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Pooled Standard Deviation

Pooled standard deviation is the square root of the pooled variance. Pooled variance is a method for estimating the variance of several different populations when the mean of each population may be different, but one may assume that the variance of each population is the same.

The pooled standard deviation increases with the square root of the sum of the squares of the sample standard deviations weighted by the sample sizes.

Formula

QuantityVariable[Subscript["s", "ρ"], "Unitless"] == Sqrt[((-1 + QuantityVariable[Subscript["n", "1"], "Unitless"])*QuantityVariable[Subscript["s", "1"], "Unitless"]^2 + (-1 + QuantityVariable[Subscript["n", "2"], "Unitless"])*QuantityVariable[Subscript["s", "2"], "Unitless"]^2)/(-2 + QuantityVariable[Subscript["n", "1"], "Unitless"] + QuantityVariable[Subscript["n", "2"], "Unitless"])]

symbol description physical quantity
sρ pooled standard deviation "Unitless"
n1 first sample size "Unitless"
n2 second sample size "Unitless"
s1 first sample standard deviation "Unitless"
s2 second sample standard deviation "Unitless"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Pooled Standard Deviation"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Pooled Standard Deviation"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject["Pooled Standard Deviation"], {QuantityVariable[ \!\(\*SubscriptBox[\("s"\), \("1"\)]\),"Unitless"] -> 3, QuantityVariable[ \!\(\*SubscriptBox[\("n"\), \("2"\)]\),"Unitless"] -> 10, QuantityVariable[ \!\(\*SubscriptBox[\("s"\), \("\[Rho]"\)]\),"Unitless"] -> Sqrt[29], QuantityVariable[ \!\(\*SubscriptBox[\("s"\), \("2"\)]\),"Unitless"] -> 7}]
Out[3]=

Publisher Information