Spearman RankOrder Correlation

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Spearman Rank-Order Correlation

• HED 489 Biostatistics

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• When your data are skewed or you have ordinal
  data that you want to evaluate for a significant
  relationship, you can use Spearman Rank Order
  Correlation, often called Spearmen rho, or
  Kendall's tau. They give comparable results, so
  we're going to limit our discussion to Spearman.
  If you need to use Kendall, refer to the
  textbook.

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Spearman Rank-Order Correlation (rho)

• A non-parametric, inferential test of
  relationship between two, related sets of data.
• Requires at least ordinal data can use interval
  data.
• Does not require normal distribution.

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Spearman Formula

• Ddifference score between the ranks of each X
  and Y pair
• Nnumber of pairs of scores

Spearman operates on the differences between the
ranks of the X and Y variables. If the
relationship between the two variables were
perfect, every difference would be zero. The
greater the differences, the less perfect the
relationship.
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In Step 1, you rank the two variables. Note that
you assign the same rank to tied scores. Because
of space, I'm not showing you the entire ranked
table in the slide. Look at the textbook for the
whole thing.
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Step 2 involves calculating the differences
between the ranks. Subtract one variable from the
other. This is D.
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Step 3 squares the difference scores in order to
get rid of those negative numbers that all
respectable statisticians hate, and then totals
the resulting values. This is square first, then
sum.
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In Step 4, you multiply the sum of the squared
difference values by six. Note you always use
six. This completes the numerator of the formula.
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Step 5 is the denominator of the formula. I've
broken it into three parts. For 5a, count the
number of values.
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To complete the second part of Step 5, you
subtract one from the number of values squared.
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Finally, you multiply the number of values (Step
5a) by the number of values squared minus one
(Step 5b). This completes the denominator.
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For Step 6, you divide the number of values times
the number of values squared minus one into six
times the sum of the squared difference values.
This is divide Step 5 into Step 4.
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Finally, to calculate rho, subtract the results
of Step 6 from one. Notice that you always use
one. Be sure to indicate whether the value is
positive or negative.
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As you noted from the textbook, in order to
determine the significance of the rho value you
calculated, you have to calculate either z or t.
Because t is the harder of the two, I'll go
through it with you. After that, you should be
able to calculate z by yourself, if you need to.
The is Step 9 from the textbook. I've split it
up into five parts. In Step 9a, you simple
subtract two from the number of values. That
takes care of the numerator.
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Step 9b calculates the denominator of the
formula. Here, you square rho and subtract it
from one.
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In Step 9c, you divide Step 9a by Step 9b. That
takes care of the stuff under the square root
sign.
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For Step 9d, you take the square root of the
results of Step 9c.
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Finally, to complete Step 9e, divide results of
Step 9d by rho. This gives you t. To determine
whether the t value is significant, look it up in
the t table, using N-2 as degrees of freedom.
Your calculated value has to exceed the tabled
value. In this case, t is 1.02, and the critical
value at plt.05 is 2.10. So, you conclude that the
rho you calculated is NOT statistically
significant, and that the two rankings, that of
the teacher and that of the IQ test are NOT
related.
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Assignment

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