Sample Size Justification: Sample is 1500, latent variables 9 Indicator variables 45
The sample size for this study was 1500. Its appropriateness/justification was tested through three different methods:
In method 1, the sample size was computed on Statsoft Statistica software Structural Equation Modeling. At 95% confidence level with statistical power =0.90, df=909,R=0, R0=0.01 the appropriate sample size for meeting model fit standards yielded a sample size of 1471(Hooper, Coughlan, & Mullen, 2008; Statistica help, 2017).
In method 2, A-Priori Sample size calculator for Structural Equation Models (version 4.0), was used. Using anticipated effect size w = 0.15, alpha = 0.05, statistical power = 0.99 for 9 latent variables and 45 observed variables, it yielded a sample size of 1587 (Soper, 2017; Cohen 1988; Westland 2010).
In method 3 a sample size a sample size of 1436 was computed for chi-square goodness of fit indices through a-priori power analysis goodness of fit test on G-power software using anticipated alpha = 0.05, statistical power = 0.80, effect size w = 0.10 and df = 7, which suffices the statistical power standards (Faul, et al., 2013; Cunningham, 2007)
Based on above analysis it can be safely assumed that the sample size of 1500 used in this study is appropriate in terms of model fitting standards, and model fitting standards.
For inferential statistics, it doesn't make much sense to try to justify sample size after the data have already been collected; the p-value or confidence interval for your effect already tells you what effect sizes your sample was able to reject and what effect sizes it wasn't. Sample size calculations should be made before observing the data.
For inferential statistics, it doesn't make much sense to try to justify sample size after the data have already been collected; the p-value or confidence interval for your effect already tells you what effect sizes your sample was able to reject and what effect sizes it wasn't. Sample size calculations should be made before observing the data.
You have a sample size of 1500. Are you going to go back and gather 87 more observations to get the sample size calculated by method 2? If not, then this exercise is pointless.
Do other research reports in this research field tend to have larger sample sizes?
Do some cells (treatment combinations/states/cohorts) have few replicates while others have many?
One use for sample size calculations is to answer this question: Given your results, what sample size should I use if I want to replicate your experiment with sufficient power to be able to determine if we have the same outcome? While the safe answer is 1500 or more, it would be nice if I could get away with only 600.
I agree with Stephen and Timothy.
These sample size requirements are only suggestive and need to be done before you begin data gathering.
And note that any sample size requirement calculation is VERY conservative. Recall the sample-size calculation you did so long ago based on proportions.
- n = (Zα/2+Zβ)^2 * (p1(1-p1)+p2(1-p2)) / (p1-p2)^2,
- where Zα/2 is the critical value of the Normal distribution at α/2 (e.g. for a confidence level of 95%, α is 0.05 and the critical value is 1.96), Zβ is the critical value of the Normal distribution at β (e.g. for a power of 80%, β is 0.2 and the critical value is 0.84) and p1 and p2 are the expected sample proportions of the two groups.
Recall that with no other information about the population parameters, we always set p1 and p2 at 50% each. That's because 50*50 gives the largest sample size.
Sample-size calculations for SEM apply the same logic. For example, zero correlations and high variances probably are assumed. As true correlations move away from zero and variances decrease, then the "required" sample size falls, sometimes dramatically.
As Timothy Ebert implied above, you would probably get sound results with a sample of 600.
I didn't say that you would get sound results with a sample size of 600. I said it would be nice if it worked out that way. Without a great deal of other information (experimental design, variability, sensitivity, goals, prospective journal, field of study) I have no way of knowing what would be a good sample size. Sample size needs to be somewhere between 3 and millions. You also need to be careful about how you are discussing sample size. "I have a sample size of 1500" might mean that I have 1500 samples in hand for the entire experiment, or that I have 1500 samples for each "treatment."
Treatment does not have to be applied. So I could test a new drug for curing cancer on 1500 people. I then have males and females: 750 males and 750 females. Smokers and non-smokers: MS=345 MN=405 FS=230 FN=520. Race might be a factor: C=Caucasian, M=Mexican, A=African-American, N=native American. Of the 345 male smokers I have MSC=135, MSM=145, MSA=61, and MSN=4. Income might also be a factor: R=rich, M=middle income, P=poor. Of the 4 MSN I have MSNR=0, MSNM=1, and MSNP=3. Suddenly, my "huge" sample of 1500 looks kind of weak, and reducing the sample size to 600 will make everything worse.
I could have done purposive sampling and made sure that of the 2 (gender) x 2 (smoking) x 4 (race) x 3 (income) = 48 non-treatment conditions times two treatments (placebo-drug) for a total of 96 "treatments" I have equal sample sizes (n=16, 16*96=1536 or roughly 1500). If all the data comes from a text mining program 16 replicates sounds a bit small. If the data are surveys of company CEOs, then my perception changes because I assume that it is more difficult to gather another data point.
There is no one fixed value that defines a good or sufficient sample size, and statistical considerations are sometimes irrelevant.
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