inst/help/BinomialTest.md

In jasp-stats/jaspFrequencies: Frequencies Module for JASP

Binomial Test

The binomial test allows the user to test whether a proportion of a dichotomous variable is equal to a test value (=presumed population value). The analysis returns a binomial test for each level of the dependent variable against all other levels, so it will also work for variables with more than two levels.

Assumptions

• The variable should be a dichotomous scale.
• Observations should be independent.

Input

• Test value: The proportion of the variable under the null hypothesis.

Alt. Hypothesis

• ≠ Test value: Two-sided alternative hypothesis that the proportion is not equal to test value.
• > Test value: One-sided alternative hypothesis that the proportion is larger than the test value.
• < Test value: One-sided alternative hypothesis that the proportion is smaller than the test value.

Additional Statistics

• Confidence interval: Coverage of the confidence intervals in percentages. The default value is 95.
• Vovk-Sellke Maximum p-Ratio: The bound 1/(-e p log(p)) is derived from the shape of the p-value distribution. Under the null hypothesis (H0) it is uniform(0,1), and under the alternative (H1) it is decreasing in p, e.g., a beta(α, 1) distribution, where 0 < α < 1. The Vovk-Sellke MPR is obtained by choosing the shape α of the distribution under H1 such that the obtained p-value is maximally diagnostic. The value is then the ratio of the densities at point p under H0 and H1. For example, if the two-sided p-value equals .05, the Vovk-Sellke MPR equals 2.46, indicating that this p-value is at most 2.46 times more likely to occur under H1 than under H0.

Plots

• Descriptive plots: The proportion and confidence interval of the two different values of your dichotomous variable
• Confidence interval: Coverage of the confidence intervals in percentages. The default value is 95.

Output

Binomial Test

• Level: The two options of the dichotomous variable
• Counts: the count of the instances at the certain level of the dichotomous variable. The counts of all possible levels will result in the total.
• Total: the total number of observations.
• Proportion: calculated by counts/total.
• p: p-value.
• VS-MPR: Vovk-Sellke maximum p-ratio.

Descriptive Plots

• Displays the proportion of the level of interest (black dot) and the width of the 95% credible interval. The horizontal dotted line represents the when the proportion of both levels would be equal (= 0.5).

References

• Sellke, T., Bayarri, M. J., & Berger, J. O. (2001). Calibration of p values for testing precise null hypotheses. The American Statistician, 55(1), 62-71.
• Moore, D. S., McCabe, G. P., & Craig, B. A. (2012). Introduction to the practice of statistics (7th ed.). New York, NY: W. H. Freeman and Company.

R Packages

• ggplot2
• stats

jasp-stats/jaspFrequencies documentation built on April 5, 2025, 3:53 p.m.