A hypothesis test of the correlation coefficient can be structured as either two-tailed or one-tailed. A two-tailed test is utilized when a researcher has no prior expectation regarding the direction of the relationship, whereas a one-tailed test is selected if a specific directional relationship (either strictly positive or strictly negative) is anticipated.

Tails of a Correlation Test

What does the alternative hypothesis state in a test of a correlation coefficient?

The alternative hypothesis in a test of a correlation coefficient states that a true relationship does exist between the variables within the target population. It is mathematically expressed as $$ho 
eq 0$$, representing any non-zero population correlation.

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In a hypothesis test of a correlation coefficient, the null hypothesis posits that there is absolutely no relationship between the variables in the overall population. This parameter is mathematically represented using the Greek letter rho ($$ho$$), where the null hypothesis is precisely $$ho = 0$$.

Null Hypothesis for a Correlation Test

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KPU Research Methods in Psychology - 4th American Edition

Alternative Hypothesis for a Correlation Test

In a hypothesis test of a correlation coefficient, what does the null hypothesis posit about the relationship between variables in the overall population?

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