All MCQs

The null often states no difference, no effect, or a specified parameter value.
A test assesses whether the data are sufficiently inconsistent with it.

Higher confidence requires covering a broader range of parameter values.
This is achieved through a larger critical value and wider interval.

Larger samples usually reduce the standard error of an estimate.
Reduced uncertainty produces a narrower interval at the same confidence level.

Confidence intervals combine an estimate with its sampling uncertainty.
Their interpretation depends on the confidence procedure and assumptions.

Examples include the sample mean estimating the population mean.
A point estimate does not by itself express uncertainty.

Association may arise from confounding, reverse direction, bias, or coincidence.
Causal conclusions require stronger design and assumptions.

A confounder provides an alternative explanation for an observed relationship.
Stratification, design, and modeling are needed to assess it.

With p variables, there are p(p-1)/2 distinct pairwise correlations.
Ordering, clustering, and selective annotation can improve readability.

A correlation matrix summarizes linear associations for all variable pairs.
It is often visualized as a colored correlogram.

Human color discrimination and legend lookup are limited.
Faceting, filtering, or highlighting selected groups may communicate more clearly.

Color can distinguish groups or represent another quantitative variable.
This extends a bivariate plot into a multivariate display.

A smoother helps reveal trends that may be hidden by point noise.
It should be shown together with data and interpreted with uncertainty.