Normality testing in binary variables (0/1)

[Maria Majeed]

Hello
I would like to know what would be the appropriate test/method to check the normality of a binary outcome variable? other than Shapiro-Wilk and Shapiro-Francia tests for normality (as histogram gives only two bars)
Secondly, Logistic regression does not require the distribution of the outcome variable to be normal, that is my understanding if I am mistaken please enlighten me.
If the above statement is right then we do not need to check normality (via swilk or any other test for a binary outcome)?

Thank you very much

[Maarten Buis]

There is no need to test for normality, as we already know before we do any testing that a binary variable just cannot be normal.

[Nick Cox]

The distribution of a binary variable consists of two spikes, in principle, and in practice, so long as both values are present in data

There is no sense in which it is, or can be, normally distributed.

Logistic regression plain sense requires an outcome that is binary. As you say, the implication is that such an outcome is not required to be normally distributed, and indeed that would be impossible, as said. Normality of outcome is not even an assumption, or an ideal condition, for linear regression.

[Maria Majeed]

Thank you Maarten Buis thanks for the confirmation, appreciate you both Nick Cox