30th Mar, 2021

The National Academies of Sciences, Engineering, and Medicine

Question

Asked 8th Jul, 2020

The calculated sample size for my study is 324 with 5% margin error. However, only 230 respondents responded the questionnaire completely. In this case, what is the margin error for this actual sample size? What is the acceptable margin error in a good research? Any formula to calculate margin error from actual sample size?

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Yes, you would want 524 responses with a population of 4,100. Note that you need to estimate the response rate to calculate the desired sample size; for example, if you expect a 70% response rate, then divide 524 by .7, for a sample size of 749. This assumes you will be performing a simple random sample (each person has the same probability of selection). After data collection is completed, you should check to see if some types of respondents had higher rates of response than others, and adjust the weights to compensate.

Kavitha Selvaraja - Since the calculated sample size for your study is 324 with 5% margin error and only 230 respondents have responded the questionnaire completely. In your case, the non-response rate is 30.02% as out of 324 respondents only 230 have responded. The margin of error can be calculated in two ways, depending on whether you have parameters from a population or statistics from a sample: Margin of error = Critical value x Standard deviation for the population. Margin of error = Critical value x Standard error of the sample.

As sample size increases, the margin of error decreases. As the variability in the population increases, the margin of error increases. As the confidence level increases, the margin of error increases.

You can use the following methods to decrease the margin of error: a) Increase the sample size. Often, the most practical way to decrease the margin of error is to increase the sample size. b) Lower the confidence level.The margin of error decreases as the sample size n increases because the difference between the statistic and the parameter decreases. This is a consequence of the Law of Large Numbers.

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The sample size required is partly based on the size of the target population, which you do not give. Assuming it is large (>10,000), then with a sample of 230, you will have approximately +/- 6% margin of error. You can easily find this by using the usual sample size software, and working backwards.

Dr Manzoor Hussain , thanks for the comprehensive explanation. Can you share any reference related to this for my reading?

Safaa K. Kadhem thank you so much for the link.

Adrian Esterman thanks a lot for the link

Adrian Esterman May I check if the link you have provided is a recognised link?

Sampling error depends on the number of respondents and the population size, not on the sample size. The other factor to consider is nonresponse bias: i.e., whether those who didn't respond are systematically different from those who did respond. You may be able to correct for that through weighting, if you have enough information about the nonrespondents. As to what degree of error is acceptable, that depends on what you are researching. Values near 50% will have larger confidence intervals than those at the extremes.

Data

- Feb 2018

Sample size, mean and s.e.m. and statistical calculations are presented.

Article

- Jun 1994

Recently, Anoulova, Fischer, PP olt, and Simon 1] applied Valiant's PAC-learning model to the eld of statistical pattern recognition. They presented a sample-and time-eecient algorithm for learning nearly optimal classiiers with high conndence. In this context, they introduced the probably almost Bayes (PAB) decision model, which is a special case...

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