Methods and formulas for Randomization Test for 1-Sample Mean

Select the method or formula of your choice.

Mean (bootstrap sample)

Formula

Notation

TermDescription
mean of the ith resample
B number of resamples
N number of observations in the original sample

Standard deviation of the bootstrapping distribution

Formula

Notation

TermDescription
mean of the resamples
B number of resamples
mean of the ith resample

P-Value

Formula

The calculation of the p-value depends on the alternative hypothesis.
  • Mean less than hypothesized value:
  • Mean not equal to hypothesized value:
  • Mean greater than hypothesized value:

Notation

TermDescription
lnumber of bootstrap means that are less than or equal to the sample mean
unumber of bootstrap means that are greater than or equal to the sample mean
βnumber of resamples
nlnumber of bootstrap means that are less than or equal to μ0d
nunumber of bootstrap means that are greater than or equal to μ0 + d
μ0hypothesized value
d
mean of the observed sample
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