Parameter of interest is a descriptive statistic, often labeled as α=?
When researchers are interested in whether two groups differ from one another, the parameter being of interest is usually the null hypothesis H0- that they are not different. For example, when considering whether the voting habits of conservative versus liberal people are different then we might describe α= 0.05- meaning that we have a 5% chance of incorrectly concluding that there is a difference where none exists.
If an experiment doesn’t generate enough data to reject or support H0 (often because it wasn’t large enough), at this point our parameter b would be our unknown value for β – the population parameter and we should not make formal inferences about the population.
The parameter of interest (α) is the probability that we would make an incorrect decision about H0. The larger α needs to be, the more stringent our tests must become, because it becomes less likely that we will reject H0 when it is true.
For example, if α= 0.01 then only 1% of the time H0 could be rejected when it is true.
A significance level, or p-value, measures how extreme a test statistic is in relationship to the null hypothesis. The null hypothesis represents no difference between groups so the comparison needs to be made against this value. If you are comparing two different treatments then your parameter of interest is no longer the null hypothesis but rather the difference between treatments. In this case you would reject H0 if the difference between treatments was sufficiently large.
The term parameter of interest can be used in many different ways depending on who is using it and for what purpose. The most common use relates to statistical testing where it represents a test statistic of interest.