Statistics and Data Analysis: Key Concepts for Experiments and Observational Studies

Error (Residual)

The difference between a predicted value and the actual observed value.

Experiment

A study where researchers actively change something (an independent variable) and measure the effect on something else (a dependent variable). Used to establish cause and effect.

Observational Study

A study where researchers just observe and collect data without changing anything. Can show an association, but not a cause-and-effect relationship.

Experimental Units

The things you perform an experiment on. For example, the people, animals, or objects you are giving a new drug or treatment to.

Observational Units

The individual things you are collecting data on in an observational study. For example, the individual customers or cities whose behavior you are tracking.

Variable

A characteristic or attribute that can be measured or observed. Examples include age, income, or product category.

Quantitative Variable

A variable that can be measured with numbers. Examples include height, temperature, or the number of items sold.

Categorical Variable

A variable that describes a group or category. Examples include gender, brand of car, or city of residence.

Statistic

A number that describes a sample. For example, the average height of 100 people selected from a group.

Parameter

A number that describes an entire population. For example, the true average height of all people in a country.

Sample

A small, representative group taken from a population. Data scientists use samples to make estimates about the larger group.

Population

The entire group you are interested in studying. For example, all the customers of a company, or every car on the road.

Inference

Using data from a sample to make a conclusion or prediction about the entire population. This is a key goal of data science.

Cause and Effect

When one event directly causes another. This can only be reliably proven with a well-designed experiment.

Association

When two variables are related, but one doesn't necessarily cause the other. For example, ice cream sales and shark attacks might both increase in the summer, but one doesn't cause the other.