Once upon a time in a reference I can not nail down at the moment, G.
E. P. Box published a short paper, in which he showed that when
comparing two sample sets using estimated standard deviations
determined from the data,
(a) When the variances are equal, (the assumption of the Student 't'
equation), and the samples size are equal [n(1) = n(2)] the equation
merging the variances can be used, and the calculated p-value is
valid, and can be used against a predetermined critical value to
establish a valid conclusion. [this was the original paper using the
equation, perhaps by Student/ Gossett.]
(b) when n(1) is not equal n(2), but var(1) = var(2), the equation
for (a) above remains mathematically valid. (this may have been
done prior to Box's paper, perhaps by Student/ Gossett)
(c) when the variances are not equal (i. e., more than a ratio of 3,
or significantly different by an F test), but n(1) = n(2), the
equation for (a) above is still mathematically valid.
(d) Only when n(1) is quite a ways different than n(2), AND var(1)
is quite a ways from var(2) (i. e., greater than that ratio of 3), do
we need to use the (more complex) different equation that merges the
variances differently, and calculate a different degrees of freedom.
My question to you, the knowledgeable community:
i) what is the Box ref., exactly (I can find it, but maybe someone
already knows it by heart)
ii) Have there been follow-on papers that support or dispute Box's
claims?
iii) Is there a consensus that for "practical purposes," Box's
claims are valid, or invalid?
Side note: The phrase "practical purposes," means medical studies
that are unlikely to be repeated are exempt from consideration. :)
[OK, OK already! That's a joke!]
iv) in proper English text writing, should the possessive be
Box' and Santos' or
Box's and Santos's ?
Jay
Jay Warner on the road,
Working out of Racine, WI, USA
[log in to unmask] [that's letter 'a' - number '2' - letter 'q']
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