So as a reminder of what a standardized difference is in general.

So right now we're not thinking about waiting just

imagine we want to look on our raw data, for example.

Where we have treated subjects and control subjects.

Well what we would do to get a standardized difference is just take

the sample mean for the treated subjects.

And the sample mean for the control subjects, take the difference, and

then divide by what's essentially a pooled standard deviation.

So you could take the variance for

the treated subjects, the variance for the control subjects divided by 2 and

take the square root as an example, to get a pooled standard deviation.

So this would give us a standardized difference, so what's the standardized

difference in the mean and you would do this for each covariant.

So this X bar here, this sample mean is for a particular covariant and

we would do it for every covariant.

And also as a reminder, it's very common to just report absolute values.

So you might want to take the absolute value of it.

Standardized differences could be positive or negative.

But a lot of times people just report the absolute value.

Because we're mostly interested in the magnitude of the difference as opposed to

the direction of the difference.

Okay, so how do we obtain standardized differences after waiting?

Well it ends up being the same kind of idea where we are interested in a mean

difference divided by a pooled standard deviation.

Except here, it's just going to be weighted means and

then essentially a weighted pooled standard deviation.

So what we would do is we would stratify on treatment group.

And then for each covariate, separately for each covariate,

we would calculate a weighted mean and weighted variance.

And then we would put them together using the same kind of formula.

And so you could do essentially by hand, you have the weights,

the data, you could go ahead and calculate them.

Or there is a lot of software packages that were developed for

surveys that you could use.

So I mentioned this survey design package in R, for example.

So there's a lot of statistics software have options where you can

get weighted means and weighted variances and so on.

So once we can weight our data and

then get these standardized differences on the pseudo population.

And then of course, the goal is that hopefully these standardized differences

are low after we've waited.