2 - Statistical Hyphothesis Test

Ho - Equality: Your null hyphothesis is usually one of equality.

Ha - Inequality: Alternative hyphothesis is typically what you suspect or what you try to show.

How to Decide

If p >= α then Ho is not rejected.

If p < α then Ho is rejected.

The p-value is a statistical measure that helps to determine the significance of research results. When p value is lower than our cut-off value (α), it produces doubt about the truth of null hyphothesis.

If we set our α to 0.05 then it means that our cut-off probability value is one chance in twenty, so any extreme p values lower than that are not expected if our null hyphothesis is true.

If we reject null hyphothesis when it is actually true then we make Type I Error α, if we fail to reject null hyphothesis when it is actually false then we make Type II error β.

The power of a statistical test is equal to 1 - β where β is the Type II error rate. Note that the given information does not imply that α+β=1. α is a fixed value, but β varies depending on factors such as sample size, effect size and the power of the test.

So in summary;

• Type I Error (α): Incorrectly rejecting the null hypothesis when it is actually true.
• Type II Error (β): Failing to reject the null hypothesis when it is actually false.
• Power of a test (1 - β): The probability of correctly rejecting a false null hypothesis.

Effect Size and Sample Size Influence

Effect Size: The difference between the observed statistic and the hypothesized value.

Sample Size Influence: The effect of the sample size on the p-value. As the sample size increases, the p-value decreases, making you more confident in rejecting the null hypothesis when its p-value falls below the cutoff value.

• Sample size: As sample size increases, β decreases (the power of the test increases).
• Effect size: As the true effect size increases, β decreases.
• Power of the test (1 - β): As β decreases, the power of the test increases, .