Does an influence run through an intermediate step? (mediation)

In brief

A variable X presumably affects an outcome Y, and the effect runs (in part) through an intermediate step M, the mediator. Example: social support (X) raises self-efficacy (M), and that raises well-being (Y). Choose three number columns; X may also have exactly two values (e.g. 0/1). Statable estimates the indirect effect a·b with a bootstrap confidence interval. Covariates are not yet possible.

What Statable calculates

• Three regressions: path a (X → M), paths b and c′ (Y from X and M), total effect c (Y from X); per path B, standard error, β, t, p and 95% confidence interval.
• Indirect effect a·b, with c = c′ + a·b. The confidence interval comes from the bootstrap (5000 new samples, fixed seed: the same data give the same interval). The default is the percentile interval; BCa can be chosen under "More options" (see "Bootstrap intervals").
• Also the standardized indirect effect and the proportion a·b / c; the proportion is given only if it lies between 0 and 1.

Reading the result

• What matters is the bootstrap interval of a·b: if it excludes 0, this is statistical evidence for an indirect effect (it does not establish a cause).
• If the direct effect c′ is also significant and points in the same direction, the effect runs only in part through M; if it points in the opposite direction, this is called competitive mediation. Statable avoids the words "full" and "partial" mediation because they depend on sample size.
• The chart shows X → M → Y with B on each path; solid means p < .05, dashed means no clear evidence.

Requirements and limits

• At least 10 people with all three answers; from about 50 the bootstrap is reliable.
• Linear relationships, roughly equal spread of the residuals, independent people; outliers can strongly drive the indirect effect.
• The order X → M → Y is an assumption from theory that the data cannot test. With data from a single survey, mediation does not establish causality.

ab = 0.42, 95% bootstrap CI [0.27, 0.58]; a = 0.47, p < .001; b = 0.91, p < .001; c′ = 0.42, p = .002; c = 0.84, p < .001

For specialists

PSPP calculates the paths, Statable the indirect effect itself (percentile interval). Standardized: a·b · SD(X) / SD(Y). Checked against R (lm, boot, lavaan, mediation::mediate): the point estimate matches exactly, the bootstrap limits within random error.

Conditional and serial mediation (under "More options")

• Model 7 (PROCESS): a moderator W changes the path from X to M. Model 14: W changes the path from M to Y. Then the indirect effect depends on W. A fourth number column (or a column with two values) is chosen.
• What matters is the index of moderated mediation: if its bootstrap interval excludes zero, the indirect effect depends on W. The conditional indirect effects (at the 16th, 50th and 84th percentile of W by type 6, alternatively at the mean ± 1 SD or at your own values) only describe how large it is there. If they differ from zero one by one but the index does not, the data do not establish a moderation.
• Model 6: two intermediate steps in sequence (X → M1 → M2 → Y). Statable shows the three indirect effects, their sum and the three contrasts between the paths. The order of the intermediate steps is an assumption from theory; the reverse order fits the data equally well.
• There is no p for indirect effects, the index and the contrasts, only the bootstrap interval (B = 5000, fixed seed); all effects come from the same draws. The two factors of a product are centered at the mean; this does not change the effects but the single coefficients (they then hold at W = mean).
• Not included: further covariates, robust standard errors and further PROCESS models. This calculation is blocked with a case weight.

Typical examples

• Parental support → self-efficacy → exam performance: does the influence run through self-efficacy?
• Stress → sleep → concentration.