Chi-square Test Power and Sample Size

Consider the following scenarios that describe Type 1 and Type 2 errors. Imagine you are the researcher in each situation:

In a Type 1 error you reject a null hypothesis when it is true. The tests conducted on your samples lead you to believe a difference exists between the populations the samples were drawn from when, in fact, the difference does not exist.

An example: You draw a sample of 5th grade boys from two different environments and test their height to see if the environment they live in affects their growth. You compute the 2-sample independent t-test and determine that the means of the two samples are significantly different. You reject the null hypothesis that there is no difference in mean height between these two populations. In reality, there is no difference but something about the way you drew the samples, or perhaps even the size of the samples, has caused you to commit a Type 1 error.

In a Type 2 error you fail to reject a null hypothesis when it is false. This time the tests lead you to believe there was no significant difference between the populations the samples were drawn from when, in fact, there is a significant difference.

An example: Consider the same example used to describe a type 1 error. Except now the 2-sample independent t-test suggests that there is no difference in mean height between the two populations from different environments. In reality, there is a significant difference in growth for these boys but something in the way you sampled the population has led you to commit a type 2 error.

Unfortunately, when researchers decrease one error, they increase the other. The only way to decrease both types of errors is to increase the sample size. Often in Public Health researchers are forced, by a limited sample size, to choose between increasing the risk of a type 1 or a type 2 error.

In preparation for this week’s Discussion, consider these examples in light of the information presented in the course text readings and chapter 8 lessons:
Essentials of Biostatistics in Public Health, Second Edition
Lisa M. Sullivan
Jones & Bartlett Learning, 2012
978-0-7637-9531-3

Using the example given above, or one of your own choosing, discuss which type of error you feel would be worse from a Public Health point of view. Also, state how you could adjust the power of your test to limit that type of error in your study. Support your opinions with the literature and cite your sources.