Sampling Distributions
Simple random sample (SRS)
In statistics, a simple random sample from a population is a sample chosen randomly, so that each possible sample has the same probability of being chosen. One consequence is that each member of the population has the same probability of being chosen as any other. In small populations such sampling is typically done "without replacement", i.e., one deliberately avoids choosing any member of the population more than once. Although simple random sampling can be conducted with replacement instead, this is less common and would normally be described more fully as simple random sampling with replacement.
Conceptually, simple random sampling is the simplest of the probability sampling techniques. It requires a complete sampling frame, which may not be available or feasible to construct for large populations. Even if a complete frame is available, more efficient approaches may be possible if other useful information is available about the units in the population.
Advantages are that it is free of classification error, and it requires minimum advance knowledge of the population. It best suits situations where the population is fairly homogeneous and not much information is available about the population. If these conditions are not true, stratified sampling may be a better choice.
Drawing Simple Random Samples using a Table of Random Numbers
An easy way to select a SRS is to use a random number table, which is a table of digits 0,1,…,9, each digit having equal chance of being selected at each draw. To use this table in drawing a random sample of size n from a population of size N, we do the following:
1. Label the units in the population from 0 to N 1.
2. Find r, the number of digits in N 1 . For example; if N = 100, then r = 2.
3. Read r digits at a time across the columns or rows of a random number table.
4. If the number in (3) corresponds to a number in (1), the corresponding unit of the population is included in
In statistics, a simple random sample from a population is a sample chosen randomly, so that each possible sample has the same probability of being chosen. One consequence is that each member of the population has the same probability of being chosen as any other. In small populations such sampling is typically done "without replacement", i.e., one deliberately avoids choosing any member of the population more than once. Although simple random sampling can be conducted with replacement instead, this is less common and would normally be described more fully as simple random sampling with replacement.
Conceptually, simple random sampling is the simplest of the probability sampling techniques. It requires a complete sampling frame, which may not be available or feasible to construct for large populations. Even if a complete frame is available, more efficient approaches may be possible if other useful information is available about the units in the population.
Advantages are that it is free of classification error, and it requires minimum advance knowledge of the population. It best suits situations where the population is fairly homogeneous and not much information is available about the population. If these conditions are not true, stratified sampling may be a better choice.
Drawing Simple Random Samples using a Table of Random Numbers
An easy way to select a SRS is to use a random number table, which is a table of digits 0,1,…,9, each digit having equal chance of being selected at each draw. To use this table in drawing a random sample of size n from a population of size N, we do the following:
1. Label the units in the population from 0 to N 1.
2. Find r, the number of digits in N 1 . For example; if N = 100, then r = 2.
3. Read r digits at a time across the columns or rows of a random number table.
4. If the number in (3) corresponds to a number in (1), the corresponding unit of the population is included in