# help identifying name of statistic, logistic regression

#### Alex S

##### New Member
Hello,

This is probably a very basic question, but I'm wanting to identify the name of a statistic. A professor I consulted with had written out the formula for me (attached) and I had thought this was a z-score, but she said at some point that it's not, it's another kind of statistic. She is now on sabbatical so I am no longer able to ask her. I am just wondering what I should refer to this as when writing about it.

For more background: I have a sample that I split into two separate non-overlapping groups (top 25th percentile and bottom 75th percentile), and then I conducted logistic regression on those two groups. I then used this formula in the picture to determine whether the odds ratios that resulted were significantly different from one another for each of the independent variables for the two groups.

In case the picture is not viewable, this is the formula written out to the best of my ability:

Stat = | (Beta1 - Beta2) / √ (SE1^2 + SE2^2) |

Any help greatly appreciated!

#### Attachments

• 894.9 KB Views: 5

#### Alex S

##### New Member
A Wald test, (also sometimes called a z-test).
Yes, that is what I had thought it was, but the professor said it wasn't a z-test, but was something else. (but she hadn't said what the something else was)

#### noetsi

##### No cake for spunky
formally they are not the same although in practice they work the same way (or are used the same way). A z test assumes a normal distribution I believe and a wald test uses a chi square distribution

#### obh

##### Well-Known Member
formally they are not the same although in practice they work the same way (or are used the same way). A z test assumes a normal distribution I believe and a wald test uses a chi-square distribution
The result is the same ...as chi-squared distribution is calculated based on the normal distribution.
The chi-squared random variable is the sum of "df" squared standard normal random variables. (of course the chi-squared is by default 2-tailed)

So it doesn't matter which distribution you use (and the appropriate statistic) you will get the same result.

In statistics, there are many names for the same...
I assume when you use a z-test over the logistic coefficient you may call it also called Wald test ...
Probably the first one that used the z-test for the logistic coefficient was Abraham Wald