1) What is more important for the researcher to be concerned about in a study, Type I or Type II errors? Why? How does the type of data collected and the way in which the data is collected affect the possibility of Type I or Type II error?
2) Give two examples when practical significance would outweigh statistical significance. Explain your rationale.
Please see response below.
Interesting questions! Let's take a closer look through discussion and example.
1) What is more important for the researcher to be concerned about in a study, Type I or Type II errors? Why?
Type I errors (or error, or false positive) and type II errors (error, or a false negative) are two terms used to describe statistical errors. Scientists recognize two different sorts of error:
Type I error: "rejecting the null hypothesis when it is true". (False positive)
Type II error: "accepting the null hypothesis when it is false". (False negative)
A type I error is often considered to be more serious, and therefore more important to avoid, than a type II error. The hypothesis test procedure is therefore adjusted so that there is a guaranteed 'low' probability of rejecting the null hypothesis wrongly; this probability is never 0. This probability of a type I error can be precisely computed as
P(type I error) = significance level
The exact probability of a type II error is generally unknown. If we do not reject the null hypothesis, it may still be false (a type II error) as the sample may not be big enough to identify the falseness of the null hypothesis (especially if the truth is very close to hypothesis). For any given set of data, type I and type II errors are inversely related; the smaller the risk of one, the higher the risk of the other (Source: http://www.stats.gla.ac.uk/steps/glossary/hypothesis_testing.html#1err).
More information of the type I and type II error
1. TYPE I Error
For example, Type I error, also known as an "error of the first kind", an error, or a "false positive": the error of rejecting a null hypothesis when it is actually true. In other words, this is the error of accepting an alternative hypothesis (the real hypothesis of interest) when the results can be attributed to chance. Plainly speaking, it occurs when we are observing a difference when in truth there is none (or more specifically - no statistically significant difference). A false positive normally means that a test claims something to be positive, when that is not the case.
For example, a test saying a woman is pregnant when she is actually not pregnant is an example of a false positive. This is not ...
This solution discusses how researchers need to be concerned about in a study e.g. Type I or Type II errors, how the type of data collected and the way in which the data is collected affect the possibility of Type I or Type II error. It also provides two examples when practical significance would outweigh statistical significance.