202406061356
Status: #idea
Tags: Regression Analysis, MAT3375 ~ Regression Analysis
State: #nascient

Hypothesis Testing about Rho

The estimator for $\rho$ is:

The Simple Case

To check for significance of the correlation, we use an hypothesis test with the following t stat, under the assumption that $\rho =0$

In R, we use cor.test

The Harder Case

Sadly, when we want to check for cases where we thing $\rho$ is different from $0$, we need to use a transformation. Indeed, if $H_0$ is $\rho ={\rho }_0\ne 0$ , then we use:

Where ${\mu }_z$ is:

Besides the fact these formulas come from nowhere, since $Z_{obs}$ is normally distributed, we can reject if $|Z_{obs}|>Z_{\frac{\alpha }{2}}$

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