Here's a statistical dilemma for me....
We use the alpha and power for sample size calculation, however, we do not directly enclose the beta error as we do for the alpha... what accounts for this paradox?
I understand that 1- beta = power.
But what is the explanation that beta itself is not considered and 1- beta is.
Might sound stupid and apologies for that but it's really bothering me
Thank you
Hi Arvinder-Singh. Well, I'd say it's just a matter of a somewhat arbitrary protocol. It does not matter if you consider beta or 1-beta. They both contain the same amount of information. ... Except that assumes you aren't looking at a discrete set of events where the event which occurred has a substantial probability under each hypothesis. Then it would matter whether you count that value and more extreme values, or just more extreme values (in a given direction), and when.
But if you are estimating sample size requirements, I recommend staying away from hypothesis tests if you can. They are often misinterpreted. The basis behind sample size requirements is 'What sample size is needed with a given population standard deviation to obtain a desired standard error for an estimated mean or an estimated total or an estimated proportion? (This can be further complicated by sample design, possible auxiliary data, and assumes bias is under control, but is more straightforward than hypothesis testing.)
Cheers! - Jim
Dear James R Knaub aka Jim
Good day to you and thank you for your reply. Should the basis of sample size then be calculated on effect size rather than the sample alone?
Thank you
Arvinder
The current system works well if the statistics are used correctly. In frequentist statistics the two choices are:
1) Reject the null-hypothesis
2) Insufficient data to determine. This is not proof of the null-hypothesis, though sometimes in this event we decide to behave as if we now believe the null-hypothesis to be true e.g. tests for normality in data distribution. The first part is statistics, the second is human psychology.
In this dichotomous framework I can really only make a mistake by rejecting the null-hypothesis when the null-hypothesis is true. I can only get to a type II error by first mistakenly accepting the null hypothesis as true given that I have failed to reject the null-hypothesis.
Dear Timothy A Ebert ,
Thank you for your explanation sir. Fantastic stuff
Arvinder
This might be of interest:
https://www.researchgate.net/publication/262971440_Practical_Interpretation_of_Hypothesis_Tests_-_letter_to_the_editor_-_TAS
Dear Arvinder-Singh -
Yes, effect size is important. No point hypothesis is ever exactly correct.
If you express the sample size problem as one of obtaining a desired standard error based on a methodology and standard deviation(s), then I think you will find support for that in each of the following survey sampling textbooks, and others:
Thompson, S.K.(2012), Sampling, 3rd ed, John Wiley & Sons.
Cochran, W.G(1977), Sampling Techniques, 3rd ed., John Wiley & Sons.
Blair, E. and Blair, J(2015), Applied Survey Sampling, Sage Publications.
Lohr, S.L(2010), Sampling: Design and Analysis, 2nd ed., Brooks/Cole.
Särndal, CE, Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling, Springer-Verlang.
Brewer, KRW (2002), Combined survey sampling inference: Weighing Basu's elephants, Arnold: London and Oxford University Press.
An Introduction to Model-Based Survey Sampling with Applications, 2012, Ray Chambers and Robert Clark, Oxford Statistical Science Series
Finite Population Sampling and Inference: A Prediction Approach, 2000, Richard Valliant, Alan H. Dorfman, Richard M. Royall,
Wiley Series in Probability and Statistics.
Survey Sampling: Theory and Methods, Second Edition
Arijit Chaudhuri, Horst Stenger
March 29, 2005 by CRC Press
Hansen, M.H., Hurwitz W.N. and Madow, W.G. (1953). Sample Survey Methods and Theory (2 vols.) (Republished 1993) Wiley, New York.
Kish, Leslie, 1965, Survey Sampling, John Wiley & Sons, Wiley Classics Library Edition Published 1995
Also, for model-based sampling and estimation/prediction, for the case of the classical ratio estimator in one stratum, please note:
https://www.researchgate.net/publication/261947825_Projected_Variance_for_the_Model-based_Classical_Ratio_Estimator_Estimating_Sample_Size_Requirements
Note that in simple random sampling, that if you can form a t-statistic, you have all you need. The additional step of an hypothesis test then just "muddies the water." (That is, it takes away from the clarity.)
However, the Blair & Blair book noted above does describe the use of hypothesis tests in sample size determination. That book is on a fairly introductory level.
Note also that if you have more than one item of data, you may have to determine sample size needs for each, and choose the largest sample size, unless some items are not very important.
Cheers - Jim
Thank you Jim. Very comprehensive insight. Appreciate it very mich
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