# Methods and formulas for Bootstrapping for 2-Sample Means

Select the method or formula of your choice.

## Average

### 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

### 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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