The Arrangement Dispute

Decompose total satisfaction variation into between-group and within-group components (ANOVA) to determine if relationship arrangement type genuinely matters.

Compute the F-statistic to formally assess whether the satisfaction differences across groups are statistically significant.

Apply the Markov and Chebyshev inequalities to establish credible bounds on client metrics for which only partial data is available.

Use Jensen's inequality to compute a bound on the expected value of a transformed engagement metric, given only the group's average engagement.