A sample is a subset of individuals in the population from which we actually collect data.
The population in a statistical study is the entire group of individuals we want information about.
A census collects data from every individual in the population.
In order to sample correctly:
- Say exactly what population we want to describe
- Say exactly what we want to measure
- Decide how to choose a sample from the population
Bad Sampling and Bias
There are ways to sample badly so that the sample would not be representative of the population you want to measure. It’s important to make sure you’re sampling correctly since any work you do with incorrect data will only represent a small portion of the entire population. Any inferences you make from that data set could be misleading.
Convenience sampling chooses individuals from the population who are easy to reach. When trying to sample everyone in your neighborhood, convenience sampling would be selecting people in the houses that are closest to yours.
Voluntary response sampling is when people choose themselves by responding to a general invitation. Online surveys are an example of voluntary response sampling because generally people who respond to a survey voluntarily tend to have strong opinions about the subject matter. This way, the results you get from this survey may only show the thoughts of the people who are most passionate about the topic.
Sampling badly could lead to bias which is consistently underestimating or overestimating the value you want to know.
If a problem asks you to identify the bias in the sampling,
- Identify a problem with the design
- Explain how the problem would lead to an underestimation or overestimation of what you’re trying to find
Types of good sampling:
Random sampling uses a chance process to determine which members of a population are included in a sample.
Simple Random Sample (SRS) of size n is chosen in such a way that every group of n individuals in the population has an equal chance to be selected as the sample.
The difference between the two above methods is that every group has the same chance of being selected in an SRS while every individual has the same chance of being selected in random sampling.
3 ways to choose a SRS:
- Manually: Number each member on equally sized pieces of paper which are placed in a bowl/hat. Mix them well and draw one at a time without replacement.
- Using a random number generator: Number each member of the population, then use a random number generator to obtain n different integers
- Using a random number table: Label (number each individual) using the same number of digits. Read groups of digits the size of your labels from left to right across a chosen line. Ignore unused labels or repeats.
When describing how to select a sample using a random integer generator, be sure to specify that repeated integers should be ignored or that you will generate random integers until you get n different numbers in the specified range.
While taking a SRS is the next best thing to taking a census, it’s not always the most time or cost-effective method of sampling, not to mention difficult to do accurately when depending on information from other sources. Therefore, additional types of sampling are used.
Other methods of good sampling
A Stratified Random Sample classifies the population into groups, then chooses a SRS in each stratum and combines them for the sample. Strata are groups of similar individuals, and they must be picked before the sampling is done.
A Cluster Sample classifies the population into clusters, then chooses an SRS of the clusters. A cluster is a group of individuals that are located near each other. Cluster sampling works best when the clusters look just like the population (representative) but on a smaller scale.