A curve has been found representing the frequency distribution of standard deviations of samples drawn from a normal population.
-Gosset. 1908, Biometrika 6:25.
last updated: 2021-10-11
A curve has been found representing the frequency distribution of standard deviations of samples drawn from a normal population.
-Gosset. 1908, Biometrika 6:25.
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# Let's simulate some fake weight data for 10,000 cats set.seed(42) cats <- rnorm(n = 10000, mean = 4, sd = 0.5)
Things you can measure with continuous precision
Mean
# Data myvar <- c(1,4,8,3,5,3,8,4,5,6) # Mean the "hard" way (myvar.mean <- sum(myvar)/length(myvar))
## [1] 4.7
# Mean the easy way mean(myvar)
## [1] 4.7
Standard Deviation
# (NB this is the sample variance with [n-1]) (sum((myvar-myvar.mean)^2 / (length(myvar)-1)))
## [1] 4.9
# Variance the easy way var(myvar)
## [1] 4.9
# Std dev the easy way sqrt(var(myvar))
## [1] 2.213594
Counts of rare events (like deaths from being kicked by a horse in the Prussian army…)
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set.seed(42) mypois <- rpois(n = 100, lambda = 3) hist(mypois, main = "Ewes with triplets", xlab = "Count of Triplets")
Counts of events with exactly two outcomes, one of which might be a “success” (like ‘deaths from being kicked by a horse in the Prussian army…’heads’ or ‘tails’, live or die, disease or healthy, etc.)
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A very common task faced when handling data is “diagnosing the distribution”. Just like a human doctor diagnosing an ailment, you examine the evidence, consider the alternatives, judge the context, and take a guess.
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