PyData Global 2022 - Lightning Talk - Bessel's Correction
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The document discusses Bessel's correction, specifically the use of (n-1) as the denominator in calculating sample variance and standard deviation to avoid bias when estimating population parameters. It highlights that using the sample mean instead of the population mean leads to biased estimates due to closer proximity of sample values to the sample mean. The correction helps provide an unbiased estimator, especially for small sample sizes.
PyData Global 2022 - Lightning Talk - Bessel's Correction
- 1. Bessel's Correction: Effects of (n-1) as the denominator in Standard deviation Saradindu Sengupta PyData Global 2022 Senior ML Engineer @Nunam Where I work on building learning systems to forecast health and failure of Li-ion batteries.
- 2. Mean, Variance and Standard Deviation Sample Variance Sample Standard Deviation Population Variance Population Standard Deviation Mean PyData Global 2022
- 3. Why (n-1) Assume n number of samples are drawn from a population N with mean μ and variance s^2. The sample standard deviation and variance would contain a bias in all the scenarios because sample mean(x) would be used to calculate sample variance and standard deviation instead of population mean (μ) Any value in the sample n is going to be closer to sample mean(x) population mean(μ). The sum of squares in variance and standard deviation would be large with population mean(μ) than sample mean(x) PyData Global 2022
- 4. What to do To get an unbiased estimator, multiplying both sides by constant (N-1)/N would give When To use In cases where the sample size is small compared to the population, because the sum of square deviation is going to be severe PyData Global 2022
- 5. Demo Link: https://pydata-global-2022-lightning-talk.streamlit.app/ Low Sample Size High Sample Size PyData Global 2022
- 6. Thank You 6 PyData Global 2022 /in/saradindusengupta @iamsaradindu /saradindusengupta