CORRELATIONRAN
The macro is designed to test the significance of the correlation between two variables.
RUNNING THE MACRO
Calling statement
correlationran c1 c2 ;
nran k1 (999) ;
corrs c1.
Input
C1
First variable
C2
Second variable
C1 and c2 must be columns, of the same length, containing only numerical values.
Subcommands
nran
Number of randomizations used.
corrs
Specifya column in which to store correlation coefficients for randomization samples.
Output
 Number of observations, and means for each variable
 Observed correlation coefficient
 Number of randomizations
 Randomization p-values
Speed of macro : FAST
Missing values : Allowed.
ALTERNATIVE PROCEDURES
Standard procedures
Correlation C2 C1.
This finds the correlation between the data in c1 and the data in c2, and gives the p-value for this
correlation.
TECHNICAL DETAILS
Null hypothesis : The two variables are uncorrelated, i.e.  = 0.
Test-statistic : The Pearson correlation coefficient.
Randomization: We randomize the allocation of the values to the second variable to the values of the
first variable, since under the null hypothesis the pairing of the two variables will be independent.
Note : This macro operates in exactly the same way as the simple linear regression macro,
REGRANSIMPLE. The output is substantially different, reflecting the different emphasis of correlation
as opposed to regression.
REFERENCES
MANLY, F.J. (1997) Randomization, bootstrap and Monte Carlo methods in biology,
Chapman and Hall, London (Chapter 8).
WORKED EXAMPLE FOR CORRELATIONRAN
Name of dataset
HEXOKINASE
Description
The data is taken from part of a study by McKechnie, concerning electrophoretic frequencies of the
butterfly Euphydryas editha. For each of 18 units (corresponding either to colonies, or to sets of colonies),
the reciprocal of altitude (originally measured in feet * 103) is recorded, together with the percentage
frequency of hexokinase 1.00 mobility genes from electrophoresis of samples of Euphydryas editha. We
choose to label these variables "invalt" and "hk" respectively.
Our source
MANLY, F.J. (1997) Randomization, bootstrap and Monte Carlo methods in biology,
Chapman and Hall, London.
Original source
MC. KECHNIE, S.W., EHRLICH, P.R. & WHITE, R.R. (1975), Population genetics of Euphydryas butterflies.
I. Genetic variation and the neutrality hypothesis, Genetics, 81, pp. 571-594.
Data
Number of observations = 18
Number of variables = 2
For each observation, HK (top) and INVALT (bottom) are given.
98.00 36.00 72.00 67.00 82.00 72.00 65.00 1.00 40.00 39.00 9.00
2.00 1.25 1.75 1.82 2.63 1.08 2.08 1.59 0.67 0.57 0.50
19.00 42.00 37.00 16.00 4.00 1.00 4.00
0.24 0.40 0.50 0.15 0.13 0.11 0.10
Plot
100
80
hk
60
40
20
0
0
1
2
invalt
Minitab worksheet
C1
HK measurements
C2
INVALT measurements
Aims of analysis
To investigate whether HK and INVALT measurements are correlated.
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Standard procedure
Welcome to Minitab, press F1 for help.
MTB > Retrieve "N:\resampling\Examples\Hexokinase.MTW".
Retrieving worksheet from file: N:\resampling\Examples\Hexokinase.MTW
# Worksheet was saved on 06/07/01 14:15:38
Results for: Hexokinase.MTW
Correlation c1 c2.
Correlations: hk, invalt
Pearson correlation of hk and invalt = 0.770
P-Value = 0.000
Resampling procedure
MTB > % N:\resampling\library\correlationran c1 c2 ;
SUBC> nran 499 ;
SUBC> corrs c4.
Executing from file: N:\resampling\library\correlationran.MAC
Data Display (WRITE)
Number of observations 18
Mean of first variable
39.11
Mean of second variable
0.98
Correlation coefficient
0.770
Number of randomizations 499
One sided randomization p-value, H1: -ve correlation
One sided randomization p-value, H1: +ve correlation
Two sided randomization p-value
0.0040
1.0000
0.0020
Modified worksheet
C4
A column containing 499 correlation coefficients, one for each randomized dataset
Discussion
There is clearly a strong positive correlation between the variables. The standard p-value is 0.000, whilst the randomization pvalue is 0.004, the smallest possible value for 499 randomizations.
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