If the alpha error gets lower then why does the power reduces ?
How does the Beta errror becomes lower with increased sample size?
In what condition we would prefer more Beta error than alpha error and more alpha error than beta error and vice versa?
Does sample size have any effect on alpha error?
Kindly explain with examples in context of medicine especially public health?
James,
My mistake, and I also made some really bad grammatical errors like using a period when I had a question. Answering research gate questions the day after the children have had a sleep over (without sleep) may not have been the best choice. In review, it is a little odd that I typed Type !! rather than Type II in the third paragraph. However, the real problem is with paragraphs 4 and 5 which are revised below. The other paragraphs are ok.
Decreasing sample size reduces the probability of rejecting the null hypothesis. This INCREASES the probability of making a Type II error. Increasing the probability of a false negative (Type II error) reduces power.
This as a problem in risk analysis. What is the consequence if my company discards an effective treatment for cancer? What is the consequence of selling an ineffective product, or worse selling a product to cure cancer that increases heart attacks? My sample size was too small to correctly reject the null hypothesis that there were no adverse side effects.
Power is the probability of rejecting the null hypothesis when the alternative hypothesis is true. Power = 1 - probability of Type II error. Type II error is a failure to reject an incorrect null hypothesis.
Alpha is the probability of rejecting the null hypothesis when the null hypothesis is true. This is also referred to as a Type 1 error, or the probability of incorrectly rejecting the null hypothesis.
If I make alpha smaller it becomes harder to reject the null hypothesis. This increases the probability of not rejecting the null hypothesis when I should (Type !! error). Thus Power will decline.
Decreasing sample size reduces the probability of rejecting the null hypothesis. This reduces the probability of making a Type II error.
This of this as a problem in risk analysis. What is the consequence if my company discards and effective treatment for cancer. What is the consequence of selling an ineffective product, or worse selling a product to cure cancer that increases heart attacks. My sample size was too small to correctly reject the null hypothesis that there were no adverse side effects.
In a perfect world, increasing sample size should decrease the probability of making an incorrect conclusion. However, that assumes that there are no problems. So I run a clinical trial at the local hospital. For various reasons, that hospital has an unusually high proportion of drug addicts of Northern European descent, and persons of Arab descent. So now I want to extrapolate to the entire population of the United States. To improve my statistics I increase my sample size at the hospital. However, this practice will not help me because my sample is not representative of my target population. You also need to be careful because there may be additional factors at that hospital that you are unaware of that ultimately influence the outcomes of your experiments.
Increasing sample size will also not help you if your error is caused by the inappropriate application of the statistical model. If the model assumes a normal distribution, but the actual distribution is bimodal, log-normal, etc... Or you focus on mean differences, but the real effect is on the variance.
The statistics are no better than the methodology used to gather the data. No amount of additional sampling will correct these problems.
re Tim's answer.:
surely decreasing sample size increases the probability of type ii error and thus decreases power.
see attached for worked example and explanation.
from Armitage and Berry Statistical Methods in Medical Research 2nd ed Blackwell 1987
James,
My mistake, and I also made some really bad grammatical errors like using a period when I had a question. Answering research gate questions the day after the children have had a sleep over (without sleep) may not have been the best choice. In review, it is a little odd that I typed Type !! rather than Type II in the third paragraph. However, the real problem is with paragraphs 4 and 5 which are revised below. The other paragraphs are ok.
Decreasing sample size reduces the probability of rejecting the null hypothesis. This INCREASES the probability of making a Type II error. Increasing the probability of a false negative (Type II error) reduces power.
This as a problem in risk analysis. What is the consequence if my company discards an effective treatment for cancer? What is the consequence of selling an ineffective product, or worse selling a product to cure cancer that increases heart attacks? My sample size was too small to correctly reject the null hypothesis that there were no adverse side effects.
Please refer to the following literature. Hope it helps.
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2993982/
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3545151/
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC137461/pdf/cc1521.pdf
http://www.nejm.org/doi/pdf/10.1056/NEJM199003153221119
- Badges
- Science topic
- Similar topics
- Medicine
- Public Health