Statistics Tutorial: Simple Random Sampling
To understand sampling, you need to first understand a few basic definitions.
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The total set of observations
that can be made is called the population.
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A sample is a subset
of a population.
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A parameter is a measurable characteristic of a population,
such as a mean or
standard deviation.
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A statistic
is a measurable characteristic of a sample, such as a mean or standard
deviation.
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A sampling method
is a procedure for selecting sample elements from a population.
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A random number
is a number determined totally by chance, with no predictable relationship to
any other number.
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A random number table is a list of numbers, composed of the
digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Numbers in the list are arranged so
that each digit has no predictable relationship to the digits that preceded it
or to the digits that followed it. In short, the digits are arranged randomly.
The numbers in a random number table are random numbers.
Simple Random Sampling
Simple random sampling refers to a sampling method that has the
following properties.
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The population consists of N
objects.
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The sample consists of n
objects.
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All possible samples of n objects are equally likely to occur.
The main benefit of simple random sampling is that it guarantees that the sample
chosen is representative of the population. This ensures that the statistical
conclusions will be valid.
There are many ways to obtain a simple random sample. One way would be the
lottery method. Each of the N population members is assigned a unique
number. The numbers are placed in a bowl and thoroughly mixed. Then, a
blind-folded researcher selects n numbers. Population members having the
selected numbers are included in the sample.
Random Number Generator
In practice, the lottery method described above can be cumbersome, particularly
with large sample sizes. As an alternative, use Stat Trek's Random Number
Generator. With the Random Number Generator, you can select n random
numbers quickly and easily. This tool is provided at no cost - free!! To access
the Random Number Generator, simply click on the button below.
It can also be found under the Stat Tools
tab, which appears in the header of every Stat Trek web page.
Sampling With Replacement and Without Replacement
Suppose we use the lottery method described above to select a simple random
sample. After we pick a number from the bowl, we can put the number aside or we
can put it back into the bowl. If we put the number back in the bowl, it may be
selected more than once; if we put it aside, it can selected only one time.
When a population element can be selected more than one time, we are sampling
with replacement. When a population element can be selected only
one time, we are sampling without replacement.
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