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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 variance increases quadratically with the sample standard deviations weighted by the sample sizes.

Formula

QuantityVariable[Superscript[Subscript["s", "ρ"], "2"], "Unitless"] == ((-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
sρ2 pooled variance "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 Variance"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Pooled Variance"]]
Out[2]=

Use some values:

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

Publisher Information