For our purposes these are modern ways of getting **Confidence Intervals** around any sample estimate of a population value. Bootstrap estimates make almost no assumptions about the distribution of observations in the data so are “non-parametric methods”.

#### Detail #

Bootstrapping is the most common of the “computationally intensive statistical methods” which became possible as computer power grew in the second half of the 20th Century. The only other such method you are likely to encounter with OM data is the “jack-knife”.

Bootstrapping a sample of data to find the confidence interval around a sample estimate involves “resampling”: say you have a sample of 127 clients’ first session scores on an OM and you want the confidence interval around the mean to tell you how precisely that mean might represent a population value. Say the mean of the 127 values is 1.39. Resampling involves creating a new sample of n = 127 by sampling “with replacement” from the actual 127 observed values and computing the mean for those and doing this again and again. “With replacement” means that any observation may occur in the resampled data set any number of times: zero, once, twice, even theoretically 127 times (but the probability of that happening is so low it can be ignored in the likely life expectancy of our planet). Doing this repeatedly creates a set of computed means and that distribution is used to get the confidence interval around the observed statistic, here the mean. There are actually a number of different ways to get the confidence interval from that distribution, you are likely to see “simple”, “BCA” (Bias Corrected and Accelerated”, “Normal” and “Percentile”. There are a few others but they are essentially esoteric for us.

There are some subtleties being left out here but this is a fair introduction to the method. When bootstrap methods are used in a research paper the methods section of the paper should state the software used, the number of bootstrap resamples and what method of determining the CI and how many resamples were computed.

See Bootstrap methods for more detail.

#### Try also … #

Bootstrap methods

Confidence Intervals

Precision

Sampling frame

Population

Jack-knife method

Computer intensive statistics/statistical methods

#### Chapters #

Not covered explicitly in the book

#### Further reading #

#### Online tools #

Should create tools for mean, median, Cronbach alpha, correlations and other statistics