# Re: Help on the subject of random samples

related questions:

1) Suppose I had 4 million items (let's say widgets), clearly
delineated into 4 equal strata (1 million each). If one were to take
each separate strata of population of items, respectively shuffle them
to some extent, then package them in boxes haphazardly/conveniently
(and I use that in technical sense ) in boxes of 20, would the boxes of

items represent random samples from each strata? Or would the widget
boxes be haphazard samples? Let's assume that the strata shuffling
was unintentional and modest. >>

Let's name the original strata red, yellow, blue and green. The boxes
represent a sample, but the samples aren't samples of 20.
To see this, let's suppose there was NO shuffling. Then each box of 20
would come from a single strata, and would really represent a sample of
1 (given the correlation among items) from the point of view of color.
They would all be either red, or yellow, or blue, or green. In terms
of widget quality the 20 widgets would represent the quality of the
particular stratum they were drawn from (assuming random packing).

Another phrase for "unintentional and modest" is "I have no idea". One
person's "unintentional and modest" is another person's "chaos". So one
can't be extremely precise here.

<<2) If I set out to find one box from each of the strata from which
to
draw inferences to the entire widget population, would I be pursuing a
representative/random sample of the population, or would I be engaging
in non-random quota sampling? >>

If you picked the boxes randomly, you would represent the population
OK. There's the possibility of cluster effects within a box (e.g. the
20 items are those made between 12:01 and 12:02) so once again you
might not be able to consider it a sample of 20. You can think of it
as picking a sample of 1 box from 100 boxes, not 20 units from
20*100=2000 widgets and you will be OK.

<<3) If I were to then blindly reach into the box of items (say they
are
widgets) and grab four of them, could I be confident that those 4
widgets represent a random sample from the box itself? >>

No. For example, let's suppose the red ones were dumped into the box
first, then yellow, then green, then blue, and the widgets were not
shuffled. Then when you grab 4 you will tend to grab 4 of the same
color.

<< 4) Suppose that I do genuinely have 4 randomly selected widgets
from
each of the first three strata... but for whatever reason, I selected
only 2 random widgets from the fourth strata. I aggregate all 14
widgets... could I draw a reliable inference to the entire 4 million
widget population, or will even that limited difference in the 4th
strata hopelessly skew my results? >>

You can draw a reliable inference, but you should double weight the
fourth stratum.

.

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