One must exist, but for some reason I was not able to find a function to
compute the
pooled variance,
which is merely the weighted variance in which the weights are proportional
to *N _{i}* - 1 for each

*i*th population sample size.

Here is a simple function to do this in R, in which `y`

is a
numerical vector & *x* is a factor indicating population membership:

```
vars<-function(x) mean(x^2)-mean(x)^2
pooled.var<-function(y,x){
k<-length(levels(x))
N<-summary(x)
sum(sapply(levels(x),function(l,y,x) vars(y[x==l]),y=y,x=x)*
(N-1))/(sum(N)-k)
}
```

For instance:

```
y
```

```
## [1] 1.66643347 3.58241307 3.40930188 -0.96244911 3.01537895
## [6] 3.22039153 2.04945935 1.79276033 0.98006731 0.98435105
## [11] 2.21611933 0.99441260 4.76126946 3.67653758 2.05488395
## [16] 3.52969225 1.39656560 2.59958819 2.58375755 3.71407970
## [21] 1.78405433 2.14309964 3.13001545 2.08055789 2.24084935
## [26] 2.58348915 1.64146883 1.02864576 1.92799065 2.43943986
## [31] 1.15720010 2.13305540 0.01381969 0.74266785 1.81005551
## [36] 2.11757020 2.89246446 1.43198968 0.22427963 2.06503921
## [41] 2.25585299 1.40974141 -0.15913367 2.71146586 2.61244346
## [46] 4.75615711 2.00224151 1.76408595 3.84962963 0.76250972
## [51] 2.10770717 -0.74763840 2.68343365 2.91244893 2.77712141
## [56] 2.22598145 2.39142779 3.97542995 4.92703017 2.59852609
## [61] 4.46669762 2.68039345 0.50455457 3.51400883 1.19135850
## [66] 0.91997801 4.12391415 2.12656807 1.29092722 1.89407708
## [71] 3.10823065 0.73155236 1.72465298 -1.13770643 3.27578802
## [76] 0.14202787 2.15587529 3.09957313 2.14737089 2.21819412
## [81] 1.01937433 0.61840772 3.06101451 3.09378180 0.67329345
## [86] 1.14656171 3.59971781 3.27936076 2.53420574 2.78287851
## [91] 2.00604970 3.13107129 1.31622894 4.38502427 0.54058999
## [96] 2.79645069 2.61484882 4.33965617 3.42823455 1.88759749
```

```
x
```

```
## [1] a c c a a b b c b b b b c c c c c c c b a b c c a a b a a b b b b a c
## [36] b a a a a b a a c c c b b b a b a c b c c c c c c c b b c b a c b a b
## [71] c b c a b b b b c c a a b c a c c b b c b b b c a b b c b c
## Levels: a b c
```

```
pooled.var(y,x)
```

```
## [1] 1.011426
```

That's it.

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