pooled standard deviation
/ poold STAN-derd dee-vee-AY-shun /
Imagine two short surveys, each asking only a handful of people the same question. Neither alone gives a confident sense of the spread of opinions, but if you reasonably believe both groups have similar variability, you can pool their answers to get one sturdier estimate. The pooled standard deviation does this for measurements.
The pooled standard deviation combines the scatter from two or more sets of measurements, assumed to share the same true precision, into a single best estimate of that precision. It is a weighted blend that gives each set influence according to its degrees of freedom, so a larger set counts for more. The result rests on more data than any one set alone, and so is more reliable.
It matters because it is the workhorse behind comparing two means with a t-test: you need one common measure of scatter to weigh the difference against, and the pooled standard deviation supplies it. The crucial caveat is the assumption it leans on — the sets must genuinely have similar variances. That assumption is exactly what an F-test should check first; pooling sets with very different spreads gives a misleading number.
Analyst A makes four measurements and analyst B makes five on the same sample. To compare their means with a t-test, their scatters are first pooled into a single standard deviation carrying seven degrees of freedom.
Two small datasets share their scatter to build one firmer estimate.
The degrees of freedom of a pooled standard deviation is the total number of measurements minus the number of sets pooled, because one mean is estimated for each set.