If the sample to be taken from pharmacists population of around 25000 pharmacists, what will be the reliable sample size?
Fadia -
For a given quantitative question/variable, that depends upon type of data (continuous, yes/no), methodology (a probability of selection method most likely here, I suppose, such as cluster sampling or simple random or stratified random sampling, or perhaps a model-based approach given regressor data, but I doubt you have that), standard deviation, and desired accuracy. Statistical bias is generally assumed under control, and you need to have a preliminary standard deviation(s) estimate or good guess based on other information to then see what sample size, under your methodology, will attain a desired standard error.
You can find statistics textbooks such as the classic, Cochran(1977), 3rd ed, Sampling Techniques, Wiley, or perhaps online help such as the online course information, such information freely available, from the Pennsylvania State University. You could do a search on a term to research, and include "Pennsylvania State University" or "Penn State" with the search term.
Cheers - Jim
http://biostat.mc.vanderbilt.edu/wiki/pub/Main/TheresaScott/SampleSize.TAScott.handout.pdf
https://watermark.silverchair.com/ilar-43-4-207.pdf?token=AQECAHi208BE49Ooan9kkhW_Ercy7Dm3ZL_9Cf3qfKAc485ysgAAArMwggKvBgkqhkiG9w0BBwagggKgMIICnAIBADCCApUGCSqGSIb3DQEHATAeBglghkgBZQMEAS4wEQQMDSNTUjkCV-WRPv4xAgEQgIICZpGMIatG2iZzExqMaVqT9Oqvbsn7csn1IvlwN19grB8ye0rjENdHoFMiC_x7jVIYc_TJgVo6ydQ0FTlta6dssRdc3Uy87JyKS_5CocKwR5hG7s45lwO2aGn6iJ-StyJ9Jl8wzGIbo8syKMoi88bJAwF3rLuGqK5R8z98G-LkIzdy6MdFYChurMQUXX-9VhSRhdbvup0JXLK6vS9smOkVfBMKC45_2hNsYQZiZTEDP6FV9ImP2a0o7kMt9sHo6eQxjrO0SNBbsazE3pytWB4aox8Y9ZoDo5xai7DFmR1ERXQ9TdpQbTr0TvdIfXxqT2zMu-i7t4d9159uGfb_2-q0SBowGoWEJ17-lEHZD0nXVWyVWcaS9WaK3MkOGQqPjMy39XHLwrGZ3fztLs0fSC1sFOFMaxDZnolRtuCTk62EVTxI-0FKk1rBOpJRhP9qRa-4646n60C2S_B5wbpDLL_t-0KUTaKwwMU5VeDmBEas__HHry8RmJFtbgDuyrTlGzBhTdSylvJd83AxuXb9Kt3Uc5g43_nXpMdqZwu-6KasGWzSnJCznGF8oX40ofM7MlCD9_X5yLDHfgHlz6bDJPGloxx4TX36-tFqOZiYlRP1p3DqONTEoHlIW6thHRNg2rXagIeLGERS4mzpAk1G77e2N3bEQ4i9nR7Hv8blpew2qUKL1EwvVNXQhLbuIOmz1q5Q-FWfKj_rwq2EBF376jGbOMk4klmjjzRafGizRq2PVEAeymtV1w7xYcnN3GZxraAYYnLr9xDPfqQF-kp5Iu8Bc0A7VRiCsbawdA6xF4nhb9RBsnlG7ojm
https://pdfs.semanticscholar.org/ae57/ab527da5287ed215a9a3bf5f542ae19734ea.pdf
I would say use 95% confidence level and 5 confidence interval. Use the system below to calculate
https://www.surveysystem.com/sscalc.htm
Be wary of online sample size calculators. I've noted this on a number of occasions. They generally are only for yes/no questions, assume simple random sampling, assume that that N is enough larger than n that you do not need a finite population correction (fpc) factor, and pick the worst case for yes/no at p=q=0.5. If you have a better idea as to what p and q (always adding to 1) are, then that gives you a better idea of standard deviation. But using the worst case will likely overestimate your sample size need. If your sample isn't a simple random sample, and your data aren't yes/no type data (for proportions), then using such a calculator is problematic then also ... or perhaps I should say further problematic.
One paper I saw above mentioned both (1) estimation as I did (you have a methodology, data type, standard deviation, and then find what sample size gives you the standard error you want), and (2) power analyses when applying a statistical test (which is similar and generally standard deviation also leads to the accuracy you require, but sample design is more problematic). However, a quick look at that paper showed (1) used for descriptive statistics, and (2) used for inference, when they can both be used for either. I don't know if that was mentioned anywhere in that paper.
We should also consider model-based approachs, or at least model-assisted ones, when there are auxiliary/regressor data available.
@James R Knaub
Dear Dr. Thank you so much your answer has been so helpful.
From this formula--
S= X^2 NP (1-P) + d^2 (N-1) +X^2(1-P);
Where,
X^2 = the table value of chi-square for 1 degree of freedom at the desired confidence level (3.841)
N= Population size
P= Population Proportional (assumed to be 0.50 since this would provide the maximum sample size) D=degree of accuracy expressed as a proportion (0.05)
(Source: Krejcie, R.V., & Morgan, D.W. (1970). Determining Sample Size for Research Activities. Educational and Psychological Measurement, 30, 607-610.)
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