Spearmans Rank correlation coefficient

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Spearmans Rankcorrelation coefficient

• used with ordinal data . . .

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Inferential statistics
We move from descriptive to inferential
statistics. Nor longer are we simply comparing
data sets we are now seeking cause and effect
relationships. Note that a statistical
relationship can occur where no meaningful
relationship is possible. Such a relationship
is spurious. So any positive statistical
result must always be backed up by sound
reasoning.
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Scatter graphs
It is usually wise to draw a scatter graph, if
undertaking any correlation. It is an easy way
to highlight any relationship that may exist and
its type, whether direct or inverse.
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GNP and adult literacy
Let us test whether there is a relationship
between GNP per capita and educational provision.
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GNP and adult literacy
First, construct a null hypothesis (Ho) that
there is no relationship between GNP per capita
and adult literacy.
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GNP and adult literacy
Spearmans Rank correlation coefficient (Rs) is
the best method to use, as the GNP data is skewed.
Remember, Spearmans Rank can only be used with
ordinal data. It is necessary, therefore, to
rank-order the data first.
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Setting out Spearmans Rank . . .
Set the data out as shown with columns for
ranking the variables and n and Sd2 at
base
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Ranking the X data . . .
The GNP (X) is already rank-ordered all it
needs is to enter the ranking, in this case from
lowest to highest.
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Ranking the Y data . . .
Ranking is now complete for GNP. Do the same for
adult literacy (again start with the lowest
value. . .)
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Rank ordering completed . . .
Both variables X and Y are now ranked. It is
time to find the difference of (Rank X - Rank Y)
or d.
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Squaring d . . .
To get rid of the minuses, square (d) . . .
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Summing d2 . . .
Now sum d2 . . . . . . which gives the
answer 44.
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Getting n . . .
There are ten countries so n 10
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Calculating Spearmans Rank . . .
Insert the figures into the equation . . .
( 6 x 44 ) (1000 100)
Rs 1 -
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The answer to Spearmans . . .
. . . and, he presto, the answer to Rs is 0.733.
264 990
Rs 1 -
Rs 1 0.267
Rs 0.733
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Your (Rs) findings . . .
Null hypothesis (Ho) was that there was no
relationship between GNP per capita and adult
literacy. The degrees of freedom are (n 1).
So df 9. Spearmans Rank correlation
coefficient (Rs) result of 0.733 exceeds the 95
probability value of 0.60 at 9 degrees of
freedom. Therefore the Ho must be rejected
and replaced by the alternative hypothesis (H1)
that there is a relationship between GNP per
capita and adult literacy.