Descriptive vs. Inferential Statistics + Population/Sample/Parameter

Descriptive Statistics

Statistics that summarizes and describes characteristics of data (percentages, averages). It tells us what happened

Example of Descriptive Statistics

Out of 4 teachers, 2 are female so:

“50% of the teachers are female”

Descriptive statistics can be used for:

A sample or population

Inferential Statistics

Statistics that use sample data to make conclusions or predictions about a population. It answers: “What does this mean?”

Example of Inferential Statistics

Using sample spelling scores to decide whether girls and boys differ in spelling ability in population:

“Girls likely score higher in spelling than boys in general”

“New math program likely improves achievement across ontario “

Difference between descriptive and inferential statistics

Descriptive: summarizes data not generalizing beyond the sample (sample or population)

Inferential: Uses sample data to generalize, predict or uses likely to a population (sample only)

Population

Entire group of interest.

Including every element to draw conclusioms about

Ex. all kindergarteners in Ontario

Sample

Subset of population we collect data from

Ex. 50 kindergartners from one school

What makes a sample representative

When it accurately reflects characteristic of population

What is an element

A single member of a population or sample (e.g., one student, one voter)

When is a group considered a population vs. a sample?

Depends on the research question.

Ex: Toronto = sample if the population is Canada, but Toronto = population if the study focuses only on Torontonians

Parameter

A number value describing a population

Ex. μ = Average score of all Ontario kindergarteners

Statistic

A number value describing a sample

Ex. x̄ = Average score of 50 schools kindergarteners

What symbols are used for statistics vs parameters

Statistics → Roman (x̄).

Parameters → Greek (μ).

What happens if a sample is truly random and large?

The statistic will be very close or identical to the population parameter.

Why is a random but small sample not enough?

Small samples increase the chance of error and may not represent the population accurately

Why is a large but biased sample still a problem?

Large samples can produce misleading statistics if they don’t represent the population (e.g., online polls of specific readers)

Implications when certain statistics are computed

• Biased sample: the statistic may differ greatly from the true parameter.

• Random and large sample: the statistic is a reliable estimate of the parameter.

• Misinterpreting a statistic as a parameter leads to false generalizations.

Example of of misleading computation

A newspaper poll of 23,521 readers found 91 % planned to vote, but the true population parameter was 65 %. The sample was large but biased, so the statistic was inaccurate.

What is the relationship between descriptive and inferential statistics here?

Descriptive statistics summarize the sample or population

Inferential statistics use sample statistics to estimate or test population parameters.