Cambridge International A Level Biology Revision Guide

Cambridge International A Level Biology
504
Substituting into this formula, we can calculate
Spearman’s rank correlation coefficient for the distribution
of species R and species S.
(6 × 12)
r s
= 1 −
(10 3 – 10)
= 1 − 72
1000 – 10
= 1 − 72
990
= 1 − 0.072
= 0.928
= 0.93 (to 2 decimal places)
This number is the correlation coefficient. The closer the
value is to 1, the more likely it is that there is a genuine
correlation between the two sets of data.
Our value is very close to 1, so it certainly looks as
though there is strong correlation. However, as with the
t-test and the χ 2 test, we need to look up this value in a
table, and compare it against a critical value. As in most
statistical tests used in biology, we use a probability of
0.05 as our baseline; if our value indicates a probability
of 0.05 or less, then we can say that there is a significant
correlation between our two samples. Another way of
saying this is that the null hypothesis, that there is no
correlation between the two samples, is not supported.
Table P2.8 shows these critical values for samples with
different numbers of readings.
Notice that, the smaller the number of the readings we
have taken, the larger our value of r s
needs to be in order
to say that there is a significant correlation. This makes
logical sense – if we have taken only 5 readings, then we
would really need them all to be ranked identically to be
able to say they are correlated. If we have taken 16, then we
can accept a smaller value of r s
.
Remember that showing there is a correlation between
two variables does not indicate a causal relationship – in
other words, we can’t say that the numbers of species R
have an effect on the numbers of species S, or vice versa.
There could well be other variables that are causing both
of their numbers to vary.
For our data, we have 10 quadrats, so n = 10. The
critical value is therefore 0.65. Our value is much greater
than this, so we can accept that there is a significant
correlation between the numbers of species R and the
numbers of species S.
Table P2.9 summarises the circumstances in which
you would use each of the statistical tests that help you to
decide whether or not there is a relationship between two
sets of data.
Evaluating evidence
It is important to be able to assess how much trust you can
have in the data that you have collected in an experiment,
and therefore how much confidence you can have in any
conclusions you have drawn. Statistical tests are a big help
in deciding this. But you also need to think about the
experiment itself and any sources of error that might have
affected your results.
Sources of error were discussed in Chapter P1, on
page 263. You will remember that sources of error stem
from two main sources – limitations in the apparatus and
measuring instruments, and difficulty in controlling key
variables.
In a written practical examination at A level, you
will often be analysing data that you have not collected
yourself, so you will have only the information provided
in the question and your own experience of carrying out
experiments to help you to decide how much confidence
you can have in the reliability of the data. Important
things to think about include the following questions.
■■
■■
■■
■■
How well were the key variables controlled?
Was the range and interval of the independent variable
adequate?
Do any of the results appear to be anomalous? If so,
what could have caused these anomalous readings?
Have the provided readings been replicated sufficiently?
Another aspect of the experiment that needs to be
considered is its validity. A valid experiment really does
test the hypothesis or question that is being investigated.
n 5 6 7 8 9 10 11 12 14 16
Critical value of r s
1.00 0.89 0.79 0.76 0.68 0.65 0.60 0.54 0.51 0.51
Table P2.8 Critical values of r s
at the 0.05 probability level.