Methods and formulas for Bootstrapping for 1-sample proportion

Select the method or formula of your choice.

In This Topic

Proportion of the observed sample
Average
P-Value

Proportion of the observed sample

When the chosen statistic is a proportion, Minitab displays the proportion from the observed sample.

Formula

Notation

Term	Description
x	number of events in the original sample
N	number of trials in the original sample

Average

Formula

Note

Minitab does not take resamples from the original column of data. Instead, Minitab takes the resamples by randomly sampling from a binomial distribution. The parameters for the distribution are taken from the original sample.

Notation

Term	Description
	proportion of the i^th resample
B	number of resamples
N	number of trials in the original sample

P-Value

Formula

The calculation of the p-value depends on the alternative hypothesis.

Proportion less than hypothesized value:
Proportion not equal to hypothesized value:
Proportion greater than hypothesized value:

Note

In some cases, Minitab performs a one-sided test because the p-value for the two-sided test cannot be calculated. For more information, go to Why do I get a one-sided test instead of a two-sided test?.

Notation

Term	Description
l	number of bootstrap proportions that are less than or equal to the sample proportion
u	number of bootstrap proportions that are greater than or equal to the sample proportion
β	number of resamples
n_l	number of bootstrap proportions that are less than or equal to ρ₀ − d
n_u	number of bootstrap proportions that are greater than or equal to ρ₀ + d
ρ₀	hypothesized value
d
	proportion of the observed sample