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. 2020 May 7;8:e9089. doi: 10.7717/peerj.9089

Box 1. Key concepts in frequentist statistics.

  • A sampling distribution is the distribution of sample statistics computed using different samples of the same size from the same population.

  • A bootstrap distribution is a distribution of statistics computed using different samples of the same size from the same estimated population formed by merging many copies of the original sample data. Alternatively, the sample data may be used to estimate parameters of a statistical distribution, and then this distribution can be used to generate new samples. This alternative is termed the parametric bootstrap.

  • A null or randomization distribution is a collection of statistics from samples simulated assuming the null hypothesis is true.

  • The standard error of a statistic is the standard deviation of the sampling distribution. When forming confidence intervals, we can estimate the standard error using the standard deviation of a bootstrap distribution. When calculating p-values, we can estimate the standard error using the standard deviation of the randomization distribution.

  • 2 SE rule: when statistics have bell-shaped (i.e., approximately Normal) sampling distributions, we expect roughly 95% of sample statistics to be within 2 standard deviations of the mean of the sampling distribution.

  • A confidence interval for a parameter is an interval computed from data using a method that will include the parameter value for a specified proportion of all samples (e.g., 95% of the time for a 95% confidence interval).

  • The p-value is the chance of obtaining a sample statistic as extreme as (or more extreme than) the observed sample statistic, if the null hypothesis is true.