Performing the Binomial Test in R | A Statistical Test for Proportions

Binomial Test in R

The binomial test is a statistical test used to determine whether the observed number of successes in a fixed number of trials is significantly different from what would be expected by chance alone, assuming a specific probability of success

The binomial test is a statistical test used to determine whether the observed number of successes in a fixed number of trials is significantly different from what would be expected by chance alone, assuming a specific probability of success. In other words, it helps in evaluating whether the observed data provides evidence in favor or against a given hypothesis.

In R, the binomial test can be performed using the `binom.test()` function. The syntax for this function is:

“`R
binom.test(x, n, p = NULL, alternative = c(“two.sided”, “less”, “greater”),
conf.level = 0.95)
“`

Here’s a breakdown of the function arguments:

– `x`: The number of successes observed in the trials.
– `n`: The total number of trials.
– `p`: The hypothesized probability of success. If not provided, the null hypothesis assumes a proportion of success equal to the observed proportion.
– `alternative`: Specifies whether the alternative hypothesis is “two.sided” (default), “less”, or “greater”. Note that “less” corresponds to the alternative hypothesis that the true success proportion is less than the hypothesized proportion.
– `conf.level`: The confidence level for the confidence interval estimation. The default value is 0.95.

The function returns a binomial test result object including the following components:

– `p-value`: The probability of observing the number of successes (or fewer or greater) given the null hypothesis.
– `conf.int`: The confidence interval for the true success proportion.
– `estimate`: The estimated success proportion.
– `alternative`: The alternative hypothesis specified.

Here’s an example usage of the `binom.test()` function:

“`R
# Suppose we have 20 trials with 15 successes
binom.test(15, 20)

# Output:
#
# Exact binomial test
#
# data: 15 and 20
# number of successes = 15, number of trials = 20, p-value = 0.4202
# alternative hypothesis: true probability of success is not equal to 0.5
# 95 percent confidence interval:
# 0.5636594 0.9275472
# sample estimates:
# probability of success
# 0.75
“`

In this example, we performed a binomial test to assess whether the observed proportion of successes (15 out of 20 trials) is significantly different from 0.5. The p-value is 0.4202, indicating that there is no strong evidence against the null hypothesis (the observed proportion can be reasonably explained by chance alone).

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