LPLS cheat sheet

Reliability is the consistency of a measure across repetitions, raters, or items; validity is the degree to which the measure captures the intended construct. Reliability is necessary but not sufficient for validity.

Classical test theory: observed score = true score + error (X = T + E); reliability = true-score variance divided by observed-score variance.

Pearson correlation r ranges from −1 to +1; squaring it gives r², the proportion of variance in one variable statistically explained by the other.

Sensitivity = TP / (TP + FN); specificity = TN / (TN + FP); positive predictive value = TP / (TP + FP) and falls sharply as base rate (prevalence) falls.

Standard error of the mean = σ / √n; the sampling distribution of the mean approaches normality as n grows, regardless of the population's shape (central limit theorem).

Sample variance uses n − 1 in the denominator (Bessel's correction); population variance uses N. The correction removes the systematic downward bias of the sample estimate.

Necessary versus sufficient: A is necessary for B if B implies A; A is sufficient for B if A implies B. A condition can be one, both, or neither.

Causal inference requires association, temporal precedence (cause precedes effect), and elimination of plausible confounders; correlation alone establishes none of these.

Type I error = rejecting a true null hypothesis (probability α, conventionally 0.05); Type II error = failing to reject a false null hypothesis (probability β); power = 1 − β.

Design decision rule: random assignment of participants to conditions supports causal claims; random sampling from a population supports generalization. The two address different threats and are not interchangeable.

Total measurement error decomposes into systematic error (bias, which shifts results consistently in one direction) and random error (noise). Increasing n reduces random error but does not remove bias.

Statistical power increases with larger effect size, larger sample size, lower variability, and a more lenient α; power is computed as 1 − β.

A 95% confidence interval means that the procedure captures the true parameter in 95% of repeated samples; it is not a 95% probability that a fixed parameter lies inside one computed interval.

A p-value is the probability of data at least as extreme as observed, assuming the null hypothesis is true; it is not the probability that the null hypothesis is true.

When comparing event rates, report the absolute risk difference alongside relative risk: at low baseline risk, a large relative risk can correspond to a trivially small absolute change.

Blinding rule: single-blind controls participant expectancy; double-blind additionally controls assessor bias. Randomization, not blinding, is what controls selection and confounding.

Dimensional analysis check: both sides of any equation must carry identical units; a unit mismatch signals an algebra or conversion error before any numbers are computed.

Decision rule under uncertainty: choose the action maximizing expected value, computed as the sum over outcomes of (probability × payoff) for each available option.