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Data-Centric Statistical Inference Using R and Tidyverse

Statistical Definitions

Explore important statistical definitions related to sampling, focusing on sampling distributions, standard error, and the concepts of accuracy and precision. Learn how sample size affects variation and how random sampling produces unbiased estimates centered on true population values.

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Now, for some important statistical definitions related to sampling, let’s take another look at our 1,000 repeated/replicated virtual samples of size 𝑛𝑛= 25, 𝑛𝑛= 50, and 𝑛𝑛= 100.

Comparing distributions of proportions of red for three different shovel sizes
Comparing distributions of proportions of red for three different shovel sizes

These types of distributions have a special name, which is sampling distributions. Their visualization displays the effect of sampling variation on the distribution of any point estimate, in this case, the sample proportion p^\hat{p}. Using these sampling distributions for a given sample size nn, we can make statements about what values we can typically expect.

For example, observe the centers of all three sampling distributions—they’re all roughly centered around 0.4 = 40%. Furthermore, observe that while we’re somewhat likely to observe sample proportions of red balls of 0.2 = 20% when using the shovel with 25 slots, we’ll almost never observe a proportion of 20% when using the shovel with 100 slots. Observe also the effect of sample size on the sampling variation. As the sample size𝑛𝑛 ...