[rwilson4]

The author is using the technical definitions of confounders and covariates without sufficient explanation, and the technical definitions do not match the normal English definitions.

In English, a confounder is any factor that distorts an observation. (My dictionary defines it as throwing into confusion or disarray.)

In causal inference, a confounder is a factor that is correlated with both treatment and outcome. If the treatment is randomly assigned, by construction it is independent of all other factors. This, there can be no confounders.

Your example is about observed occurrences of imbalance, but the technical definition is about probabilities. Observed imbalances can still skew inference, but that causes high variance (or low precision). It doesn't cause bias (or affect accuracy).

Adjusting for observed imbalances can reduce variance, but in some circumstances can actually cause bias.

[usgroup]

Picking a specific definition of a word, expounding its consequences, and then referring to the colloquial usage of the word as a “myth” is just word-play as I said.

Many do think of confounders in an experimental context as just those effects which correlate with both outcome and treatment. The non-sequitur — barring a specific definition — is concluding that since nothing can correlate with random allocation, confounders are impossible by construction.

Why impossible? Because we are talking about the probability of allocation, not the actual allocation, and confounding does not refer to the result. We’d instead say there are imbalanced covariates, but that’s ok because randomisation converts “imbalance into error”. Yet, the covariates may be unknown, and without taking measurements prior to the treatment, how are we supposed to know whether the treatment itself or just membership of the treatment group explains the group differences?

Had we not tested the samples prior to treatment, the result would be what many would call “confounded” by the differences in the samples prior to treatment.

From https://en.wikipedia.org/wiki/Confounding#Decreasing_the_pot..., please note the use of the word:

The best available defense against the possibility of spurious results due to confounding is often to dispense with efforts at stratification and instead conduct a randomized study of a sufficiently large sample taken as a whole, such that all potential confounding variables (known and unknown) will be distributed by chance across all study groups and hence will be uncorrelated with the binary variable for inclusion/exclusion in any group.