Sex Ratio Forecast

[Jota Melgar <jsmelgar@compuserve.com>]

Dionigi wrote:

> Point 1: =

> Say that a scientist like Romer performs a study on the sex ratio of
> Apistos in relationship to pH and temperature.
> He or she will use a given number of pairs to replicate a given number
> of spawns for each specific water condition, from which the average of
> the sex ratio for each will be calculated. Given perfect study
> conditions, this average will be very realistic if it is based on an
> adequately large number of pairs for each pH and temperature condition,=

> because each individual spawn will have a different sex ratio, but all
> together, when averaged, they will provide a good GENERAL description o=
f
> the situation. The mean will in other words summarize the variability o=
f
> the individual spawn observations. =


I do partly agree with you. The key word here is "adequately large number=
s
of pairs for each pH and temperature condition". My main criticism for
Romer's paper is that in several species he did not use enough replicates=
=2E =


I do disagree in that the mean does not summarize variability, only
variance and standard deviation summarize variability. All the mean does =
is
measure central tendency. For example, if you get the mean (average) of s=
ay
10 and 2 you get 6. The same mean you would get for 7 and 5. So, even
though both sets of numbers have the same mean, the first one has the
larger variance.

> Point 2:
> Now, say that a week later Mr. Scientist receives a donation of another=

> large batch of pairs of apistos, he/she has free time, and it is decide=
d
> to duplicate the experiment.
> Well, this time not only as before each individual spawn (replicated in=

> exactly the same condition) will have a sex ratio different from each
> other, but also their mean will not be absolutely identical the one
> previously found. It will be in fact different, on the basis of the
> number of pairs used in this second experiment, and on the basis of the=

> intrinsic variability of the phenomenon being investigated.    This is
> due to the fact that there is also a variability in the sample mean.

Given that the second experiment is also done with an adequately large
sample size and having a high level of significance (i.e. <0.001) in the
first experiment, the results Mr. Scientist gets might not be exactly the=

same but, they should fall between the confidence interval of the first
experiment.

> This is way there are indeed statistical procedures that allow the
> scientist to say  (instead of  "in such conditions you should see such
> and such sex ratio"), "if you duplicate my conditions you have a very
> high probability to observe a sex ratio comprised between ....(low end
> of the ratio) and .... (upper limit of the ratio)", which gives a much
> more realistic presentation of what to expect. Depending on how large
> the original study is, and the natural variability of the event, these
> intervals of probability can be very narrow (say, between 1:1 and 1:1.2=
)
> or very large (say, expect between 5:1 and 1:30).  =


Exactly. When we look at the results we should not focus on absolute
numbers alone but on the numbers in association with their significance
level / confidence interval, which is a fancy word for how certain I am o=
f
my results.

> I do not have Romer's paper (is there anyone available to fax or mail i=
t
> to me, if it is in English? E-mail me, thanks), but unless the study wa=
s
> extremely large, it is unlikely that the estimates calculated allow a
> very precise forecast. They may however provide a useful guidance of th=
e
> general rules and trends of the gender ratio determination, which is
> still an extremely important discovery. =


That's the way how I take Romer's paper for most species. Send me your fa=
x
number and I'll send you a copy of it.

Good discussion by the way.

Regards,

Julio Melgar