Statistics

[KafeelBasha]

Hello

I have came across below statement

"By increasing the sample size, both Type I and Type II errors will be reduced"

I would like to have an example which proves above statement.

Kafeel

[Rick_SAS · Accepted solution]

?? Can you provide a reference? Just because you see something on the internet doesn't make it true.  And examples do not "prove" anything.

What does your experiment look like? In the situation that I am familiar with, there is always a tradeoff between Type I and Type II errors. A large sample size increases your power, which can reduce Type II error. However, the sample size doesn't control Type I error. 

[KafeelBasha]

Got your point. Thanks

How can we prove that a large sample size reduces Type II error. Any reference.

Kafeel

[Rick_SAS]

I might have been too quick to assume that I understood what you are asking for.  Let me try again.

You are asking for the relationship between Type I and Type II error rates.  They depend on the null hypothesis AND A PARTICULAR FORM of the alternate hypothesis.  This topic is covered in most standard textbooks that have a chapter on hypothesis testing.  On my bookshelf I have an old copy of Walpole and Myers (1978).  It has a dozen of more pages about Type I and Type II errors, and that is typical of most undergrad or beginning grad textbooks for an Intro to Statistics course.

On p. 242, Walpole and Myers say, "For a fixed sample size, a decrease in the probability of one error will usually result in an increase in the probability of the other error."  When I posted my first answer, I was thinking about this fact and the fact that the significance level of the test (alpha = probability of committing a Type I error) is usually specified a priori.

However, the very next sentence on W&M p. 242 is almost exactly the quote you provided: "Fortunately, the probability of committing both types of error can be reduced by increasing the sample size."  The book then provides an example of an experiment, a null hypothesis, and a one-sided alternative for which the computation can be worked out by using the normal distribution.

Sorry for the confusion, but I think your best course of action is to find a "Stats 101" textbook that has a chapter about Tests of Hypothesis and read the examples in that text.  I should have suggested that in my first response.

[SteveDenham]

As a mental exercise, let the sample size go to infinity.  The probability of either error will necessarily go to zero, as you now have perfect knowledge of the situation, and under any null hypothesis and alternate hypothesis formulation, no error can be made.  However, Type I and Type II errors are peculiar to NHST, so this all becomes yet another argument in the ongoing discussion regarding hypothesis testing as a useful framework for decisionmaking in statistics.

Steve Denham

[Rick_SAS]

I did a googl search for "NHST" and found some good online resources that include pictures. Here's one:http://rpsychologist.com/d3/NHST/ 

[SteveDenham]

From my mathematical statisitcs and linear models professor (who also happened to be Peter Westfall's prof, so he must have trained at least 2 decent statisticians )

https://matloff.wordpress.com/

Several blog articles on the p value issue.

Steve Denham