So, what is Hypothesis testing? In plain English, Hypothesis Testing is a way to figure out if an idea or assumption about a group of people is actually true, based on the data that are available. Hypothesis testing is widely used in biomedical research to confirm whether there’s a connection between different variables, like if having a certain disease affects levels of a specific biomarker in the body.
What is hypothesis testing?
During hypothesis testing, we test the data against two hypotheses: the null hypothesis and the alternative hypothesis.
Null hypothesis:
The null hypothesis states that there is no relationship or difference between the variables of interest. So, for example, if we’re looking at a group of people and comparing their insulin resistance based on whether they smoke or not, the null hypothesis would be that there’s no difference in insulin resistance between smokers, former smokers, and non-smokers.
Alternative hypothesis:
The alternative hypothesis states that there is a relationship or difference between the variables of interest. It is the opposite of the null hypothesis. Using the same example as above, the alternative hypothesis would suggest that there is a significant difference in insulin resistance between smokers, former smokers, and non-smokers. Generally, the alternative hypothesis represents what the researcher is trying to prove.
Simply put, hypothesis testing involves comparing the observed data to what we would expect if the null hypothesis were true. To test the null hypothesis, we gather all the data we need and use statistical methods to figure out something called a “test statistic”. This test statistic tells us how different our observed data is from what we would expect if the null hypothesis were true. Then, we calculate what’s called a “p-value”, which shows us the probability of getting our observed data if the null hypothesis were actually true. We also set a limit or cut-off for the p-value, which is called the significance threshold. Most studies use a cut-off for the p-value at.05, but sometimes people use .01 or .001 instead.
What are significant and non-significant results?
If the p-value falls below the cut-off we have set, we reject the null hypothesis and accept the alternative hypothesis. A p-value below the significance threshold indicates that the observed data are unlikely to have occurred by chance and that there is likely to be a relationship or difference between the variables under consideration. This relationship or difference is termed “statistically significant.”
It is important to note that rejecting the null hypothesis does not prove the alternative hypothesis. A p-value below the significance threshold only indicates that the alternative hypothesis is a more plausible explanation for the observed data than the null hypothesis is. The goal of hypothesis testing is to determine which of these two hypotheses is more likely to be true based on the available data.
What are directional and non-directional hypotheses?
While performing hypothesis testing, you can set two types of alternative hypotheses: directional and non-directional.
Directional hypothesis:
A directional hypothesis, also called a one-tailed hypothesis, specifies the direction of the expected difference or relationship between the variables being tested. One such example would be that X treatment lowers serum creatinine levels in patients with chronic kidney disease. In this case, the direction of the change is specified.
Non-directional hypothesis:
A non-directional hypothesis, also termed a two-tailed hypothesis, does not specify the direction of the expected difference or relationship between the variables being tested. In the above example, a two-tailed hypothesis would be that X treatment changes serum creatinine levels in patients with chronic kidney disease (i.e., it could increase or decrease these levels).
Depending on your research goals, you can choose to use a directional or non-directional hypothesis. In the above scenario, it makes sense to use a directional hypothesis since you need to find a treatment that can lower serum creatinine levels. However, if you were exploring whether serum vitamin D concentrations differ between children with and without sickle cell anemia, you could choose a non-directional hypothesis since you might not be sure whether the concentrations are higher in children with sickle cell anemia or vice versa.
What is the multiple testing problem?
When multiple hypotheses are tested simultaneously, there is an increased likelihood of obtaining at least one false positive result by chance alone, even if all of the hypotheses are actually false. This is because the probability of obtaining a statistically significant result by chance increases with the number of tests being performed. This can lead to incorrect conclusions and can compromise the quality of the study.
To tackle this problem, statisticians have come up with various techniques to account for multiple testing. For example, the Bonferroni correction or the Benjamini-Hochberg procedure. These methods can help you control for the risk of making false discoveries by adjusting the significance level for each individual test or by ranking the tests based on their p-values. That way, you can be more confident that any significant findings you get are truly meaningful.
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