exam 5 Flashcards
What is an association in statistics?
An association is a relationship between two variables, where changes in one variable relate to changes in another.
What types of data are needed to describe an association?
You need paired data for two variables, typically measured quantitatively.
What is correlation analysis?
It’s a statistical method that quantifies the strength and direction of a relationship between two continuous variables.
How do you identify the direction of an association?
By the sign of the correlation coefficient: positive (+) or negative (−).
How do you identify the strength of an association?
: By the magnitude of the correlation coefficient (r): closer to ±1 indicates a stronger association.
How is the Pearson correlation coefficient generally calculated?
: By dividing the covariance of the two variables by the product of their standard deviations.
What are the assumptions of correlation analysis (Pearson’s)?
Linearity, continuous variables, normal distribution, and homoscedasticity.
How do you interpret a correlation coefficient of r = 0.85?
A strong positive linear association between the two variables.
When should you use Spearman’s correlation instead of Pearson’s?
hen data are ordinal or not normally distributed, or when the relationship is monotonic but not linear
When is an association evidence of a cause-effect relationship?
When there’s consistent correlation, temporal precedence, control for confounding variables, and a plausible mechanism.
What is regression analysis?
A statistical method to model the relationship between a dependent variable and one or more independent variables.
How does regression differ from correlation?
Regression predicts values and implies directionality; correlation only measures association without implying causality.
What are the assumptions of linear regression?
Linearity, independence, homoscedasticity, and normality of residuals.
How do you determine the y-intercept and slope in least-squares regression?
By minimizing the sum of the squared differences between observed and predicted y-values.
How do Frequentists define probability?
As the long-run relative frequency of an event occurring in repeated trials.
How do Bayesians define probability?
As a degree of belief or certainty about an event, updated with evidence
What are major differences between Bayesian and Frequentist inference?
Bayesian uses prior beliefs and updates with data; Frequentist relies only on sample data without incorporating prior knowledge.
What is a prior probability distribution?
A Bayesian estimate of the likelihood of a hypothesis before observing the current data.
Why is the prior distribution used in Bayesian inference?
To incorporate previous knowledge or assumptions into the analysis.
Where is Bayesian inference commonly used?
In fields like medicine (diagnostic testing), machine learning, and decision-making under uncertainty
