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Positive correlation = the slope of the scattered dots will rise from left to right (positive slope) Negative correlation = the slope of the scattered dots will fall from left to right (negative slope) No correlation = no real visible slope, the dots are too scattered to tell.
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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.
Fisher's exact probability test, chi-square test for independence, Kolmogorov-Smirnov test, Spearman's Rank correlation and many, many more.
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.