In determining the number of social research subjects, there are many opinions that the data must be more than 30 as a condition to be tested for parametric statistics. What theory underlies this?
The number of participants in quantitative research can be specified through formulas that determine either the accuracy of an estimate or the likelihood of obtaining a significant result. There is no need for "magic numbers" when solid statistics are available.
Hello Dendy,
As Professor Morgan's reply indicates, there is no single threshold value which suddenly makes analytic method "X" defensible. Parametric methods may be used as long as there are sufficient cases to permit estimation of the relevant parameters.
For example: Minimum N to conduct:
1. One-sample t-test: Two cases.
2. Independent groups t-test: Four cases (two in each batch).
3. (Test of a) Pearson product moment correlation: Three cases.
and on...
Running these analyses with such N sizes would be unwise, however, due to the imprecision associated with any parameter estimates as well as to the very low statistical power which would be the case for any hypothesis test.
Maybe the advice about "30 cases" has something to do with statistical power, but that sort of calculation depends as well on: (a) alpha level (Type I error risk); (b) target effect size; (c) specific analytic method/statistical test chosen; (d) number of variables (and levels); and (e) target statistical power desired.
The implication that smaller sample sizes suggest a requirement for non-parametric methods is just as meaningless, in my opinion. The choice of the two major families (parametric, non-parametric) should hinge on the specific hypothesis (or associated research question) one wishes to address, the nature of the variables involved (and their quantification), and how the data were collected.
Good luck with your work.
From your question, I infer that you need a theoretical underpinning / justification for a certain sample size. This cannot simply be substantiated with a threshold value (like 30), because it strongly depends on the (expected) effect size, chosen alpha, number of variables, etc. Assuming that your research is single-level, I recommend you to determine your sample size in advance, for example by using G*Power. You can find many demo-video's on YouTube that can help you to apply G*power. Good luck!
Article G*Power 3: A flexible statistical power analysis program for...
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