Dear Friends,
I want you to read section 4.2 of the following paper and comment.
https://authors.elsevier.com/c/1iIAGXj-jfuSV.
Happy New Year
For ready reference, here it is:
4.2. Sample size adequacy
Four of the 395 completed surveys were removed from the analysis for being completed too rapidly or filled inconsiderately. Moreover, six of the 59 items were deleted (see 5.2 for details). Therefore, the sample-to-item ratio was 391/53 = 7.4, i.e., there were 7.4 subjects per item. Regarding sample size requirements, “no simple rule of thumb about sample size works across all studies” (Kline, 2023, p. 16). In the absence of a sampling frame (non-probability sampling), the sample size issue remains “ambiguous,” and “there are no rules” (Saunders et al., 2019, p. 315).
In structural equation modeling (SEM), a factor analysis-based technique, there are at least two perspectives, “entrenched camps” arguing to look at total sample size (minimum sample sizes) or the ratios (number of cases required per item, N:p ratio) (Kline, 2023, Osborne and Costello, 2004). There is widespread consensus in the first camp that a sample of 100 or less is “untenable” or “poor,” and for a sample of less than 200, journals “routinely reject for publication” (Comrey and Lee, 1992, Kline, 2023). Traditionally, “more is always better” (Osborne & Costello, 2004, p. 8). In contrast, researchers believe that “more is not always better.” (Wolf et al., 2013, p. 14). Sekaran and Bougie (2016, p. 264) said that “too large a sample size (say, over 500) could become a problem” due to the possibility of Type II errors.” They went on to say that “neither too large nor too small sample sizes help research projects.” (Sekaran & Bougie, 2016, p. 264). The minimum sample size of 250 is acceptable (Hoyle, 1995, p. 186). For many, a sample size of 300 or above is acceptable/appropriate/good (Comrey and Lee, 1992; Floyd and Widaman, 1995; Tabachnick and Fidell, 1996).
In the second camp, N:p of 10:1 has been advocated for ages (Everitt, 1975, Nunnally, 1978). Osborne and Costello (2004, p. 2) said this “recommendation was not supported by published research.” Streiner (1994, p. 140) suggests the ratio should be at least 5:1, provided “there are at least 100 subjects. If there are fewer than 100, the ratio should be closer to 10:1.” Several authors consider a 5:1 ratio acceptable (e.g., Bentler and Chou, 1987; Comrey and Lee, 1992; Gorsuch, 1983; Hatcher, 1994; Tabachnick and Fidell, 1996). Rather than a threshold ratio, Cattell (1978) suggested a 3 to 6. Not one ratio is likely to work in all situations. According to Bentler and Chou (1987, p. 91), “when there are many indicators of latent variables and the associated factor loadings are large,” the ratio may go as low as 5:1. In other words, more indicators and loading are critical to deciding optimal sample size. MacCallum et al. (1999,p. 96) concluded N:p ratio depends upon some aspects of variables and design, “most importantly, level of communality plays a critical role.” Where communality (squared factor loadings) represents the “squared multiple correlations among variables” (Tabachnick & Fidell, 2019, p. 481). MacCallum et al., (2001,p. 636) summarized that “samples somewhat smaller than traditionally recommended are likely sufficient when communalities are high.” In a nutshell, for this study, a sample size of 391 is not only sufficiently large but all communalities (ranges from 0.5 to 0.9) are also high. Therefore, N:p ratio of 7.4:1 is adequate for this study.
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