If we say that here is no significant association between two variable and if truly an association exists. Then it is called:
**Core Concept**
The question is testing the understanding of statistical errors in hypothesis testing. Type I and Type II errors are two common types of statistical errors that can occur when testing a hypothesis. A Type I error occurs when a true null hypothesis is rejected, while a Type II error occurs when a false null hypothesis is not rejected.
**Why the Correct Answer is Right**
When we say that there is no significant association between two variables, but in reality, an association exists, it means that we failed to detect the true association. This is because the sample size was too small or the study design was not robust enough to detect the association, leading to a false conclusion. This type of error is called a Type II error, also known as a **beta error**. It occurs when the null hypothesis is not rejected, even though it is false. In other words, we failed to detect a significant effect when it actually exists.
**Why Each Wrong Option is Incorrect**
**Option A:** Type I error refers to the rejection of a true null hypothesis, which is not the case here. A Type I error occurs when we conclude that there is an association between two variables, but in reality, there is none.
**Option C:** Systematic error refers to any error that is consistently in the same direction, such as a measurement error that always results in a higher or lower value. This is not related to the scenario described in the question.
**Option D:** Random error refers to any error that is due to chance, such as measurement errors that occur randomly. While random error can occur in any study, it is not the type of error described in the question.
**Clinical Pearl / High-Yield Fact**
When designing a study, it's essential to power it adequately to detect a significant effect if it exists. This means ensuring that the sample size is sufficient to detect the effect with a reasonable level of confidence. A common rule of thumb is to use a sample size that is at least 10 times the number of variables being tested.
**✓ Correct Answer: B. Type II error**