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8.8 Using Simulations to Understand Statistics

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  • I am a strong beleiver in the use of computer simulations to understand statistical concepts, and in later sessions we will dig deeply into their use. Here we will introduce the idea by asking whether we can confirm the need to subtract 1 from the sample size in computing the sample variance.

    Let’s treat the entire sample of children from the NHANES data as our “population”, and see how well the calculations of sample variance using either nn or n1n-1 in the denominator will estimate variance of this population, across a large number of simulated random samples from the data. We will return to the details of how to do this in a later chapter.

    Table 8.4: Variance estimates using n versus n-1; the estimate using n-1 is closer to the population value
    Estimate Value
    Population variance 725
    Variance estimate using n 715
    Variance estimate using n-1 730

    This shows us that the theory outlined above was correct: The variance estimate using n1n - 1 as the denominator is very close to the variance computed on the full data (i.e, the population), whereas the variance computed using nn as the denominator is biased (smaller) compared to the true value.