Is it permissible for the number of samples to be reduced or not reach the number of sample calculation results because many respondents are not willing to join the study as respondents? what should i do?
Thank you
Ainul Q K -
It sounds as if you have estimated the sample size needed to obtain a given standard error for a given quantitative variable result, say for continuous data or for a proportion, noting this would have to be investigated for all important items on a survey, and hopefully the data collection method is consistent with the method used in your sample size "calculation." For example, if your calculation assumed simple random sampling for a proportion, say with a finite population correction factor, then you did try to collect data according to a simple random sample, or whatever you had decided.
Now it sounds like your problem is nonresponse. That does not just make your attainable standard error larger, which it does, it may also introduce bias because the mean of, or proportion for the nonrespondent data might have been very different from that of the responses obtained.
To reduce that bias, you could consider "response propensity." You could weight data in groups so that data like cases not obtained will be weighted more. You could research response propensity groups.
If you have covariate data, there are other things you could do, but they could be very complex. See, for example, "Comparing Alternatives for Estimation from Nonprobability Samples," by Richard Valliant, December 2019, Journal of Survey Statistics and Methodology 8(2),
DOI: 10.1093/jssam/smz003
https://doi.org/10.1093/jssam/smz003. Richard Valliant has other papers on ResearchGate. Another place to look for papers on nonprobability sampling would be under J. Michael Brick.
If you are able to obtain the missing responses on a second try, that might help. You could also try asking other 'similar' members of the population - something called "nearest neighbor."
I like using a ratio model-based approach if you have a census of good, highly related data, which form a straight-line relationship to the origin.
At any rate, you are correct in being concerned about nonresponse, but not just because of higher variance, but also adding bias from the mean which also increases mean square error. You should at least note the problem, and perhaps you could do a sensitivity analysis to see how far off you might reasonable be.
Best wishes - Jim Knaub
It is not ideal to have a reduced sample size due to respondents' unwillingness to join, as it can impact the study's validity and generalizability. However, if unavoidable, consider the following:
Ideally, the number of samples collected should be sufficient to achieve the desired statistical power and precision for the analysis. However, in some cases, it may not be possible to collect the intended number of samples due to practical or logistical constraints.
In such cases, reducing the sample size or not reaching the intended sample size can impact the validity and reliability of the study results. A smaller sample size may result in lower statistical power, wider confidence intervals, and an increased risk of type II errors (false negatives) or false positive results.
If the sample size is reduced or does not reach the intended sample size, it is important to acknowledge this limitation in the study report and discuss the potential implications for the analysis and interpretation of the results. It may be necessary to adjust the study design or analysis methods to account for the smaller sample size and any associated biases or limitations.
It is important to note that the impact of reduced sample size on the study results will depend on the specific research question, the variability of the data, and the effect size of the variables of interest. In some cases, a smaller sample size may still be sufficient to provide meaningful and valid results, whereas in other cases, a larger sample size may be necessary to achieve the desired level of precision and accuracy.
As I noted earlier, it isn't just the sample size, it's how you collected it. If you aren't using a model, and have no covariates, you must be depending completely upon randomization. Missing data will degrade your randomization design. That is your biggest problem.
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