Page 61 - Petrology of Sedimentary Rocks

The X2 test is used when you are comparing counts of of discrete objects between
discrete
test
The
is used
counts
are
comparing
between
you
when
X2
objects
larger
than
number
formations (like the number of grains larger than a given size in formation; or the
of grains
formations
the
formation;
in
or
the
(like
size
given
a
in
number
a
mineral;
certain
the
life,
ordinary
heavy
grains
number
number of of grains of of a certain heavy mineral; or or in ordinary life, the number of of
city
runs
hit by a team
each
of home
each
month;
or the number
accidents in a given city each month; or the number of home runs hit by a team each
accidents
in a given
week). In some cases it is possible to use both the X2 test or the t test, as in heavy
mineral counts (which may be converted to percentages); but the X2 test has this
advantage, that more than one item or property can be compared at a time. For
instance, if we count the number of tourmaline, rutile and zircon grains in two
formations, we can use this whole stack of data at once with X2 test and see if the
formations are significantly different. If we used the t test we’d have to make a
separate test for the tourmaline, another one for the zircon, another one for the rutile
and there would be no simple way to combine them.
To use the XL test we must in some way arrive at a predicted or expected
frequency or occurrence, based on a prior reasoning or else on long experience. We
then compare our observed frequency with the given frequency. For example, if we roll
a dice 600 times, we would expect that if the dice is well balanced each number (I
through 6) would appear equally and our expected frequency would therefore be 100.
Y/hen we actually do roll the dice, we may find that we got only 95 I’s, 123 2’s, 82 3’s,
etc. The purpose of the X2 test is to compare the observed with the expected
frequency and see how likely it is that the deviations are due to chance, or whether the
dice really is loaded. As another example, say that data collected over a period of 20
years shows that American League teams hit a grand total of 1,035 homers per season,
on the average; thus we would expect them to hit about 1,035 homers this season. Well,
this season they actually slammed 1,230 round trippers; is this “deviation” just due to
chance, or to a new “lively” ball ? The X2 test helps us to answer this question.
There are a number of different ways to set up the XL test. The one we’ll use
most is called a “2 by t-r” table--usually we are comparing two formations based on
counts of “r-r” types of heavy minerals, where “n” may be anythingfrom I to 20 or more.
For example, let us say that we count varieties of tourmaline in the Eli and Nineteenten
formations and want to know if a siqnificant difference exists between them in this
respect. We tabulate the number of grains thus:
Nineteenten Total
Eli fm. fm.
Green tourmal ines I5 25 40
(This is a 2 by n table
Brown tourmal ines IO I2 22 where n, the number of
different mineral types
Other colors 20 I4 34
equals 3)
Total 45 51 96
Does this data indicate that there is a real difference in the types of tourmaline
between the two formations? Or could we have gotten counts as different as this by
chance sampling of formations that were identical in tourmaline varieties?
Please remember, to use the X2 test, data must be stated in terms of actual numbers of
grains counted--you cannot convert to percentages and then use the X2 test.
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