STAT 151 Module 1

Population

the entire group we are interested in studying

Parameter

the characteristic of the population we are interested in studying; the numerical summary of a population

Sample

Statistic

used as an estimate for the population parameter; a numerical summary of a sample

Census

a survey or study of every member of the population

Statistics

the science of how to collect, summarize, analyze, present, and interpret data and to make decisions

Inference

statements about the population based on the sample data (generalising)

Data

a collection of numbers, characters, images, or other items that provide information about something

Variable

a characteristic, number, or quantity that can be measured or counted and can vary from one individual or observation to another (something that can change or take different values in dataset); eg. gender, temp., income, age; we collect data on variables, analyze patterns and relationships between variables, test hypotheses using variables,and predict future outcomes based on variable behavior.

Quantitative (Numerical) variables

represent measurable quantities; either discrete (countable values - no decimals) or continuous (any value with a range - decimals); eg. age, income, temperature, test scores

Qualitative (Categorical) variables

represent categories or groups; either nominal (no inherent order like eye color) or ordinal (ordered categories like satisfaction levels); eg. gender, type of car, education level

Nominal variable

are categories with no inherent order and are used for labeling or classifying - cannot rank or measure the differences between categories

Ordinal variable

categories with a meaningful order, but the differences between levels are not measurable or equal; used to rank data

Interval variable

can be ordered but the differences are meaningful; no natural zero (natural zero means the complete absence of the quantity being measured). Example: Example: temperature in °C or °F (0°C doesn’t mean “no temperature”)

Ratio variable

all properties of interval variables plus a natural zero; ratios make sense (e.g., 4 kg is twice as heavy as 2 kg). Examples: height, weight, age, amount of money.

Natural zero

means the absence of something

Identifier variable

not a quantitative variable as it doesn’t have units, but is a categorical variable with one individual in each category; eg. Student ID, SIN, ISBN

Who

… are the cases/subjects?

When

… was the data collected?

Where

… were data collected?

Why

… were data collected (research question)?

What

… variables were measured?

Convenience sampling

involves selecting a sample that is easiest to access or collect; often bias; eg. the first ten people to walk into a store about consumer preferences

Experiment

involves intervention by the researcher and manipulation is applied to the subjects and does not take place in the natural setting

Prospective study

focuses on the now and future, making predictions based on previous knowledge