# What is the minimum sample size, regardless of total number of population, that can be considered as reliable for performing advanced statistical tests?

I have 32 patients with tuberculous meningitis, if I determined the sensitivity and specificity of cerebrospinal fluid adenosine deaminase and I got significant results, does it mean the result can be generalized? Can I determine the predictors of mortality from this sample?

## Popular Answers

Tim Edwin Colbourn· University College LondonThe confidence interval surrounding your statistical test results will tell you how much you can generalise your results to the whole population as it will tell you the likely range that the result will take in the total population with, e.g. (if a 95% confidence interval), 95% confidence. The larger your sample, the narrower your confidence interval and the more accurate your results are (the more powerful your statistical tests of the null hypothesis will be). A sample size of 32 is quite small so I imagine your confidence intervals (for sensitivity, specificity, predictors of mortality etc.) will be quite large, meaning that you won't be that confident of what the true population values are (assuming your sample is representative of the population).

Hope this helps,

Tim

Martin Schmettow· Universiteit TwenteIn addition, simple random sampling is just one way to ensure representativeness of your sample. If you have an idea of how your target population is composed, you could also go for a stratified random sampling scheme.

Another issue with small sample sizes that has not been mentioned is that classical statistical tests are asymptotic. They make certain assumptions that are only reached in infinity. In particular, this is the case with confidence limits. There is a solution to that however: use resampling techniques, such as the bootstrapping. Or you take the Bayesian route via MCMC sampling.

## All Answers (23)

Jörg Fiedler· Universität UlmAshish Awasthi· Sanjay Gandhi Post Graduate Institute of Medical SciencesSample size basically depends on the statistical test you will apply for comparison, for sample size calculation in case of sensitivity and specificity you can read

PMID: 15195324

PMID: 9249923

Tim Edwin Colbourn· University College LondonThe confidence interval surrounding your statistical test results will tell you how much you can generalise your results to the whole population as it will tell you the likely range that the result will take in the total population with, e.g. (if a 95% confidence interval), 95% confidence. The larger your sample, the narrower your confidence interval and the more accurate your results are (the more powerful your statistical tests of the null hypothesis will be). A sample size of 32 is quite small so I imagine your confidence intervals (for sensitivity, specificity, predictors of mortality etc.) will be quite large, meaning that you won't be that confident of what the true population values are (assuming your sample is representative of the population).

Hope this helps,

Tim

Sandro Sperandei· Fundação Oswaldo CruzResearches have some kind of fixation on sample size. Although size matters, because size will determine the confidence intervals (as stated above), it's even more important to ensure that sample was random! A biased sample has no salvation...

Robert Thomas Brennan· Harvard UniversityYou asked if you can determine predictors of mortality from this sample. You didn't say how. If you are thinking of using multiple regression, you won't get too far because you don't have a lot of degrees of freedom. Your model will only accommodate a couple of, maybe three, predictors, and you would have to be careful that the predictors themselves or a combination of them aren't just identifying individual cases or maybe two or three specific cases.

Finally, with a small sample, you have very low stastical power. That is an ability to find something that really is there in the population. Your chances of finding something that is in the population aren't very good unless it is somethng very big. This is also called Type II error. You can learn more by Googling "statistical power" and "effect size." Bob

Robert Thomas Brennan· Harvard UniversityPatrick Mitchell· AstraZenecaChih-Long Yen· Ming Chuan UniversityDr.Deepak Wankhede· Government of MaharashtraAzubuike Victor Chukwuka· National Environmental Standards and Regulations Enforcement Agency (NESREA)Martin Schmettow· Universiteit TwenteIn addition, simple random sampling is just one way to ensure representativeness of your sample. If you have an idea of how your target population is composed, you could also go for a stratified random sampling scheme.

Another issue with small sample sizes that has not been mentioned is that classical statistical tests are asymptotic. They make certain assumptions that are only reached in infinity. In particular, this is the case with confidence limits. There is a solution to that however: use resampling techniques, such as the bootstrapping. Or you take the Bayesian route via MCMC sampling.

Sandro Sperandei· Fundação Oswaldo CruzI am saying that because stratified non-random sampling is the quota sampling, which is not a probabilistic sampling method and can bias the results...

Martin Schmettow· Universiteit TwenteRamana K v· Prathima Institute of Medical SciencesAndreas Lindén· Novia University of Applied Sciences NOVIAA low p-value indicates that something rare has happened, given that the nullhypothesis is true. The setting is turned on its head, and the conclusion made is that the nullhypothesis is rejected (and some alternative hypothesis is consulted). This also explains why we don't interpret p-values quantitatively, but have to decide whether we accept or reject the nullhypothesis. Bayesians can calcuate probabilities for different hypotheses, but they first have to assign prior probabilties to all of them.

Jeffrey E. Jarrett· University of Rhode IslandRamana K v· Prathima Institute of Medical SciencesIn public interest and not influenced by personal prejudice such results should be not over interpreted...generalising..

Jeffrey E. Jarrett· University of Rhode IslandJeffrey E. Jarrett· University of Rhode IslandThe 95% interval state that if the process was repeated 100 time, 95 such interval would approximate the parameter correctly. The parameter is a constant and the contrustucted confidence intervals vary from sample to sample. Tweite committed an elementary mistake but I am sure he will rectify quickly.

Patrice S. Rasmussen· University of South FloridaThere is no minimal depending on the type of research design. For instance if you are working with qualitative or case studies then the popoulation may be 5 people for a case study. However, especially if you are not an expert right away at statistics. You should try to have a large sample size. This will help you meet the internal and external validity of the study. The larger your sample size in any study follows the law of the Central Limit Theorum. Look this up and become familiar with it. Even if you have a really serious skewness or kurtosis problem, if you increase the sample size you will most always end of with a normal curve as that is the law.

However, to speak in regards to learning about the importance of population size, it is very important. You want to have a demographically balanced population and then look at how the results may be applicable to different populations and situations as this is also a factor. However, to be succinct, you should especially when there is uncertainty increase that sample size and Mr. Central Limit Theorem.

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Shesh Kafle· The International Federation of Red Cross and Red Crescent Societiesif the population size is just 32, you better do the census NOT sampling...

Jeffrey E. Jarrett· University of Rhode IslandMinimum or optimum sample size is related to your risk of incurring Type ! and Type 2 errors, the assumed standard deviation of the population and the tolerance level. Read a book of statistics of sampling and you will never ask this question again. The issue was solved many years ago.

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