Course Notes
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A sample is a subset of data.
The easiest data collection method is convenience sampling
Simple random sampling = random balls
Systematic sampling = samples the data in regular intervals. It is only safe if it doesn't have a pattern.
For small sample sizes, each additional increase in the sample leads to smaller relative error
A sampling distribution is a distribution of several replicates of point estimates.
The standard deviation of the sampling distribution is approximately equal to the population standard deviation divided by the square root of the sample size.
Bootstrapping; the opposite of sampling: bulilding up a theoretical population from your sample.
The bootstrap distribution standard error times the square root of the sample size estimates the standard deviation in the population.
The 2 most important things
1. The standard deviation of the sampling distribution (a.k.a the standard error) of a statistic is well-approximated by the standard deviation of the bootstrap distribution of a statistic.
2. When calculating confidence intervals, it is OK to assume that bootstrap distributions are approximately normally distributed.
Take Notes
For small sample sizes, each additional increase in the sample leads to smaller relative error
A sampling distribution is a distribution of several replicates of point estimates.
The standard deviation of the sampling distribution is approximately equal to the population standard deviation divided by the square root of the sample size.
Bootstrapping; the opposite of sampling: bulilding up a theoretical population from your sample.
The bootstrap distribution standard error times the square root of the sample size estimates the standard deviation in the population.
The 2 most important things
-
The standard deviation of the sampling distribution (a.k.a the standard error) of a statistic is well-approximated by the standard deviation of the bootstrap distribution of a statistic.
-
When calculating confidence intervals, it is OK to assume that bootstrap distributions are approximately normally distributed.
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