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cofficient of rank correlation
not otherwise....split half method is one way of determining reliability of your test and Spearman-Brown formula is a technique used to re-calculate the correlation of your test when you split your test items into half.... this means that the result of Spearman-Brown provides you the correlation of your test in full length.
The correlation analysis is use in research to measure and interpret the strength of a logistic relationship between variables.
yes
If measurements are taken for two (or more) variable for a sample , then the correlation between the variables are the sample correlation. If the sample is representative then the sample correlation will be a good estimate of the true population correlation.