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→Formal definition: Added paragraph on independence with Normal random variables
The results of this test should be evaluated against the standard t-distribution with degrees of freedom equal to n-2. As usual in significance tests, a result described as significant (i.e. a low value of ''P'' in the ''t'' test) means that the chance of getting a correlation coefficient at least as large (whichever the direction) as that observed, if there is in fact no correlation, is small. A statistically significant result can therefore arise if the actual correlation is strong, even if the dataset is small, or if the actual correlation is weak but many data are observed.
The results of this test should be evaluated against the standard t-distribution with degrees of freedom equal to n-2. As usual in significance tests, a result described as significant (i.e. a low value of ''P'' in the ''t'' test) means that the chance of getting a correlation coefficient at least as large (whichever the direction) as that observed, if there is in fact no correlation, is small. A statistically significant result can therefore arise if the actual correlation is strong, even if the dataset is small, or if the actual correlation is weak but many data are observed.
One should note that for most random variables a correlation of 0 does not imply that they are independent. However, if the two variables come from the [[Normal Distribution]] then it can be claimed that a correlation of 0 implies independence.
It is important to note that the correlation coefficient should not be calculated when either of the variables is not continuous. That is, when they do not vary continuously and have a meaningful zero. As such, correlating a dichotomous variable (e.g. sex) with a ratio variable (e.g. IQ) is inappropriate and will return uninterpretable results.
It is important to note that the correlation coefficient should not be calculated when either of the variables is not continuous. That is, when they do not vary continuously and have a meaningful zero. As such, correlating a dichotomous variable (e.g. sex) with a ratio variable (e.g. IQ) is inappropriate and will return uninterpretable results.