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# Basic Counting Rules

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Sampling

Sampling

We use sampling to gather statistics on a group because the entire population is too large to investigate each individual representative.

Types of Sampling:

Random Sampling: choosing representatives entirely randomly, so that each representative has the same chance of being chosen. For example, rolling a die.

• Simple Random Sample: Use a random number generator or a random number table to identify the members of your sample directly from your list.  If you get a number from the random source that does not directly correspond to one on your list, pick another until you do.  Continue the process until you have enough members of your sample.
• Systematic Random Sample: First divide the total number of members in the population to be sampled by the number of members you want in your sample.  The result is your step size.  Use a random generator to identify a starting number, then skip down from the starting number by your step size and pick the result, skip down again and pick, until you get as many results as you need for your sample.

Stratified Sampling: choosing a proportional number of representatives from each of a number of subgroups (called stratum) of the initial population. These divisions are chosen based on the belief that the subgroups differ significantly with respect to the variable that you are measuring.  For example you might stratify by age or by income.

Cluster Sampling: we use a simple random sample to choose a limited number of groups or clusters of samples from a population, and then again apply SRS to the chosen clusters in order to identify specific samples.

• The prime benefit of cluster sampling is that it can do an excellent job of reducing the size of a very large population down to something more manageable without ruining your ability to gather a representative sample.  representative sample is a smaller number of members of a population whose responses to events model those of the entire population.

Multi-Stage Sampling: narrowing down a field of representatives by successively applying multiple different sampling methods. For example you might stratify and then take a simple random sample from each stratum.

Non-Probability Sampling: a type of sampling that does not use random selection

• Convenience Sampling – Choosing samples based on easy or convenient access
• Volunteer (or Snowball) Sampling – Asking for volunteers or for recommendations from other samples
• Judgment Sampling – Deliberately choosing samples based on a desired characteristic
• Quota Sampling – Choosing samples to fill a specific quota of each of several sup-populations of the original

For most studies, it makes much more sense to use a sample than to try to collect data on an entire population, but sometimes a sample is not enough.  A census is when we survey the entire population.  The most famous census is the U.S. Population Census, conducted once every 10 years.

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