CORRTEST DATA1(VAR1,VAR2),DATA2(VAR1,VAR2),L tests the equality of correlation coefficients in two samples and CORRTEST DATA(VAR1,VAR2),L tests whether the correlation coefficient in one sample is 0.If only sample correlation coefficient(s) and sample size(s) are available, the following alternative forms of CORRRTEST can be used: CORRTEST TWO-SAMPLE,R1,N1,R2,N2,L tests equality of correlation coefficients R1,R2 from samples of sizes N1,N2, respectively. CORRTEST ONE-SAMPLE,R,N,R0,L tests the hypothesis R=R0 from a sample of size N. Parameters can be given either as numeric constants or through specification like R1=0.5679 . In these alternatives the standard test based on Fisher's z transformation is used. However, in the latter case when R0=0 the standard t test is used.CORRTEST DATA1(VAR1,VAR2),DATA2(VAR1,VAR2),L for Survo data DATA1 and DATA2 (no IND, CASES, SELECT specifications are accepted; see COMPARE?) compares correlation coefficients in two samples by using the test statistics U=[Fisher(R1,N1)-Fisher(R2,N2)]/sqrt[1/(N1-3)+1/(N2-3)] where R1 and R2 are sample correlation coefficients, N1 and N2 sample sizes, and Fisher(R,N)=0.5*sqrt(N-3)*log[(1+R)/(1-R)] . If the samples are from bivariate normal distributions with the same correlation coefficient, U is asymptotically N(0,1) and this approximation is good already for rather small sample sizes. However, in non-normal cases the normal approximation of U may be poor. Therefore the P value (one-sided test) is calculated also by simulation. Both data sets are standardized (means=0, std.devs=1) and these modified data sets are combined. From this data set of N1+N2 observations N1 pairs of values are taken at random as `sample' 1 and the other pairs form `sample' 2. The U value of this randomized pair of samples is computed and the relative frequency of U's exceeding the original U value is counted while repeating the randomization process. Maximum number of replicates is given by SIMUMAX (default 10000000). The seed number of the random number generator (either 'rand' or 'urand') is given by RAND (default RAND=rand(123456789). See RAND? . The process may be interrupted by pressing any key. The results are displayed after each 100 replicates as a table of the form N P Confidence interval (level=0.95) # of replicates Estimate of P lower limit s.e. Standard error upper limit The confidence level for P is set by CONF=p (0.8<p<1). Default is CONF=0.95 ........................................................................... Example: DATA K1:(X,Y) 3,3 3,4 2,3 3,4 2,2 1,2 5,6 3,2 END DATA K2:(X,Y) 3,2 5,4 5,2 3,1 2,2 3,4 4,4 2,4 3,2 2,3 END CORRTEST K1(X,Y),K2(X,Y),CUR+1 / RAND=rand(19962) Comparing correlation coefficients in 2 samples: Sample 1: Data K1, Variables X,Y N1=8 R1=0.83887 Sample 2: Data K2, Variables X,Y N2=10 R2=0.12069 Test based on Fisher's z 1.87189 Normal approximation P=0.0306107 N P Confidence interval (0.95) 5176600 0.06230228 0.06209407 lower limit s.e. 0.00010623 0.06251050 upper limit CORRTEST DATA(VAR1,VAR2),L tests on the basis of the sample whether the correlation coefficient is 0. The usage is otherwise similar to the two-sample version. First the standard test based on the transformation to t distribution is performed. In the randomized test the values of the second variable are randomly permuted in each replicate. P values for both 1- and 2-sided tests are computed. ........................................................................... DATA K1:(X,Y) 3,3 3,4 2,3 3,4 2,2 1,2 5,6 3,2 END CORRTEST K1(X,Y),CUR+1 / RND=rand(19962) SIMUMAX=1000000 Testing hypothesis correlation coefficient = 0: Sample: Data K1, Variables X,Y N=8 R=0.83887 Standard t test value 3.77492 P=0.00461763 (2-tailed P=0.00923526) 1-tailed test 2-tailed test N P Conf.int. P Conf.int. (0.95) 1000000 0.01772600 0.01746738 0.02131400 0.02103092 lower limit s.e. 0.00013195 0.01798462 0.00014443 0.02159708 upper limit 1 = More information on optional multivariate operations M = More information on multivariate analysis T = More information on statistical tests

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