All statistics and graphs for Bootstrapping for 1-Sample Proportion

Find definitions and interpretation guidance for every statistic and graph that is provided with bootstrapping for 1-sample proportion.

Histogram

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 proportions from each resample. The bootstrap distribution should appear to be normal. If the bootstrap distribution is non-normal, you cannot trust the results.
50 resamples
1000 resamples

The distribution is usually easier to determine with more resamples. For example, in these data, the distribution is ambiguous for 50 resamples. With 1000 resamples, the shape looks approximately normal.

In this histogram, the bootstrap distribution appears to be normal.

Bar chart

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

Note

Minitab displays a bar chart when you take only one resample. Minitab displays both the original data and the resample data.

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

N

The sample size (N) is the total number of observations in the original sample. Minitab takes resamples of this sample size to form the bootstrap samples.

Proportion

The sample proportion equals the number of events divided by the sample size (N).

Interpretation

Minitab displays two different proportion values, the proportion of the observed sample and the proportion of the bootstrap distribution (Average). Both these values are an estimate of the population proportion and will usually be similar. If there is a large difference between these two values, you should increase the sample size of your original sample.

Because the proportion is based on sample data and not on the entire population, it is unlikely that the sample proportion equals the population proportion. To better estimate the population proportion, use the confidence interval.

Number of Resamples

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.

Average

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

Interpretation

Minitab displays two different proportion values, the proportion of the observed sample and the proportion of the bootstrap distribution (Average). Both these values are an estimate of the population proportion and will usually be similar. If there is a large difference between these two values, you should increase the sample size of your original sample.

Because the proportion is based on sample data and not on the entire population, it is unlikely that the sample proportion equals the population proportion. To better estimate the population proportion, use the confidence interval.

Confidence interval (CI) and bounds

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.

Note

Minitab does not calculate the confidence interval when the number of resamples is too small to obtain an accurate confidence interval.

Bootstrap Samples for Proportion
Number of Resamples
Average

In these results, the estimate for the population proportion is approximately 0.62. You can be 95% confident that the population proportion is between approximately 0.56 and 0.69.

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