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Interpret each mechanism for a fixed missingness pattern $r$: the observed and missing response components are the coordinates selected by that pattern, and the covariates $X$ are assumed fully recorded.

For missing completely at random, missingness depends on neither response values nor covariates:For covariate-dependent missing completely at random, response observation may depend on $X$ but not on the response after conditioning on $X$:This is conditional independence $R\perp Y\mid X$ and can still produce a marginal association between response and missingness.

For covariate-dependent missing at random, the observation probability may use observed response components and covariates, but not the values missing under that pattern:For missing not at random, there remains dependence on $Y^m$ after conditioning on $Y^o,X$; the displayed simplification is not valid. For example, refusal could depend on the unreported response itself, even among individuals sharing all recorded covariates. These mechanisms concern the reason for nonobservation, not whether the incomplete records merely look irregular. Their distinction is not generally identifiable from the observed responses alone.

Assume that, conditional on the recorded embarrassment category, answering the item is independent of virginity status. Also assume that this category is assessed comparably for both groups and that both response strata have positive observation probabilities. This is covariate-dependent missing completely at random for the item response with embarrassment as the fully observed covariate; it supports MAR standardization over a fully observed covariate.

Use the responder probabilities $0.18$ and $0.08$ within strata, but the stratum sizes in the full group of responders plus item nonresponders: $300$ and $450$. This givesEquivalently, the estimated missing positive counts are $100(0.18)=18$ and $50(0.08)=4$, adding 22 to the 68 observed positives. The marginal estimate changes because the full group contains a larger proportion judged embarrassed. Merely copying the unstratified responder percentage would ignore that difference. The conditional independence assumption cannot be verified using the missing item responses.