Populations and Samples

[A, SfS] Chapter 1: Sampling, Descriptive Statistics, Intr: 1.1: Populations and Samples

Populations and Samples

This section will teach you:

What the difference is between a population and a sample.
What is meant by a representative sample.
What is meant by descriptive statistics and inferential statistics.

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Population

A population is an entire collection of some well-defined elements about which researchers would like to obtain information.

Populations can vary in size:

If a researcher wants to make a claim about first-year medical students at a specific university, then the population is small enough that measurements can be obtained on all elements of the entire population.
If researchers want to make claims about all citizens of a large country, then it is very difficult to obtain measurements on all elements of the entire population.

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We also distinguish between tangible and conceptual populations.

Tangible and Conceptual Populations

A tangible population consists of a finite set of actual elements that exist in a particular moment.

Examples of tangible populations:

The population of all oak trees in a specified forest
The population of all registered voters in a specified country
The population of all mosquitoes of some specified species in some specified area

A conceptual population consists of a possibly infinite set of all possible outcomes of a process if it were to be repeated indefinitely under identical conditions.

Examples of conceptual populations:

The population of all possible race times for the winner of the Tour de France
The population of all possible DNA sequences for a specific gene
The population of all possible sequences of moves between two opponents in a chess game resulting in checkmate

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A common method of investigating populations is with the use of an experiment.

Experiments

In an experiment, we have in mind one tangible population, but under two or more different experimental conditions.

The population of all skin cancer patients if they were given a special new therapy, and the same population if they were given a traditional therapy, and the same population if they were given a placebo.

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Because a population is typically large or infinite, researchers must select a sample from the population.

Sample

A sample is a much smaller group of elements that are selected among all the elements in the population.

Based on that sample, researchers hope to make a claim about the entire population.

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Because researchers base their conclusions about the population on their sample, it is essential that this sample is representative of the population.

Representative

Representative means that the characteristics of the population (e.g. the variation in age and education level) should be approximately the same in the sample.

In essence, the sample should be a minimum version of the population, in the way that a photograph with reduced pixels still looks the same as the original photograph.

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The field of statistics consists of two branches: descriptive and inferential statistics.

Descriptive and Inferential Statistics

Descriptive statistics involves reporting useful information about variables, whether measured on a sample or the entire population.

Inferential statistics involves using descriptive statistics from a sample to arrive at conclusions about the population. Because there is always uncertainty about how well the sample represents the population, inferential statistics is based on the mathematical laws of probability.