Free Sample Size And Power Essay Sample
Sample size and power
In conducting a priori test on the required sample size given the effect size, alpha which is the size of the test and minimum power that is 0.80 in our case then the required sample size is 159. The actual power of the test that gives the required sample size is equal to 0.8048873. This may be because the power gives a sample size with a decimal point, and we have to round off to the nearest whole number because it does not make sense to have a sample size with a decimal point. The data points in each group will depend on the mean of the groups and the standard deviation within each of the groups.
The actual power post hoc for a sample size of 55 in conducting a chi-square goodness of fit test is 0.499.
The power of a test is the measure of its ability to correctly reject a false null hypothesis. Therefore, since the test is significant, there is no problem with the power of the test being less than 0.8. Thus since the statistical test has already shown significance, the purpose of the power was to support the significance.
When the test is insignificant, the power of the test should not be less than 0.8 because this will lead to type I error. That is the probability of accepting a false null hypothesis. The power and the size of a test are related in that an increase in the power of the test will lead to a decrease in the size of the test. It is the role of the researcher to establish a balance between these two since an increase in either of them leads to either type I or type II error and both of the errors are not appropriate for the analysis.