I want to conduct a study where the population size is infinitely lagre. In that case How much data I should take. May anyone can suggest any book on that?
There is no unique cutoff at which a sample is sufficiently large enough to be representative of a population. There will ALWAYS be some degree of sampling error. The question is: how much error is acceptable?
What matters as much (if not more) than sample size is sampling method. A smaller sample selected at random is often better than a larger sample nonrandomly selected.
Hello Shikhar Tyagi, I recommend armitage and berry; statistical methods in medical research. I have it, but not 100% sure where the book is. Does your library have it?
For a very large (infinite) population, Cochran's formula suggests a minimum of 385.
http://www.raosoft.com/samplesize.html?fbclid=IwAR2BuNhADNJAxv5DQwC8i7dxyzk2FaMmUgAIcZ3l_6SgUWD06m8fpL0yagg
When dealing with an infinitely large population, determining the appropriate sample size for a study becomes a critical task. While it may seem counterintuitive, the size of the population does not directly impact the necessary sample size when conducting a study. Instead, factors such as confidence level, margin of error, and variability within the population play a more significant role in determining sample size. It is essential to utilize statistical calculations and formulas to ensure that the sample size adequately represents the larger population while minimizing potential biases or errors. In general, larger sample sizes are preferred as they increase the reliability and precision of study results. However, achieving true randomness and representativeness in sampling can be challenging with infinitely large populations, making careful consideration of various statistical methods crucial in research design. URL: https://www.surveymonkey.com/mp/sample-size-calculator/
Your question should be phrased differently depending on the context. In the frequentist context the behaviour of the test-statistic (effect-size) is represented by a random variable X. The size of the "population"is infinite population mean=Xhat={Xi,...,XN}/N; N=Infinite. However your sample x is finite and the sample mean is known xhat={xi,...,xn}; n=sample size.
Thus if we make the explicit assuptions:
1.) X is assumed to be normally distributed.
2.) We have a single study and no repetition (no focus on error control).
3.) xhat = 1 would be accepted to be the minimal useful effect size (that at least is believed not to be due to some unaccounter error, bias or noise).
4.) We minimally accept z=2=pminimal, sigma=approx and acceptable>z
For any sample size, some initial information is required like the type of study design, how will your outcome reported, and how much is your confidence level. Ref: Adequacy of Sample Size in Health Studies, Stanley Lemeshow , David W. Hosmer Jr, Janelle Klar
Hello Shikhar Tyagi,
Assalam u Alaikum (Peace be upon you)!
When conducting a study with a very large or infinite population size, the key is to determine an appropriate sample size that balances the need for statistical precision with practical considerations such as cost and time.
Here are some key concepts to consider when determining the sample size for a study with a very large population size:
For more guidance on these concepts and how to calculate the appropriate sample size for your study, you can refer to the following resources:
Remember that these resources provide general guidance, and the actual sample size required may depend on the specific context and goals of your study. Consulting with a statistician or research methodologist may also be beneficial to ensure that your study is designed properly.
The above response is from ChatGPT (https://chat.openai.com/)
For my thesis, I used a related quality paper as a reference to guide the process of determining the sample size for a study with a very large population size. The paper provided me valuable insights into the key considerations for sample size calculation 😃.
Best of luck!
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