Types of Variables in Statistics

Study Notes

Qualitative Variables: Categorical variables that describe characteristics or attributes, e.g., gender, occupation, or country of origin.
Quantitative Variables: Numerical variables that can be measured or compared, e.g., height, weight, or temperature.
Discrete Variables: Quantitative variables that can only take on specific, distinct values, e.g., number of children or days of the week.
Continuous Variables: Quantitative variables that can take on any value within a certain range or interval, e.g., height or temperature.

Correlation Coefficient (r): A statistical measure that quantifies the strength and direction of the linear relationship between two continuous variables.
Interpretation of r:
- Positive r: positive correlation (as one variable increases, the other tends to increase)
- Negative r: negative correlation (as one variable increases, the other tends to decrease)
- r = 0: no correlation
Correlation vs. Causation: Correlation does not imply causation; a third variable may be driving the observed correlation.

Independent Variable (IV): The variable intentionally manipulated by the researcher to observe its effect on the dependent variable.
Dependent Variable (DV): The variable being measured or observed in response to the independent variable.
Control Group: A group that does not receive the treatment or intervention, used as a baseline for comparison.
Experimental Group: A group that receives the treatment or intervention.

Causal Inference: The process of drawing conclusions about cause-and-effect relationships between variables.
Causal Graphs: Visual representations of causal relationships between variables, used to identify potential confounders and mediators.
Confounding Variables: Variables that can affect both the independent and dependent variables, leading to biased estimates of the causal relationship.
Mediator Variables: Variables that help to explain the causal relationship between the independent and dependent variables.

Regression Analysis: A statistical method for modeling the relationship between a dependent variable and one or more independent variables.
Simple Linear Regression: A model that examines the relationship between a single independent variable and the dependent variable.
Multiple Linear Regression: A model that examines the relationships between multiple independent variables and the dependent variable.
Model Assumptions: Conditions that must be met for the statistical model to be valid, including linearity, independence, homoscedasticity, normality, and no or little multicollinearity.

Qualitative variables describe characteristics or attributes, such as gender, occupation, or country of origin.
Quantitative variables can be measured or compared, like height, weight, or temperature.
Discrete variables can only take on specific, distinct values, such as number of children or days of the week.
Continuous variables can take on any value within a certain range or interval, like height or temperature.

Correlation coefficient (r) measures the strength and direction of the linear relationship between two continuous variables.
Positive correlation (r > 0) means as one variable increases, the other tends to increase.
Negative correlation (r < 0) means as one variable increases, the other tends to decrease.
No correlation (r = 0) means no relationship between the variables.

Independent variable (IV) is the variable intentionally manipulated by the researcher to observe its effect on the dependent variable.
Dependent variable (DV) is the variable being measured or observed in response to the independent variable.
Control group is a group that does not receive the treatment or intervention, used as a baseline for comparison.
Experimental group is a group that receives the treatment or intervention.

Causal inference involves drawing conclusions about cause-and-effect relationships between variables.
Causal graphs are visual representations of causal relationships between variables, used to identify potential confounders and mediators.
Confounding variables can affect both the independent and dependent variables, leading to biased estimates of the causal relationship.
Mediator variables help to explain the causal relationship between the independent and dependent variables.

Regression analysis models the relationship between a dependent variable and one or more independent variables.
Simple linear regression examines the relationship between a single independent variable and the dependent variable.
Multiple linear regression examines the relationships between multiple independent variables and the dependent variable.
Model assumptions include linearity, independence, homoscedasticity, normality, and no or little multicollinearity.