Determining if the 10% Rule is Satisfied When Sampling is Done Without Replacement | Statistics and Probability (2024)

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Determining if the 10% Rule is Satisfied When Sampling is Done Without Replacement | Statistics and Probability? ›

Step 1: Identify the population size, , and calculate 10% of the population size, . Step 2: Identify the sample size, . Step 3: Compare the sample size to 10% of the population size. If n ≤ 0.1 N then the 10% rule is satisfied.

The 10% rule states that a sample size should not exceed 10% of the population when using sampling methods like simple random sampling. This helps ensure that the sample is representative of the population.

It's important to check the 10% condition before calculating probabilities involving x because we want to ensure that the observations in the sample are close to independent.

Without replacement: When sampling is done without replacement, each member of a population may be chosen only once. In this case, the probabilities for the second pick are affected by the result of the first pick. The events are considered to be dependent or not independent.

A good maximum sample size is usually around 10% of the population, as long as this does not exceed 1000. For example, in a population of 5000, 10% would be 500. In a population of 200,000, 10% would be 20,000.

10 Percent Rule: The 10 percent rule is used to approximate the independence of trials where sampling is taken without replacement. If the sample size is less than 10% of the population size, then the trials can be treated as if they are independent, even if they are not.

Step 1: Identify the population size, , and calculate 10% of the population size, . Step 2: Identify the sample size, . Step 3: Compare the sample size to 10% of the population size. If n ≤ 0.1 N then the 10% rule is satisfied.

sampling without replacement, in which a subset of the observations is selected randomly, and once an observation is selected it cannot be selected again. sampling with replacement, in which a subset of observations are selected randomly, and an observation may be selected more than once.

= N! n!( N − n)! . This is the number of combinations of n items selected from N distinct items (and the order of selection doesn't matter).

Simple random sample without replacement (SRSWOR):

It is drawn as 1/N for the first draw, 1/ (N-1) for the second, 1/ (N-r+1) for the third, and so on. Therefore, the probability of drawing “n” units from a sample and its selection in the rth draw is n/N.

What is the minimum sample size to be statistically significant? ›

The number 30 is often used as a rule of thumb for a minimum sample size in statistics because it is the point at which the central limit theorem begins to apply.

The acceptable margin of error usually falls between 4% and 8% at the 95% confidence level. While getting a narrow margin of error is quite important, the real trick of the trade is getting that perfectly representative sample.

The 10-times rule recommends that the minimum “sample size should be equal to the larger of (1) 10 times the largest number of formative indicators used to measure one construct or (2) 10 times the largest number of structural paths directed at a particular latent construct in the structural model” (Hair et al., 2017, ...

This rule assumed that the sample size should be greater than 10 times the maximum number of inner or outer model links pointing at any latent variable in the entire model and consequently, this is the very simple method to estimate the sample size compared to the other methods.

The 10% condition in statistics stipulates that when sampling without replacement, the sample size should not be more than 10% of the population.

Rule of Thumb #1: A larger sample increases the statistical power of the evaluation. Rule of Thumb #2: If the effect size of a program is small, the evaluation needs a larger sample to achieve a given level of power. Rule of Thumb #3: An evaluation of a program with low take-up needs a larger sample.

It states that if other things being equal, larger the size of the sample, more accurate the results are likely to be. Thus is because large numbers are more stable as compared to small ones. The difference in the aggregate result is likely to be significant, when the number in the sample is large.