Relative precision in sample size determination refers to the acceptable margin of error, expressed as a percentage, around the true population value that the sample estimate is expected to fall within. Essentially, it quantifies how close the sample result should be to the actual population value.
Understanding Relative Precision
Here's a breakdown of what relative precision entails:
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Margin of Error: This is the range within which you expect your sample results to vary from the true population value.
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Percentage Expression: Relative precision expresses this margin of error as a percentage of the true value. For example, a relative precision of 5% means the sample result should be within 5% above or below the actual population value.
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Influence on Sample Size: The desired level of relative precision directly impacts the required sample size. Higher precision (smaller percentage) necessitates a larger sample size. Conversely, lower precision (larger percentage) allows for a smaller sample size.
Formula and Application
The concept of relative precision (ε) is often seen in sample size calculations, particularly when estimating proportions. In this context, the goal is to ensure the sample proportion falls within ε% of the true population proportion. A simplified representation as described in the reference is "The sample result should fall within ε % of the true value."
For example, if you are trying to estimate the proportion of people who prefer a certain brand of coffee, and you want a relative precision of 3%, your sample size calculation will aim to ensure that the estimated proportion from your sample is within 3% of the actual proportion in the entire population.
Example
Let's say you want to determine the proportion of customers satisfied with a new product and aim for a relative precision of 5%. This means that if the true satisfaction rate is 70%, you want your sample estimate to be within 5% of 70%, or between 66.5% and 73.5%. To achieve this level of precision, you will need a sufficiently large sample size.
Importance in Research
Specifying relative precision is crucial in research because:
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It sets a clear objective: It defines how accurate the sample estimate needs to be.
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It informs sample size planning: It helps determine the appropriate sample size required for the study.
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It influences the validity of results: A higher relative precision leads to more reliable and generalizable findings.
Cluster Sampling Consideration
The reference also mentions a design effect (D) in the context of cluster sampling. Cluster sampling involves dividing the population into clusters and then randomly selecting clusters to sample. This method often requires a larger sample size compared to simple random sampling because individuals within a cluster tend to be more similar to each other than individuals chosen at random from the entire population. The design effect accounts for this increased variability and is used to adjust the sample size calculation accordingly. For instance, "For cluster sampling the sample size will be 3457x D (design effect)." If the design effect is 2, then the sample size would need to be doubled to maintain the same level of relative precision.
