Correlation

When discussing correlation, the significance level and power are important concepts in the context of hypothesis testing and statistical analysis.
Significance Level of 0.05
The significance level of 0.05 means that there is a 5% risk of concluding that a correlation exists when there actually is no true correlation (Type I error).
If one conducts a hypothesis test with significance=0.05, you are accepting a 5% probability of incorrectly rejecting the null hypothesis
This usually states that there is no effect or no correlation.

Power of 0.8
A power of 0.8 means there is an 80% chance of detecting a true correlation if it exists.
In other words, the test is designed to have an 80% probability of finding a statistically significant correlation when there really is one.
The power of a test is the probability that it correctly rejects the null hypothesis when the null hypothesis is false (i.e., the probability of not committing a Type II error).


Practical Example

Suppose you are studying the correlation between hours of study and exam scores among students.

Significance level is set to 0.05.
After performing the correlation test, you get a p-value of 0.03. Since 0.03 < 0.05,
you reject the null hypothesis and conclude that there is a significant correlation between hours of study and exam scores.

Power: You aim for a power of 0.8. This means that if there is a true correlation, your test has an 80% chance of detecting it.
If your test design and sample size ensure this power, you can be confident that your test is robust enough to find true correlations most of the time.


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