Question

Researchers in Norway examined the records of 85,176 children to look for a possible association between use of folic acid during pregnancy and development of autism. The null hypothesis of interest is that use of folic acid is not related to risk of autism. The researchers set \(\alpha\) at 0.05 and stated that they had \(93 \%\) power to detect a certain difference in autism rates. Explain what "93\% power" means in this context. In particular, what is the probability of a Type II error? \(^{58}\)

Short answer

In this context, having 93% power means there is a 7% probability (\(100\text{%} - 93\text{%}\text)) of a Type II error, which is failing to detect a difference in autism rates due to folic acid use when one actually exists.

Step-by-step solution

Understanding Power of a Test

Power of a test is the probability that the test will correctly reject a false null hypothesis. It is calculated as 1 minus the probability of a Type II error, which is the error that occurs when a false null hypothesis is not rejected.

Identifying Type II Error Probability

If the power of the test is 93%, it means that there is a 93% chance that the test will detect an effect (a difference in autism rates due to folic acid use) if there is one. To find the probability of committing a Type II error (also known as \( \beta \)), we subtract the power from 100%.

Calculating Probability of Type II Error

The probability of a Type II error \( \beta \) is given by 100% - Power of the test. So, it is 100% - 93% = 7%. This means there is a 7% chance that the researchers could fail to detect a difference in autism rates due to folic acid use, even if such a difference actually exists.

Key concepts

Type II Error

When scientists conduct experiments, they aim to discover if there is a true effect or relationship in their study. Imagine a scenario where a group of researchers is trying to find out if a new drug is effective against a disease. A Type II error, often symbolized as \( \beta \) error, occurs when the researchers conclude that the new drug has no effect when, in reality, it does. In simpler terms, it's a false negative—missing the detection of something that is actually there.

In the context of the given exercise, if the Norwegian researchers commit a Type II error, they would conclude that folic acid does not affect autism rates when indeed it does. This error can be particularly problematic because it might lead to a lack of necessary medical intervention or policy change. That's why understanding and attempting to minimize Type II errors is critical in medical research and other scientific inquiries. The researchers' report of having 93% power to detect a certain difference in autism rates implies that they have taken steps to reduce the chance of a Type II error as much as possible, but they do acknowledge there is still a small chance (7%) that such an error could occur.

Null Hypothesis

The null hypothesis is a concept in statistics that refers to the default position that there is no association, or no difference, between two measured phenomena. For example, if scientists wanted to test whether a new drug impacts patients' recovery times, the null hypothesis would be that the drug has no effect on recovery times.

In the exercise provided, the null hypothesis is that the use of folic acid during pregnancy is not related to the risk of autism in children. It serves as a starting point for statistical testing. Researchers then collect data and use statistical methods to determine if there is enough evidence to reject this null hypothesis. If they can reject it, they may conclude there is an association between folic acid use and autism risk. Otherwise, if they do not find sufficient evidence, by default, they will not reject the null hypothesis, though this does not necessarily prove it's true. It's essential for students to understand that 'failing to reject' a hypothesis is not the same as 'accepting' it.

Folic Acid and Autism Association

The relationship between folic acid intake during pregnancy and the development of autism in children is of significant interest within medical research. Folic acid, a B-vitamin, is crucial for proper fetal development and has been shown to reduce the risk of major birth defects of the baby's brain and spine. However, researchers are also investigating whether there is additionally an association with neurological development, such as autism spectrum disorders.

The exercise presented involves a large study in Norway that was set up to examine if such an association exists. With statistical analysis, the researchers aim to provide evidence that may support or refute the idea that folic acid use during pregnancy could influence autism risk. Understanding this association has profound implications on prenatal care guidelines and can impact the advice healthcare providers give to expectant mothers. This exemplifies how statistical analysis in health-related research can directly influence public health policies and personal health decisions.