Math Statistics
Random sample
It is often not necessary to survey the entire population.
Instead, you can select a random sample of people/or firms from the population and survey just them.
You can then draw conclusions about how the entire population would respond based on the responses from this randomly selected group of people.
This is exactly what political pollsters do - they ask a group of people a list of questions and based on their results, they draw conclusions about the population as a whole with those often heard disclaimers of "plus or minus 5%"
If your population consists of just a few hundred people, you might find that you need to survey almost all of them in order to achieve the level of accuracy that you desire.
As the population size increases, the percentage of people needed to achieve a high level of accuracy decreases rapidly.
In other words, to achieve the same level of accuracy:
Larger population = Smaller percentage of people surveyed
Smaller population = Larger percentage of people surveyed
Probability Sampling
A probability sampling method is any method of sampling that utilizes some form of random selection.
In order to have a random selection method, you must set up some process or procedure that assures that the different units in your population have equal probabilities of being chosen.
Some basic terms
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N - the number of cases in the sampling frame n - the number of cases in the sample
NCn - the number of combinations (subsets) of n from N f = n/N - the sampling fraction
1. Simple Random Sampling
The simplest form of random sampling is called simple random sampling.
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Objective: To select n units out of N such that each NCn has an equal chance of being selected.
Procedure: Use a table of random numbers, a computer random number generator or a mechanical device to select the sample.
Example
The problem
A small service agency wishes to assess client's views of quality of service over the
It is often not necessary to survey the entire population.
Instead, you can select a random sample of people/or firms from the population and survey just them.
You can then draw conclusions about how the entire population would respond based on the responses from this randomly selected group of people.
This is exactly what political pollsters do - they ask a group of people a list of questions and based on their results, they draw conclusions about the population as a whole with those often heard disclaimers of "plus or minus 5%"
If your population consists of just a few hundred people, you might find that you need to survey almost all of them in order to achieve the level of accuracy that you desire.
As the population size increases, the percentage of people needed to achieve a high level of accuracy decreases rapidly.
In other words, to achieve the same level of accuracy:
Larger population = Smaller percentage of people surveyed
Smaller population = Larger percentage of people surveyed
Probability Sampling
A probability sampling method is any method of sampling that utilizes some form of random selection.
In order to have a random selection method, you must set up some process or procedure that assures that the different units in your population have equal probabilities of being chosen.
Some basic terms
•
•
•
•
N - the number of cases in the sampling frame n - the number of cases in the sample
NCn - the number of combinations (subsets) of n from N f = n/N - the sampling fraction
1. Simple Random Sampling
The simplest form of random sampling is called simple random sampling.
•
•
Objective: To select n units out of N such that each NCn has an equal chance of being selected.
Procedure: Use a table of random numbers, a computer random number generator or a mechanical device to select the sample.
Example
The problem
A small service agency wishes to assess client's views of quality of service over the