C955 Applied Probability and Statistics - Set 2 - Part 3

Correct Answer: When the same subjects are measured under two conditions

A paired test is used when observations are naturally matched, such as before and after measurements on the same subjects, analyzing the differences directly.

Correct Answer: It removes variability between subjects from the comparison

By comparing each subject to themselves, pairing eliminates between-subject variability, so smaller genuine differences become detectable.

Correct Answer: Whether means differ across three or more groups

Analysis of variance tests whether at least one group mean differs among three or more groups, avoiding the inflated error rate of many pairwise t-tests.

Correct Answer: Multiple comparisons inflate the overall probability of a Type I error

Each test carries its own Type I error risk, so performing many tests substantially raises the chance of at least one false positive.

Correct Answer: Whether two categorical variables are associated

The chi-square test of independence compares observed and expected frequencies in a contingency table to assess association between categorical variables.

Correct Answer: A perfect positive linear relationship

A correlation of +1 means all points lie exactly on an upward-sloping line. It indicates perfect linear association, not causation.

Correct Answer: Little or no linear relationship between the variables

A correlation near zero indicates weak linear association, though a strong nonlinear relationship could still exist and would not be captured by this measure.

Correct Answer: -1 to +1

The correlation coefficient always lies between -1 and +1 inclusive, with the sign indicating direction and magnitude indicating strength.

Correct Answer: The predicted change in the response for a one-unit increase in the predictor

The slope quantifies how much the predicted response changes per one-unit increase in the explanatory variable.

Correct Answer: The proportion of variability in the response explained by the model

R squared gives the fraction of variation in the response variable accounted for by the regression model, ranging from 0 to 1.