To calculate the sample size for 200 farmers accessing agricultural information from a population of 109,977, you can use the following formula for sample size determination:
Sample Size (n) = [Z^2 * P * (1 - P)] / E^2
Where:
Z is the Z-score, which corresponds to the desired confidence level (e.g., 95% confidence level corresponds to a Z-score of approximately 1.96).
P is the estimated proportion of the population that possesses the characteristic of interest (in this case, farmers accessing agricultural information). If you don't have an estimate, you can use 0.5 for a conservative estimate.
E is the margin of error (how much you want your sample estimate to deviate from the true population proportion). It's usually expressed as a decimal (e.g., 0.05 for a 5% margin of error).
Assuming a 95% confidence level (Z ≈ 1.96), a conservative proportion (P ≈ 0.5), and a 5% margin of error (E ≈ 0.05), you can calculate the sample size as follows:
Sample Size (n) = [(1.96^2) * 0.5 * (1 - 0.5)] / 0.05^2
Sample Size (n) ≈ 384.16
You would need a sample size of approximately 385 farmers to estimate the proportion of farmers accessing agricultural information from a population of 109,977 with a 95% confidence level and a 5% margin of error.
You can find any number of sample size calculators through a Google search. They are almost all based on the assumption that you are estimating the sample size for a Yes-No variable that is split 50-50 in the population. They give you the sample size for an estimate that is 95% likely to fall between plus or minus 5% from the population value.
YOu can easily calculate sample size using Taro Tamani formula
n = N / 1+N (e)2
n = sample size
N= Poplation
(e)2= square of margin of error
This is done through regional study method. Random sampling technique and interview method should be used to collect data.
As suggested by others, there are different ways of estimating your sample size. But if you opt to use the Taro Yamene formula, which is provided below, consider playing around the confidence level. It should be around 92.95% with a margin of error (e) equal to 7.05%.
n = N/[1+N (e)2]
N= Population
n = sample size
(e)2= Margin of error (e*e) square
However, take note that the lower the margin of error the more accurate and reliable the research findings will be. Confidence in research allows you as a researcher to have faith in your data, conclusions, and recommendations. It helps in making informed decisions based on the research results and may enable you as a researcher to confidently communicate your findings to others, ultimately contributing to the progress and advancement of knowledge in respective fields.
Vishal Pradhan
Small sample sizes may well be inadequate for ANOVA because they lack the "power" to detect effects that would be significant with a larger sample. That is why I recommend the program G*Power to estimate one's sample size prior to collecting the data. This program is based on using an estimate of the size of the effect that you are likely to observe, which determines that sample size that would be necessary to detect such an effect.- Badges
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