# Comparing 3 treatments (bimodal results)

#### twentyseven

##### New Member
Hi everyone

I am new here and nearly a complete noob in statistics and my purpose is to learn as much as possible… so I will need a lot of help, so thanks in advance for your consideration.

Here I go with my first question:

• I have 3 different treatments (A, B, C).
• They are applied to patients that could be healthy or ill before they receive it.
• After receiving the treatments, they could remain in the same state they were before or they can change.
For instance:

Code:
|    ID    |    PRE-TREATMENT    |    TREATMENT    |    POST-TREATMENT    |
|    1    |    HEALTHY        |    A        |    HEALTHY        |
|    2    |    ILL            |    B        |    HEALTHY        |
|    3    |    ILL            |    A        |    ILL            |
|    4    |    HEALTHY        |    A        |    HEALTHY        |
|    5    |    HEALTHY        |    C        |    ILL            |
|    …    |    …            |    …        |    …            |
|    6    |    HEALTHY        |    B        |    HEALTHY        |
What kind of test would be adequate to determine if there are differences among treatments?

I was thinking about creating a variable EVOLUTION that could be:
• Improves.
• Remains the same.
• Gets worse.
And then just make a proportion test. But I don’t know if it would be valid and if there would be a more elegant method.

Thank you again!!!

#### fed2

##### Member
I'm going McNemar's test. = difference between #improves and #gets worse / divided by their sum.

#### twentyseven

##### New Member
I'm going McNemar's test. = difference between #improves and #gets worse / divided by their sum.
fed2, thank you for your help.

But as I said, I am a noob and I need some further explanation.

As far as I know, McNemar compares two groups of paired observations... but here we have three groups. And what is the rationale in calculating the difference between #improves and #get worse and to divide it by their sum? Do you mean to do it in an aggregate way?

Thank you. And, again, excuse my lack of knowledge.

#### Karabiner

##### TS Contributor
Is the baseline rate of illness nearly the same between treatments?

Maybe evolution is better conceptualized with 4 levels: ill/healthy healthy/healthy ill/ill healthy/ill.
You could perfom a global test of whether distribution of patients across of these 4 levels is
significantly different between treatments. If yes, you could further look into details.

With kind regards

Karabiner

#### fed2

##### Member
McNemar compares two groups of paired observations...
I believe Cochran Q is the test of equivalence across all 3 groups. mcnemars will be the 'post hoc' test. according to pass docs.
Maybe evolution is better conceptualized with 4 levels: ill/healthy healthy/healthy ill/ill healthy/ill.
You could perfom a global test of whether distribution of patients across of these 4 levels is
significantly different between treatments. If yes, you could further look into details.
thats the spirit of it. turns out the people that are healthy/healthy and ill/ill contribute nada to the test statistic, as I recall.

difference between #improves and #get worse and to divide it by their sum
thats just the formula, youd have to read about it, then you will probably know more than me on the matter.

Thank you. And, again, excuse my lack of knowledge.
my free advice is worth every penny, the real work is for you to do here.

#### joeb33050

##### Member
With 2 going in, Ill and Healthy; 3 treatments; 2 coming out, Ill and Healthy;;;;;;;;there are 12 outcomes. Why not make a bar graph, look at it, and a set of answers/conclusions should be clear. Why confuse the process with these exotic statistical tests? Turning a set of data into tables and graphs tells us what we want to know very often; and then applying statniques frequently doesn't clarify anything. Works for me, it'll work for you too.

#### fed2

##### Member
sorry not Cochran Q, that's for 3 correlated measures. Mcnemars will be for effect within each treatment. probably what Karabiner said is easiest.