on the hypothesis being tested. If this cumulative probability, also known as the p-value, is below a predetermined significance level (commonly set at 0.05), the null hypothesis can be rejected, indicating that the observed proportion of successes is significantly different from the expected proportion. On the other hand, if the p-value is higher than the significance level, the null hypothesis cannot be rejected, meaning that there is insufficient evidence to conclude that the observed proportion of successes deviates from the expected proportion.
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package com.algorithmexamples.math
import org.junit.Assert
import org.junit.Test
class BinomialTest {
@Test
fun test1() {
Assert.assertEquals(0, binomial(0, 1))
Assert.assertEquals(1, binomial(1, 1))
Assert.assertEquals(2, binomial(2, 1))
Assert.assertEquals(3, binomial(3, 1))
Assert.assertEquals(3, binomial(3, 2))
Assert.assertEquals(4, binomial(4, 1))
Assert.assertEquals(1, binomial(5, 0))
Assert.assertEquals(5, binomial(5, 1))
Assert.assertEquals(10, binomial(5, 2))
Assert.assertEquals(10, binomial(5, 3))
Assert.assertEquals(5, binomial(5, 4))
Assert.assertEquals(1, binomial(5, 5))
Assert.assertEquals(1, binomial(6, 0))
Assert.assertEquals(6, binomial(6, 1))
Assert.assertEquals(15, binomial(6, 2))
Assert.assertEquals(20, binomial(6, 3))
Assert.assertEquals(15, binomial(6, 4))
Assert.assertEquals(6, binomial(6, 5))
Assert.assertEquals(1, binomial(6, 6))
}
}
