22/07/2026
๐๐ฐ๐ฏ๐ง๐ฆ๐ณ๐ฆ๐ฏ๐ค๐ฆ ๐๐ข๐ฑ๐ฆ๐ณ ๐ฑ๐ณ๐ฆ๐ด๐ฆ๐ฏ๐ต๐ข๐ต๐ช๐ฐ๐ฏ (2021)
๐๐ซ๐ฃ๐๐ข๐ฅ๐๐ง๐ข๐ฅ๐ฌ ๐๐๐๐ง๐ข๐ฅ ๐๐ก๐๐๐ฌ๐ฆ๐๐ฆ
Exploratory Factor Analysis (๐๐๐) is a statistical technique used in data analysis and research to ๐ณ๐ฆ๐ฅ๐ถ๐ค๐ฆ a large number of observed variables (e.g., survey statements or items) into a smaller, unobserved set of ๐ถ๐ฏ๐ฅ๐ฆ๐ณ๐ญ๐บ๐ช๐ฏ๐จ factors, which are to be judiciously named as the "common denominators" of grouped items.
๐ฆ๐ฎ๐บ๐ฝ๐น๐ฒ ๐ฆ๐ถ๐๐ฒ ๐ฅ๐ฒ๐พ๐๐ถ๐ฟ๐ฒ๐บ๐ฒ๐ป๐๐
EFA requires a sufficiently large sample to produce stable correlation estimates and reliable factor loadings. General rules of thumb include:
โ ๐๐ฃ๐ด๐ฐ๐ญ๐ถ๐ต๐ฆ ๐๐ช๐ฏ๐ช๐ฎ๐ถ๐ฎ: At least 100 to 150 cases.
โ ๐๐ถ๐ฃ๐ซ๐ฆ๐ค๐ต-๐ต๐ฐ-๐๐ข๐ณ๐ช๐ข๐ฃ๐ญ๐ฆ ๐๐ข๐ต๐ช๐ฐ: Aim for a ratio of 5 to 10 participants per variable (item) being measured.
โ ๐๐ฑ๐ต๐ช๐ฎ๐ข๐ญ: 300 or more cases generally yield robust, reliable results.
๐๐ฎ๐๐ฎ ๐๐๐๐๐บ๐ฝ๐๐ถ๐ผ๐ป๐
Prior to unveiling latent factors, data assumptions must be tested to confirm the ๐ง๐ข๐ค๐ต๐ฐ๐ณ๐ข๐ฃ๐ช๐ญ๐ช๐ต๐บ of items:
โ The ๐ฐ๐ผ๐ฟ๐ฟ๐ฒ๐น๐ฎ๐๐ถ๐ผ๐ป ๐บ๐ฎ๐๐ฟ๐ถ๐
should display several correlations r โฅ 0.30
โ The diagonal elements of the ๐ฎ๐ป๐๐ถ-๐ถ๐บ๐ฎ๐ด๐ฒ ๐ฐ๐ผ๐ฟ๐ฟ๐ฒ๐น๐ฎ๐๐ถ๐ผ๐ป ๐บ๐ฎ๐๐ฟ๐ถ๐
should be greater than 0.5
โ The ๐๐ฎ๐ถ๐๐ฒ๐ฟ-๐ ๐ฒ๐๐ฒ๐ฟ-๐ข๐น๐ธ๐ถ๐ป (๐๐ ๐ข) ๐๐๐ฎ๐๐ถ๐๐๐ถ๐ฐ for ๐ด๐ข๐ฎ๐ฑ๐ญ๐ฆ ๐ข๐ฅ๐ฆ๐ฒ๐ถ๐ข๐ค๐บ should be greater than 0.5 (ideally > 0.7)
โ ๐๐ฎ๐ฟ๐๐น๐ฒ๐๐'๐ ๐๐ฒ๐๐ ๐ผ๐ณ ๐ฆ๐ฝ๐ต๐ฒ๐ฟ๐ถ๐ฐ๐ถ๐๐ should be significant at the 5% level (p < 0.05)
โ All ๐ฐ๐ผ๐บ๐บ๐๐ป๐ฎ๐น๐ถ๐๐ถ๐ฒ๐ must be at least 0.4 (ideally > 0.6)
Other assumptions that may be checked include:
โ ๐ ๐๐น๐๐ถ๐ฐ๐ผ๐น๐น๐ถ๐ป๐ฒ๐ฎ๐ฟ๐ถ๐๐ ๐ฎ๐ป๐ฑ ๐ฆ๐ถ๐ป๐ด๐๐น๐ฎ๐ฟ๐ถ๐๐
โ ๐๐ถ๐ป๐ฒ๐ฎ๐ฟ๐ถ๐๐ ๐ฎ๐ป๐ฑ ๐ข๐๐๐น๐ถ๐ฒ๐ฟ๐
โ ๐ ๐๐น๐๐ถ๐๐ฎ๐ฟ๐ถ๐ฎ๐๐ฒ ๐ก๐ผ๐ฟ๐บ๐ฎ๐น๐ถ๐๐
๐ ๐ฒ๐๐ต๐ผ๐ฑ๐ ๐ผ๐ณ ๐๐
๐๐ฟ๐ฎ๐ฐ๐๐ถ๐ผ๐ป
In popular software like ๐๐๐ ๐๐๐๐ ๐๐ต๐ข๐ต๐ช๐ด๐ต๐ช๐ค๐ด, EFA is carried out using ๐๐ณ๐ช๐ฏ๐ค๐ช๐ฑ๐ข๐ญ ๐๐ฐ๐ฎ๐ฑ๐ฐ๐ฏ๐ฆ๐ฏ๐ต๐ด ๐๐ฏ๐ข๐ญ๐บ๐ด๐ช๐ด (๐ฃ๐๐), though ๐๐ณ๐ช๐ฏ๐ค๐ช๐ฑ๐ข๐ญ ๐๐น๐ช๐ด ๐๐ข๐ค๐ต๐ฐ๐ณ๐ช๐ฏ๐จ (๐ฃ๐๐) or ๐๐ข๐น๐ช๐ฎ๐ถ๐ฎ ๐๐ช๐ฌ๐ฆ๐ญ๐ช๐ฉ๐ฐ๐ฐ๐ฅ (๐ ๐) may also be used.
๐ฅ๐ผ๐๐ฎ๐๐ถ๐ผ๐ป ๐ผ๐ณ ๐๐ฎ๐ฐ๐๐ผ๐ฟ๐
While historically ๐ผ๐ฟ๐๐ต๐ผ๐ด๐ผ๐ป๐ฎ๐น methods (e.g., ๐๐ข๐ณ๐ช๐ฎ๐ข๐น) were heavily used due to simpler hand computations, modern statistical consensus overwhelmingly prefers ๐ผ๐ฏ๐น๐ถ๐พ๐๐ฒ rotation (e.g., ๐๐ณ๐ฐ๐ฎ๐ข๐น or ๐๐ช๐ณ๐ฆ๐ค๐ต ๐๐ฃ๐ญ๐ช๐ฎ๐ช๐ฏ), as the factor correlation matrix can simply be checked to see if the factors are actually related.
๐๐ฎ๐ฐ๐๐ผ๐ฟ ๐ฅ๐ฒ๐๐ฒ๐ป๐๐ถ๐ผ๐ป ๐๐ฟ๐ถ๐๐ฒ๐ฟ๐ถ๐ฎ
Lastly, factors may be extracted according to any of the following three methods:
1. ๐๐ข๐ช๐ด๐ฆ๐ณ'๐ด ๐ค๐ณ๐ช๐ต๐ฆ๐ณ๐ช๐ฐ๐ฏ (eigenvalues greater than 1)
2. Cattell's ๐ด๐ค๐ณ๐ฆ๐ฆ ๐ฑ๐ญ๐ฐ๐ต
3. ๐๐ข๐ณ๐ข๐ญ๐ญ๐ฆ๐ญ ๐ข๐ฏ๐ข๐ญ๐บ๐ด๐ช๐ด (using Monte Carlo simulation)
For more information, please contact me via email (๐ฟ๐ฎ๐ท.๐ด๐๐ป๐ฒ๐๐ต@๐ต๐ผ๐๐บ๐ฎ๐ถ๐น.๐ฐ๐ผ๐บ) or WhatsApp (+๐ฎ๐ฏ๐ฌ ๐ฑ๐ฐ๐ต๐ต ๐ต๐ฌ๐ณ๐ฌ).
