critical_value: Calculate test critical value

In IyarLin/hype: Variuos functions for proportions difference hypothesis testing

Description

this function calculates the test statistic critical value C which guarantees significance level (false discovery rate) alpha

Usage

critical_value(p_1_hat, n_1, p_0_hat, n_0, alpha, s, h, gamma)

Arguments

p_1_hat	estimated population 1 p parameter
n_1	population 1 sample size
p_0_hat	estimated population 0 p parameter
n_0	population 0 sample size
alpha	test significance level
s	either 1 (for one sided test) or 2 (for two sided test)
h	number of hypothesis tested in the same experiment (for Bonferroni correction)
gamma	minimum required lift

Details

In 2 sided tests each usually represents a different treatment. When doing one-sided tests it's usually the case that population 1 is considered the treatment and population 0 serves as the control. At any rate, one sided tests are always of the form p_1 - p_0 > C. For that reason for 1 sided tests one must set: gamma >= 0

Value

critical value C

Examples

library(hype)

# For a thorugh simulation validation see
# https://github.com/IyarLin/hype/blob/master/inst/variuos_results_for_hypothesis_testing.pdf

# below we'll generate critical values for 2 hypothesis tests performed
# in the same experiemnt
# note that h is set to 2 in order to reflect that

## hypothesis test number 1
critical_value(
  p_1_hat = 0.225, n_1 = 10000, p_0_hat = 0.2, n_0 = 8000,
  alpha = 0.05, s = 1, h = 2, gamma = 0.01
)

# this is significant

## hypothesis test number 2
critical_value(
  p_1_hat = 0.114, n_1 = 5000, p_0_hat = 0.1, n_0 = 3000,
  alpha = 0.05, s = 2, h = 2, gamma = 0
)

# this is insignificant

IyarLin/hype documentation built on July 20, 2020, 4:07 p.m.