Within the framework of determining the size of the sample, which classical formula and/or paper do you suggest in the case of (a) random sampling and (b) stratified random sampling?
See this book:
Determining Sample Size: Balancing Power, Precision, and Practicality
Patrick Dattalo
and see the attached file:
Dear Colleague,
Please find the attachment, may be useful to you
Regards
Vishwanatha GL
Leslie Kish wrote about design effect, which typically shows a stratified random sample to be more efficient (i.e., have a lower variance) than a simple random sample.
The idea is to form strata which minimize the variances within strata and maximize the differences be them. This often happens naturally when your population falls within different categories. However, if you are publishing each of those categories, then you do not have stratified random sampling except at the higher level, but rather a set of simple random samples. I make the distinction because this may impact sample allocation. Optimal allocation for the higher level, the stratified random sample, may make use of the strata standard deviations differently than if you also need to publish at the lower level, the latter case generally taking a larger overall sample size than the former. - You may also want to use stratification by size in lieu of an unequal probability sample, either of which might be used with a skewed population, though the latter may be preferable. If the auxiliary information/data used to stratify is of a kind that may allow a model-based approach, or a design-assisted model-based approach, that can be even more efficient, but more biased.
If you are looking for stratified and simple random sampling "formulas," you should consult a textbook, such as Cochran, W.G.(1977), Sampling Techniques, 3rd ed, Wiley, and be sure you understand why you do what, and how to allocate the sample. You could start by looking at what Penn State Univ freely puts online. I suggest you read this: https://onlinecourses.science.psu.edu/stat506/node/27
Cheers!
Thanks for this information James. Cochran's book is the one I often use. I will also check the website you suggest. Thanks again.
Here's my first go equation. This isn't exactly what you are looking for, but it might help.
The is from "Standard: ASTM E122: STANDARD PRACTICE FOR CALCULATING SAMPLE SIZE TO ESTIMATE, WITH SPECIFIED PRECISION, THE AVERAGE FOR A CHARACTERISTIC OF A LOT OR PROCESS
This is an interesting read.
http://www.statisticshowto.com/find-sample-size-statistics/
Dear RG colleague,
Determining the sample sizes involve resource and statistical issues. Usually, researchers regard 100 participants as the minimum sample size when the population is large. However, In most studies the sample size is determined effectively by two factors: (1) the nature of data analysis proposed and (2) estimated response rate.
For example, if you plan to use a linear regression a sample size of 50+ 8K is required, where K is the number of predictors. Some researchers believes it is desirable to have at least 10 respondents for each item being tested in a factor analysis, Further, up to 300 responses is not unusual for Likert scale development according to other researchers.
Another method of calculating the required sample size is using the Power and Sample size program (www.power-analysis.com).
Regards,
Dear Andreas
In order to answer this question/problem, several remarks have to be studied.
1. General remarks:
Research studies are usually carried out on sample of subjects rather than whole populations. The most challenging aspect of fieldwork is drawing a random sample from the target population to which the results of the study would be generalized. The key to a good sample is that it has to be typical of the population from which it is drawn. When the information from a sample is not typical of that in the population in a systematic way, we say that error has occurred. In actual practice, the task is so difficult that several types of errors, i.e. sampling error, non-sampling error, Response error, Processing error,…
In addition, the most important error is the Sampling error, which is statistically defined as the error caused by observing a sample instead of the whole population. The underlying principle that must be followed if we are to have any hope of making inferences from a sample to a population is that the sample be representative of that population. A key way of achieving this is through the use of “randomization”. There several types of random samples, Some of which are: Simple Random Sampling, Stratified Random Sampling, Double-stage Random Sampling... Moreover, the most important sample is the simple random sample which is a sample selected in such a way that every possible sample of the same size is equally likely to be chosen. In order to reduce the sampling error, the simple random sample technique and a large sample size have to be developed.
2. Specific remarks:
The following factors are highly affected the sample size and need to be identified:
- Population Size,
- Margin of Error,
· Confidence Level (level of significance) and
- Standard of Deviation.
Then, the sample size can be estimated by,
Necessary Sample Size = (z-score or t-value)2 * StdDev*(1-StdDev) / (margin of error)2 .
Regards,
This article is also useful in determining adequate sampling size for a qualitative research: Malterud, K., Siersma, V. D., & Guassora, A. D. (2016). Sample Size in Qualitative Interview Studies. Qualitative Health Research, 26(13), 1753–1760. doi:10.1177/1049732315617444
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