Bootstrap sample statistics and graphs for Bootstrapping for 1-sample function

A histogram divides sample values into many intervals and represents the frequency of data values in each interval with a bar.

Interpretation

Use the histogram to examine the shape of your bootstrap distribution. The bootstrap distribution is the distribution of the chosen statistic from each resample. The bootstrap distribution should appear to be normal. If the bootstrap distribution is non-normal, you cannot trust the bootstrap results.

50 resamples

1000 resamples

An individual value plot displays the individual values in the sample. Each circle represents one observation. An individual value plot is especially useful when you have relatively few observations and when you also need to assess the effect of each observation.

Interpretation

With a large sample size, the bootstrap sample will usually have a similar center and spread as the original sample. However, a small sample size may result in a bootstrap sample that is not similar to the original sample. If your bootstrap sample does not look like your original sample, you should consider increasing your sample size.

Sample size of 8

Sample size of 50

The bar chart shows the proportion of occurrences for each category.

Interpretation

With a large sample size, the bootstrap sample will usually have similar proportions as the original sample. However, a small sample size may result in a bootstrap sample that is not similar to the original sample. If your bootstrap sample does not look like your original sample, you should consider increasing your sample size.

Sample size of 8

Sample size of 50

The number of resamples is the number of times Minitab takes a random sample with replacement from your original data set. Usually, a large number of resamples works best. The sample size for each resample is equal to the sample size of the original data set. The number of resamples equals the number of observations on the histogram.

The average is the sum of the chosen statistics in the bootstrapping sample divided by the number of resamples.

The standard deviation of the bootstrap samples (also known as the bootstrap standard error) is an estimate of the standard deviation of the sampling distribution of the chosen statistic.

Confidence intervals are based on the sampling distribution of a statistic. If a statistic has no bias as an estimator of a parameter, its sampling distribution is centered at the true value of the parameter. A bootstrapping distribution approximates the sampling distribution of the statistic. Therefore, the middle 95% of values from the bootstrapping distribution provide a 95% confidence interval for the parameter. The confidence interval helps you assess the practical significance of your estimate for the population parameter. Use your specialized knowledge to determine whether the confidence interval includes values that have practical significance for your situation.