Part
IV: Correlation and Regression |
| | Testing Against Zero | Testing Against Non-Zero Values | Comparing Correlations | |
Most often, the test of a
correlation is whether the correlation coefficient is
significantly different from zero. This can be run as a
t-test:
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| In other cases, we will
want to test whether a correlation coefficient derived
from a sample is significantly different from some value
other than zero. In this circumstance the distribution
under null is highly skewed. To correct for this skewness
we must use Fisher's r to z transformation, where the
transformed value is normally distributed. Here the idea is to transform the correlations (using the formula below or a table of values for both the sample value and the hypothesized population value) and conduct the test on the transformed values.
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| This is a test of whether
2 sample correlations were derived from the same
population. In this case, the null hypothesis states that
the two values are equal. Due to the skewed sampling distributions of the correlations Fisher's r to z transformation must again be used. To test the hypothesis we must first convert both correlations and then use:
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