Hi,

the recommendation of a sample size of at least 30 for basic inferential statistics such as t-tests and confidence intervals is widely accepted in the statistical community and is supported by many textbooks and academic sources.

For example, the textbook "Statistics for the Behavioral Sciences" by Gravetter and Wallnau (2016) states that a sample size of at least 30 is recommended for t-tests and confidence intervals when the data is normally distributed and the variability is not too high.

Similarly, the textbook "Introduction to Probability and Statistics" by Mendenhall et al. (2013) recommends a sample size of at least 30 for basic inferential statistics such as t-tests and confidence intervals.

However, it's important to note that the appropriate sample size for a particular analysis will depend on the specific research question, the type of analysis, and the characteristics of the data. Therefore, it's always a good idea to consult with a statistician or use statistical software to determine an appropriate sample size for a particular analysis.

Regards

Uday Bhale

In simulation studies, the t-test works fine on small, even very small samples. Your problem is bias, however. With a small sample and considerable non-participation, your ability to extrapolate from sample to population is very dubious.

The trouble with people who write textbooks is that they don't keep abreast of the literature! Here are some references that those textbooks missed.

• de Winter, J. (2013). Using the Student’s t-test with extremely small sample sizes. Practical Assessment, Research & Evaluation, 18(10), 1–12.
• de Winter, J. C., & Dodou, D. (2010). Five-point Likert items: t test versus Mann-Whitney-Wilcoxon. Practical Assessment, Research & Evaluation, 15(11), 1–12.
• Fagerland, M. W., Sandvik, L., & Mowinckel, P. (2011). Parametric methods outperformed non-parametric methods in comparisons of discrete numerical variables. BMC Medical Research Methodology, 11(1), 44. doi:10.1186/1471-2288-11-44

The textbook suggestion is aiming at the"large-sample approximation". Standard statistical procedures rely on some assumptions, and they are approximately correct even if these assumtions are not perfectly met. The larger the sample, the "more correct" are these tests, and the n > 30 suggestion is based on the demand to have "still reasonably correct inferences" when the assumptions are "moderately violated". This should warrant that you get okay-ish results even when you are doing everything wrong, so to say.

It is possible to do valid inference with n=1. Example: the number of seizures per patient-year is asusmed Poisson distributed with mean lambda. For one patient you observe 3 seizures in a year. For this it follow that the expected number of seizures per patient-year is 3 with a standard error of 1.73. The 95% confidence interval for the mean is (0.75, 7.78); say you have data from one other patient who recieved a treatment. In fact, for this patient you observed only one seizure during a year. The 95% confidence interval for the rate-ratio treated vs. control is (0.01, 2.6), the p-value for the treatment-effect is 0.34. These results are correct given the number of seizures per patient-year is Poisson distributed, and given the two patients are independent of each other and that they were not selected due to anything else but the fact that they do have seizures and that the treatment is assigned to one of the two patients disregarding everything (i.e., the treatment was assigend "randomly").

Sample selection, independence of measurments, and random assignment of treatments are under your control. The biggest problem is the assumption about the distribution. Does it make sense? If you don't know, you will need a lot of data to find out. Would a negative binomal model be more appropriate? Or is zero-inflation something that should be considered? To answer such questions, n ≈ 30 is still way too little.

And then there might be additional variables to be considered. Should all genders be treated equally or might the treatment effect be gender-specific? And what about the patient's age? The SES? The familiar and social environment? Sleeping habits? Place of living? Kind of work? etc.

This plays a role when convenient samples are taken. It might not be clear to which population the resukts will generalize. It's easy and likely to get a (severe) bias, as Ronán Michael Conroy noted above.

When the study is being conducted properly and the assumptions are justified, small samples are (typically) not at all a problem. But small samples impose a problem for the scientific community: small samples means small and cheap experiments. Small-sample experiments can often be done quickly and with little effort, so many many groups are doing many many small experiments. Most of which will result in inconclusive data, few will show existing effects, and many will be "false positives" (showing some statistically significant effect that is not true or actually has the wrong sign). Only the (still many) experiments with "significant" results are published, and most of them will be false-positives - a disservice for science. The risk of published false-positive results is much smaller for large studies because they are usually better planned and conducted, data are analyzed by experienced experts, more controls are done, data are collected to rule out competing alternatives, and sometimes results are confirmed in unrelated collectives.

Incidentally, you can do inference on single observations.

In Ireland, vehicle registration numbers include the county, the year and a number. So if you see a car registered 12 KY 5026 (the 5026th car registered in Kerry in 2012) how many cars were registered in Kerry that year? What's the best inference in this case?

different criteria for sample size seletion...u may select the sample size 5 times of total questionnaire items after discussing with ur supervisor.

Two thoughts. First, it seems like a lack of a representative sample makes the statistical discussion moot. When more than half of the population (56%) does not contribute data, you can’t possibly generalize the results to the population. But is there a way to learn something useful from the situation? Can you define non-participation vs. participation as a variable (0, 1), and then use medical records as a source of predictive variables? What are the characteristics of participants vs. non-participants? Yes, your original theory and interview questions lose relevance, but your findings might be useful to others who study hard to interview populations.

Second, if you do a new study, can you use observation measures instead of difficult to collect self-report data to test your hypotheses? Observers might rate signs of stress or agitation, amount of verbal activity, sleeping time, etc. You might find an observation scale here: https://www.osmind.org/knowledge-article/measurement-based-care-mental-health-patient-rating-scales. Also, if you have access to clinicians’ records, you may be able to use a content analysis approach to test hypotheses with their recorded observations and decisions. If you do use medical records, be very aware of ethical issues and data-use regulations. For example, who is providing consent to participate, the patient or the institution? Good luck!

The samples size should be minimum of 30

Whether you use descriptive statistics or inferential statistics, the question is what meaning cab be drawn from the statistics. Your statistics on 14 participants are unlikely to properly represent the 32 in the original sample, and you should acknowledge that even when presenting descriptive statistics. There are likely to be systematic biases in who responded (e.g., those who were too unwell to respond may have responded very differently), and the ward(s) that you picked may not be representative of other wards.

Small sample size of 14 is useable for statistical inference. First, use a suitable nonparametric method for testing your hypotheses. Secondly, do a repeated study on the same 14 patients for at least 3 times and at this point, a repeated measures analysis can be conveniently applied and the output will be robust because the data will meet the important assumptions of constant variance and approximate normality. If I am your supervisor, the second option will be the remedy for the study.

Usually minimum sample size is taken five (5) times of number of questionnaire items for inferential statistics...but u may also go for non parametric tests with sample size of 50 respondents.

There is no specific requirement for the number of samples that must be used to be able to represent the population. However, many experts agree that the number of samples used must be at least 30. The recommendation of a sample size of at least 30 for basic inferential statistics such as t-tests and confidence intervals is widely accepted in the statistical community and is supported by textbooks. However, if you use complex statistics, you may need a minimum of 100 or more in your sample (varies with the method).

In my masters and doctoral classes of the the mid-80s we were told that a "rule of the thumb" must have n (sample size) equal to 30 as minimum for any meaningful generalizations. Common sense, besides textbooks, will tell you that the larger the sample size the more realistic the findings of a research especially in surveys. However I think that for case studies and longitudinal studies, sample size should not be that much an issue as the need for elimination of bias in observations. Thank you.

According to central limit theorem, you'll require a minimum of 30 sample to get normal distribution. Based on this, the 30 minimum sample is required

whatttttt????

Salim Muhammad Ogaji This is a misunderstanding of the CLT (and sadly one that it frequently taught and thus can be found in many intro lecture notes, texts and so on).

1) The CLT does not always apply (it requires that the original distribution has a defined mean and variance - which may not be true)

2) Where it applies the n required depends on the distribution of the data sampled so it can be that even with n = 1000 or n = 1000000 (or any finite n) the sampling distribution of a statistic is not approximately normal

3) Not all statistical procedures assume normality so the CLT may not be relevant for that reason

A good review of the CLT can be found here:

How to think clearly about the Central Limit Theorem. Psychological Methods. [with Zhang, X., Astrivia, O.L.O., & Kroc, E.] (in press) http://dx.doi.org/10.1037/met0000448

The minimum sample size used for inferential statistics depends on the type of test you want to perform. A sample size of at least 30 is recommended for basic inferential statistics such as t-tests and confidence intervals.

stop bothering us... with ChatGpt...

Your dissertation supervisor is correct; a sample size of 14 may be too small for reliable inferential statistics. The "rule of thumb" suggesting a minimum of 30 participants is not strict and varies. In cases where prevalence estimates are unavailable, focusing on descriptive statistics is appropriate. Emphasizing qualitative insights from interviews can compensate for the small sample size. Acknowledge limitations and discuss findings cautiously, providing a clear picture within the constraints of your study.