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I thought that 'pooling data' simply meant combining data that was previously split into categories...essentially, ignoring the categories and making the data set one giant 'pool' of data. I guess this is a question more about terminology than application of statistics.

For example: I want to compare 2 sites, and within each site I have two year-types (good and poor). If I want to compare the 2 sites 'overall' (that is, ignoring the year-types), is it correct to say that I'm pooling the data within each site? Further to that, since several years of data comprise the good and poor year-types, is it also correct to say that I am pooling the data among years to achieve the 'good year' and 'poor year' data set within each site?

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2 Answers 2

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Yes, your examples are correct.

The Oxford English Dictionary defines pool as:

pool, v.

(puːl)

1.1 trans. To throw into a common stock or fund to be distributed according to agreement; to combine (capital or interests) for the common benefit; spec. of competing railway companies, etc.: To share or divide (traffic or receipts).

Another example would be:

you measure blood levels of substance X in males and females. You don't see statistical differences between the two groups so you pool the data together, ignoring the sex of the experimental subject.

Whether it is statistically correct to do so depends very much on the specific case.

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  • $\begingroup$ Although this definition is correct, in a narrow sense, it does not cover what is arguably a more common yet subtler usage of "pooling" in statistical analyses. Usually pooling controls for (takes out the effects of) between-group variation, as Greg Snow's answer explains. $\endgroup$
    – whuber
    Jun 8, 2023 at 14:56
  • $\begingroup$ @whuber is that not the same as my example of males and females? Just wondering if I am missing something $\endgroup$
    – nico
    Jun 9, 2023 at 9:50
  • $\begingroup$ It's different. Look at the formula for a pooled SD in a t-test, for instance. $\endgroup$
    – whuber
    Jun 9, 2023 at 11:44
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    $\begingroup$ @whuber that makes sense, thanks for clarifying $\endgroup$
    – nico
    Jun 13, 2023 at 9:00
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Pooling can refer to combining data, but it can also refer to combining information rather than the raw data. One of the most common uses of pooling is in estimating a variance. If we believe that 2 populations have the same variance, but not necesarily the same mean, then we can calculate the 2 estimates of the variance from samples of the 2 groups, then pool them (take a weighted average) to get a single estimate of the common variance. We do not compute a single estimate of the variance from the combined data because if the means are not equal then that will inflate the variance estimate.

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  • $\begingroup$ Thanks @Greg. To clarify (because I'm trying to combine variances as well from the literature), what you're saying is that to get an 'average' variance for multiple populations, I can take a weighted mean of calculated variances? How would I weight those variances? Isn't each population = 1? $\endgroup$
    – Mog
    Jun 27, 2011 at 17:07
  • $\begingroup$ If the sample sizes are equal, then the simple average tends to work. Generally we give each data point equal weight, the standard formula is to multiply each variance by the degrees of freedom (or the number in the denominator for than group, n-1), then sum all the pieces, then divide by the sum of the degrees of freedom (all the n_i-1). $\endgroup$
    – Greg Snow
    Jun 27, 2011 at 18:30

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