Association Studies: Understanding the Level of Significance

In association studies, researchers aim to determine if there is a relationship or link between two variables, such as a genetic marker and a disease, or an exposure and an outcome. To do this, they often use hypothesis testing.

Hypothesis Testing Basics

• Null Hypothesis ($H_0$): This hypothesis states that there is no association or relationship between the variables being studied.
• Alternative Hypothesis ($H_a$): This hypothesis states that there is an association or relationship between the variables.
• P-value: The P-value is the probability of obtaining the observed results (or results more extreme) if the null hypothesis were actually true. It helps measure the strength of evidence against the null hypothesis.

The Level of Significance ($\alpha$)

The level of significance, often denoted by the Greek letter alpha ($\alpha$), is a threshold set by the researcher before conducting the study. It represents the maximum risk the researcher is willing to take of making a Type I error. A Type I error occurs when you reject the null hypothesis ($H_0$) even though it is actually true (i.e., concluding there is an association when there isn't one).

Interpreting the P-value Against the Significance Level

The decision rule in hypothesis testing is based on comparing the calculated P-value to the predetermined level of significance ($\alpha$):

• If the P-value is less than or equal to the level of significance ($P \le \alpha$), the null hypothesis is rejected. This suggests that the observed association is statistically significant and unlikely to have occurred purely by chance.
• If the P-value is greater than the level of significance ($P > \alpha$), the null hypothesis is not rejected. This suggests that the observed association is not statistically significant and could reasonably be due to random variation.

Common Benchmark in Association Studies

In many fields, including genetics, epidemiology, and clinical research, the conventional level of significance is set at 0.05. Therefore, a P-value is often compared against this specific benchmark.

• When $P = 0.05$, it indicates a 5% probability of observing the data (or more extreme data) if there were truly no association (if the null hypothesis were true). This value is widely used as the cutoff point.
• A P-value greater than 0.05 ($P > 0.05$) means the results are typically considered not statistically significant at the conventional $\alpha = 0.05$ level.
• Similarly, $P > 0.1$ would also indicate a lack of statistical significance.

Based on convention and the options provided, the level of significance is commonly considered as the threshold against which the P-value is compared, and $P = 0.05$ serves as this standard benchmark.