# STA 2023 Lecture Notes - Lecture 9: Statistical Inference, Descriptive Statistics, Simple Random Sample

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● data

Consist of information coming from observations, counts, measurements, or

responses.

● statistics

The science of collecting, organizing, analyzing, and interpreting data in order to

make decisions.

● population

The collection of all outcomes, responses, measurements, or counts that are of

interest.

● sample

A subset, or part, of the population.

● parameter

A numerical description of a population characteristic.

● statistic

A numerical description of a sample characteristic.

● descriptive statistics

Involves organizing, summarizing, and displaying data.

e.g. tables, charts, averages

● inferential statistics

Involves using sample data to draw conclusions about a population.

● qualitative data

Consists of attributes, labels, or non numeric entries.

● quantitative data

Numerical measurements or counts.

● nominal level of measurement

- qualitative data only

- categorized using names, labels, or qualities

- no mathematical computations can be made

● ordinal level of measurement

- qualitative or quantitative data

- data can be arranged in order, or ranked

- differences between data entries is not meaningful

● internal level of measurement

- quantitative data

- data can ordered

- differences between data entries is meaningful

- zero represents a position on a scale (not an inherent zero - zero does not imply

"none")

● ratio level of measurement

- similar to interval level

- zero entry is an inherent zero (implies "none")

- a ratio of two data values can be formed

- one data value can be expressed as a multiple of another

● observational study

A researcher observes and measures characteristics of interest of part of a

population.

● experiment

- A treatment is applied to part of a population, called a treatment group, and

responses are observed.

- Another part of the population may be used as a control group, in which no

treatment is applied. (The subjects in both groups are called experimental units.)

- In many cases, subjects in the control group are given a placebo, which is a

harmless, fake treatment that is made to look like the real treatment.

● simulation

Uses a mathematical or physical model to reproduce the conditions of a situation

or process.

● survey

- An investigation of one or more characteristics of a population.

- Surveys are carried out on people by asking them questions.

- Commonly done by interview, Internet, phone, or mail.

● confounding variables

Occurs when an experimenter cannot tell the difference between the effects of

different factors on a variable.