# Relationship Test of Paired Data with one variable ordinal, other binomial

#### mavigozler

##### New Member
I want to find relationship between a "priority value" and "billable status."

The priority value is a numeric value that is an integer in the set of real numbers (can be negative, zero, or positive)

The billable status is basically a binomial: either billable or nonbillable.

The null hypothesis would be "priority value has no relationship to billable status."

The alternative hypothesis would be "priority value shows a clear relationship to billable status."

Here is the dataset, sorted ascending by priority (1st column). Clearly NB = nonbillable, B = billable

-143 NB
-45 NB
-45 NB
-38 NB
-21 NB
-21 NB
-21 NB
-17 NB
-17 NB
-12 NB
-11 B
-4 NB
-4 NB
0 B
0 B
0 B
0 NB
0 NB
0 NB
0 NB
0 B
7 B
10 B
17 B
21 B
21 NB
21 NB
34 B
34 NB

I was thinking a chi-square test could be done, but the other data is binomial. Looking elsewhere there was talk about "logistic regression," but I don't see how that figures.

Anyone want to suggest what I should look at?

#### GretaGarbo

##### Human
Yes, run logistic regression!

(The explanatory variable does not have to be categorical.)

This is a funny data set, because the p-value is equal to 0.0481. And therefore I believe that it is homework. Good luck!

#### mavigozler

##### New Member
Yes, run logistic regression!

(The explanatory variable does not have to be categorical.)

This is a funny data set, because the p-value is equal to 0.0481. And therefore I believe that it is homework. Good luck!
Well, thanks for the information.

But this is not homework: I'm a government analyst overseeing IT project performance of a contractor and making sure the contractor is not giving projects for which it is not reimbursed (NB) a lower priority than projects for which it is reimbursed (B). I have learned the priority value is the days to next deliverable due date, so a negative value is an overdue deliverable (and this the higher priority). It's been years since I learned statistics and I decided that this question deserves the proper statistical treatment.

That the data appears to be statistically significant by your calculation is eye-opening.

#### GretaGarbo

##### Human
From what you say it now seems more like the priority value is the dependent variable. (But I don't fully understand the situation)

You must look at the outlier (the "-143"). Is that a correct value that really should be there?

#### mavigozler

##### New Member
From what you say it now seems more like the priority value is the dependent variable. (But I don't fully understand the situation)

You most look at the outlier (the "-143"). Is that a correct value that really should be there?
This is in fact a project whose next deliverable is 143 days overdue, for whatever reason. I suppose I can calculate two probabilities, right, one with and one without that pair?