What is the minimum number of samples needed for determining source apportionment of PM through Factor analysis. I have chosen four representative sites(commercial, Industrial,Residential, Bus terminal) from Dehradun(300 sq.km).I have gone through Henry et al., formulae..but still,I have a doubt whether 30 samples from each site is needed or a total of 30 from all sites combined.
Dear Vignesh,
For factor analysis is common to use a rule of thumb: based on two references (Bryman & Cramer, 1993; Gorsuch, 1983)
Minimal: N = 100 participants; ratio of 5 subjects by each variable
Optimal: ratio of 5 subjects by each variable
Bryman, A., & Cramer, D. 1993. Análise de Dados em Ciências Sociais. Introdução às Técnicas Utilizando o SPSS. Oeiras: Celta Editora.
Gorsuch, R. L. 1983. Factor Analysis (2nd ed.). Hillsdale, NJ: Erlbaum.
The previous answer is excellent! The least restrictive sample size I have every seen recommended based on any empirical evidence is a minimum of 100 and ration of 5 subjects for each variable as referenced in the first answer.
Dear Vignesh
Total 30 will not suffice for FA. In FA you wish to reduce the dimensionality, therefore it is essentially required to capture all the variability present in the system (at each site). More to that you may also interested to evaluate the individual site (if not now then latter on), therefore, more number of samples from each site will be better for arriving at precise conclusion. Yes, for scientific deliberations and acceptance, you may refer the above mentioned papers.
Regards
Dear Vignesh
You can use G*Power software to calculate sample size.
G*Power software is effective tool to calculate sample size for many ranges of experiments. Also, you can determine effect size and power of the test, G*Power is free to download and easy to use after reading the manual, the download link:
http://download.cnet.com/G-Power/3000-2054_4-10647044.html
The link to download G*Power manual:
http://www.gpower.hhu.de/fileadmin/redaktion/Fakultaeten/Mathematisch-Naturwissenschaftliche_Fakultaet/Psychologie/AAP/gpower/GPowerManual.pdf
Good Luck
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