Methods and formulas for Bootstrapping for 2-Sample Means

Select the method or formula of your choice.

Average

Formula

Notation

TermDescription
difference in means of the ith resamples
B number of resamples
N number of observations for one group in the original sample

Standard deviation of the bootstrapping distribution

Formula

Notation

TermDescription
mean of the differences of the resamples
B number of resamples
difference in means of the ith resample

Confidence interval

Formula

Sort the difference in means of the resamples in increasing order. d1 is the lowest number, dB is the highest number.

Lower bound: dl where =

Upper bound: du where =

Note

For a one-sided case (only a lower bound or upper bound), use α instead of α/2.

When l or u are not integers, Minitab does a linear interpolation between the two numbers on either side of l or u. The formula is:

dy + z(dy+1 - dy)

For example, if l = 5.25, the lower bound equals d5 + .25(d6 - d5).

Minitab does not display the confidence interval when or .

Notation

TermDescription
α 1- confidence level/100
B number of resamples
dy the yth difference when the data are sorted from least to greatest
y the truncated value of l or u
zl-y or u - y
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