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Could someone explain what this lingo means in regular English? Example sentences for context: "The single-partition hot deck based on a metric that conditions on $X$ has the problem that it fails to preserve associations between observed and imputed components of $Y$ for each pattern"

"Another approach that preserves associations between $p$ variables, which we refer to as the $p$-partition hot deck, is the create the donor pool for $Y_j$ using adjustment cells (or more generally, a metric) that conditions on $X$ and $(Y_1, \dotsc, Y_{j-1})$, for $j=2, \dotsc, p$, using the recipient's previously imputed values of $(Y_1,\dotsc, Y_{j-1})$, when matching donors to recipients".

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Given a particular set of predictors X and their particular values in the sample, you come up with explanation for Y using these predictors. If you're given a different set of predictors and the different sample of data, your explanation for Y will be different. Everything will be different: estimated parameters, their variances, inferences, hypothesis test results etc.

For instance, you have data on students X from a particular elementary school, maybe their ages, gender, parents' income etc. You're trying to explain their grades Y. So, you build a regression model $Y=X\beta+\varepsilon$, then use $\beta$ and their variances $\sigma^2_\beta$ to test hypotheses, maybe the impact of parents' income on grades or such.

So, in this example $\beta,\sigma^2_\beta$ and your hypothesis testing results are conditioned on X. If you plug a different sample $X'$, maybe from a different school in a different country, everything may change, your conclusions may change.

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