Sampling Distributions

Sample variance ($s^2$)

Population standard deviation ($\sigma$)

Population variance ($\sigma^2$)

Sample standard deviation ($s$)

Convenience sampling

Stratified sampling

Cluster sampling

Simple random sampling

Unbiased estimator

Biased estimator

Statistically significant indicator

Variance reducer

Conservatively biased point estimates due to excessive smoothing applied across resampling iterations.

Inherently precise point estimates guaranteed by repeated sampling regardless of underlying distribution shape or spread.

Directly biased point estimates because bootstrap methods inherently increase variability beyond original data levels.

Bias-corrected point estimates based on recentering resampled statistics around original statistic values.

To reduce bias introduced by outliers through resampling methods.

To create more outliers for robustness checks.

To lower variability within each bootstrap sample created.

To ensure that all outliers are included in every sample taken.

Quadratic mean

Interquartile range

Sample proportion

Mean deviation

High variability leads to lower p-values which reduces Type I errors proportionally with variability increase.

High variability decreases Type I errors through increased sensitivity in detecting non-zero effects.

High variability increases Type I errors due to larger standard errors making it harder to detect true effects.

High variability has no effect on Type I errors as they are independent from dataset variability levels.

Simple random sample (SRS)

Cluster Sample (CS)

Stratified random sample (STRS)

Systematic Sample (SYS)

Increasing your confidence level from 90% to 95%, thus widening your interval.

Calculating margin of error using critical values corresponding to your desired confidence level.

Assuming normality when sampling from a heavily skewed distribution with small n.

Using t-distribution with degrees of freedom equal to n - 1.

Trimmed means lessen the influence of extreme scores, thus providing a more robust estimator.

Arithmetic means always give the most precise estimate regardless of the extremes in data.

Using arithmetic means avoids the need to adjust or analyze underlying distribution patterns.

Trimming extremes simplifies calculation but significantly reduces estimator's precision.