# [R-meta] Output of clubSandwich::Wald_test(...,tidy=TRUE)

James Pustejovsky jepu@to @end|ng |rom gm@||@com
Sun Jan 9 22:23:08 CET 2022

```Tim,

Wald_test() is built for doing multiple-contrast hypothesis tests
(i.e., F-tests) rather than only t-tests, which constrained several of
the design choices I made in writing it. To your specific questions:

1. Several of the small-sample corrections (HTA, HTB, and HTZ)
available in Wald_test() are based on using Hotelling's T-squared
distribution as an approximate reference distribution. Hotelling's
T-squared is a multiple of an F distribution, i.e., if HT follows a
Hotelling's T-squared distribution with df1 and df2 degrees of
freedom, then
delta * HT ~ F(df1, df2)
so delta is the constant used to transform the HT statistic into an F
statistic. For single-contrast tests (df1 = 1), then delta = 1. For
multiple-contrast tests, delta will be some number smaller than 1.

2. The reason the coefficient estimates don't show in the output is
that (as noted above), Wald_test is built for multiple-contrast tests,
where there is not one single estimate relevant to the test statistic.

3. Currently, there is not an automatic way to compute confidence
intervals for pairwise contrasts. Probably the easiest thing to do for
the moment is re-fit the model using a difference reference level so
that one of the model coefficients corresponds to the contrast of
interest. Then you can use conf_int() to get confidence intervals.

It sounds like you're using Wald_test() to do pairwise contrasts and
would like to put confidence intervals on those contrasts. I think it
would be fairly straight-forward to add this functionality to
conf_int(). I'll look into it for a future release of clubSandwich.

James

On Sat, Dec 25, 2021 at 9:55 AM Timothy MacKenzie <fswfswt using gmail.com> wrote:
>
> Dear Colleagues,
>
> I'm new to clubSandwich's Wald_test(). I have three questions about
> the output (none of which are documented).
>
> First, when I convert the output to `as.data.frame()`, a new column
> called `delta` consisting of 1s shows in the output, what is that?
>
> Second, is there a reason the estimates (say for hypothesis A - B)
> don't show in the output (other packages always do that)?
>
> Third, is there a way to add the CIs for the estimates (say for
> hypothesis A - B) to the output (other packages always do that)?
>
> Thank you for your help,
> Tim M
>
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```