At least how many samples can be taken for quantitative research specially in terms of all statistical test?
Hashmi -
My guess is that you probably want to concentrate on standard errors for means. Such standard errors become smaller with larger sample sizes, as long as you maintain data quality. They are functions of sample size, n, and population standard deviations, which are fixed, but may be better estimated by larger sample sizes. The standard error of the mean for a give n then becomes the basis for confidence intervals and estimates of required sample sizes to obtain desirable standard errors and confidence intervals. The confidence intervals might rely upon the Central Limit Theorem. At the least, one can use Chebyshev's Inequality.
Another route to take for your quantitative data could be related to hypothesis testing. However, that is often problematic.
https://www.researchgate.net/publication/262971440_Practical_Interpretation_of_Hypothesis_Tests_-_letter_to_the_editor_-_TAS
Note that a p-value should not be set against the same level in every case. It depends on the circumstances, one of which is sample size.
Cheers - Jim
PS - To estimate standard deviations for each population of interest, you might first want to do a pilot study, which might also be used to work out any logistic or other issues.
PSS - The following are examples among many textbooks/reference books that may be of interest to you:
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.
Article Practical Interpretation of Hypothesis Tests - letter to the...
Without more details it is hard to answer this question. What is the research question?
Regards, Witold
The standard error is mentioned in the first answer and this is key. The standard error (which is the measured standard deviation on a group of measurements targeting a specific parameter) is proportional to 1/ square root of n where n is the number of measurements. Thus, in advance, you need to specify your required AQL or tolerance on the outcome. To half your acceptable tolerance you'll need 4 times the number of measurements. Thus 16 experiments will provide an estimate of the true mean (1 s.d. = standard error) to 25%.
3 is number favored by the FDA and has no statistical relevance whatsoever (throw away the 2 outliers and you're left with a perfect measurement!). The SE is easily calculated as 1/root3 or around 58%....
It appears that a reasonable compromise is 6 measurements - we prefer 10 measurements minimum - and I can provide a url for this:
http://www.pharmtech.com/sample-size-n6-magic-number?pageID=1
Standard statistical texts deal with this. Last but not least, variances can be added - s.d's cannot..
Just an addition while it's fresh in my mind:
The magic number of n=6 is known as the ICH compromise (ICH, Q2(R1) Validation Of Analytical Procedures: Text And Methodology, (2005)), whereby the 95% confidence limit of the mean is approximately ± s. For this reason, the number of retests carried out as part of out-of-specification investigations to isolate an outlier should be 5 or more (4. C. Burgess and B. Renger, ECA Standard Operating Procedure 01, Laboratory Data Management; Out of Specification (OOS) Results, Version 2, (August 2012)).
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