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

### 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*.

#\text{}#

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.

#\text{}#

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

#\text{}#

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.

#\text{}#

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.

#\text{}#

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.

#\text{}#

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*.

**Pass Your Math**independent of your university. See pricing and more.

Or visit omptest.org if jou are taking an OMPT exam.