How to output bootstrap results

Bootstrap result output: Point Estimation: Estimated Value of the Popular Statistics Confidence Interval: The range of probability of the estimated value p value: When there is no significant difference, the probability of the occurrence of the observed statistics is repeated sampling. Bootstrap provides point estimates, confidence intervals and p values ​​to help evaluate the accuracy of the population statistics and the validity of the assumptions.

Bootstrap result output

Bootstrap is a statistical method for data sampling. By repeating sampling from the original data, it can provide an estimate of the population statistics.

Output format

Bootstrap results are usually output in the following format:

• Point estimation: Estimated value of the statistics of the original data sample.
• Confidence interval: The confidence interval for the population statistics, indicating the range of probability of the estimated value.
• p-value: The probability of the occurrence of an observational statistic when H0 (no significant difference) is true.

Output interpretation

• Point Estimation: It represents the best estimate of the overall statistics, but there is a confidence interval.
• Confidence interval: It represents the accuracy of point estimation. The narrower the confidence interval, the more accurate the estimate.
• p value: It is used to test hypothesis H0. A p-value is less than a predefined level of significance (e.g., 0.05) indicating that H0 may not be true.

Example

Suppose we have 100 samples of data with an average of 50. With Bootstrap, we can generate 1000 duplicate samples, the average value of each sample. The result of Bootstrap may be:

• Point Estimation: 52
• Confidence interval: [51, 53]
• p value: 0.02

explain:

• Point estimates indicate that the overall average is about 52.
• The confidence interval shows that our estimate of the overall mean is 95% confident, which is between 51 and 53.
• A p value of 0.02 means that when H0 is true, the probability of observing an average value of 52 is very low, which indicates that H0 may not be true.

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