Epidemiology & Biostatistics

There are two types of hypotheses:

1. The Statistical (Null) Hypothesis is always stated as if that there is not a relationship between the variables. This might sound funny because researchers conduct studies because they think that there will be a difference or a relationship between variables. But, statistical testing starts with the assumption that there is not a relationship or difference. This is why the statistical hypothesis is called the null (none, nothing) hypotheses. For example, even though we think that a new medication will reduce the number of strokes, and we start with a research (alternative) hypothesis that Drug X is associated with a reduction in the number of strokes, the null hypothesis would be that Drug X has no relationship to the number of strokes.
2. The Research (Alternative) Hypothesis states what the researcher 'thinks' or hypothesizes' will happen. For example, if a team of researchers wants to determine whether that a new medication will reduce the number of strokes, they would write a research (alternative) hypothesis such as, "The antihypertensive medication (Drug X) is associated with significantly fewer strokes when compared to the older medication (Drug Z).

There are two types of hypothesis testing errors:

1. A type 1 error occurs when you incorrectly reject the null hypothesis and, thus, incorrectly accept the research (alternative) hypothesis. Since the null hypothesis states that there is no relationship between the variables or no difference between the groups, when you make a type 1 error you incorrectly reject the null hypothesis and incorrectly accept the research (alternative) hypothesis. That means that the researcher incorrectly concludes that there is a relationship or difference when there really is not one. This is important because it means that you incorrectly conclude that a new drug, treatment, or other intervention works when it really does not work. Another example of a type 1 error occurs during a jury trial, when the jury decides that the person is guilty based on the evidence provided, even though the person is not guilty and did not commit the crime.
2. A type 2 error occurs when you incorrectly accept the null hypothesis and, thus, incorrectly reject the alternative hypothesis. Since the null hypothesis states that there is no relationship between the variables or no difference between the groups, when you make a type 2 error you incorrectly accept the 'no relationship/no difference' and incorrectly reject the alternative hypothesis that there is a relationship between the variables or a difference between the groups. So, you incorrectly determine that there is no relationship or difference when there really is one. This is important because it means that you incorrectly conclude that a new drug, treatment, or intervention does not work when it really does work. Another example of a type 2 error occurs during a jury trial when the jury decides that the accused person is not guilty, even though they really did commit the crime and are guilty.

It is important to note that sample size plays an important role in determining statistical significance. When the sample size is too small, there may not be enough observations to be able to determine whether there is a statistically significant difference or relationship between the variables. So, too small of a sample size increases the risk of a type 2 error and incorrectly accepting the null hypothesis when there actually is a difference or relationship present. Small sample size is a common problem in student projects, so it is important to be aware that the failure to find a statistically significant difference may be due to small sample size (lack of statistical power).

Statistical Power is the ability to discern a deviation from the null hypothesis.  In short, a researcher who wants adequate statistical power must enlist a minimal number of participants for their particular study. There are many ways to calculate the minimal number of participants. One tool is G*Power: