# What Test to Use to Compare Groups

#### nmverma

##### New Member
I'm looking through some data that I have collected from my patients over the past year and wanted to know what Statistical Test to use to see if a certain drug I have been giving my patients (different patients received different doses based on pain relief) affected how long it took their heart to contract. I've split my patients in two groups, one group that received the drug (various doses) and a control group that did not receive the drug. With regards to the statistics:

1. What test do I use to see if there is a difference in the average Age, Sex, and weight between these two groups?
2. What test do I use to see if there is a difference in the average time it takes the heart to contract between the two groups (those that got the drug and didn't get the drug)?

I haven't taken a course in statistics for almost 20 years and was curious about this subject, not sure the difference of using the t-test, ANOVA test, or other tests with regards to this subject.

#### nmverma

##### New Member
The group that I gave the drug is around 40-50 patients and the group that didn't receive the drug is around 30 patients. In the group that got the drug, the dosage differed.

#### CB

##### Super Moderator
From what you're saying it sounds like it may be best not to treat this as a question of comparing groups. Instead you could treat dose size as a continuous predictor, and time to contract as a continuous response variable. You could add sex, weight, and age as control variables if you are concerned that these variables differ across the groups. A multiple regression approach could work here. The primary assumptions are that the errors (i.e. the differences between observations' value on the dependent variable and the values predicted by the true regression model) are homoscedastic, independent, normally distributed, and have mean zero for any combination of value on the predictor variables (i.e. that you've correctly specified the shape of the relationship).

#### nmverma

##### New Member
1, The first question I wanted to answer was if certain variables (sex, weight, and age) were similar between these two groups. If they were similar, I wanted to see if the average time to contract differed. I agree with you, I should also look at the affect of dose with time to contract but I think I'll have to use other medications that the patients are on as control variables since they may differ across groups. For the first two comparisons, what tests do you recommend?

#### CB

##### Super Moderator
1, The first question I wanted to answer was if certain variables (sex, weight, and age) were similar between these two groups.
If you are interested in whether they are similar, the best thing is simply to look at the sample means. You could run an independent samples t-test to formally compare the means, but this test tests a null hypothesis that the two samples are drawn from populations with exactly equal means, which actually doesn't sound like a hypothesis you're interested in. The t-test is more "objective" than a subjective evaluation of the similarity of the means, but in my humble opinion a subjective answer to the right question is better than an objective answer to the wrong one!

#### nmverma

##### New Member
I looked at the sample meand and sd, I just wanted to confirm that they were similar (along with weight), I'll run an independent t-test to compare that. With regards to the difference between these groups in time to contract, would I also use a t-test and then use a regression analysis to compare dosage vs change in time to contract?

#### CB

##### Super Moderator
I just wanted to confirm that they were similar (along with weight), I'll run an independent t-test to compare that.
Like I just said, the t-test does not test whether the sample means are similar.

With regards to the difference between these groups in time to contract, would I also use a t-test and then use a regression analysis to compare dosage vs change in time to contract?
You could yes.

#### nmverma

##### New Member
Thanks for the help. When people do compare the means of values like age, and weight and confirm with a p-value that there is no difference, what test are they running?

#### CB

##### Super Moderator
When people do compare the means of values like age, and weight and confirm with a p-value that there is no difference, what test are they running?
There is no test that does this (or at least not one using p values). A non-significant p value does not confirm no difference, it only means that there isn't enough evidence to reject a null hypothesis of equal means. This could be because the means are exactly equal in the population, or it could be because there is a difference but the sample size is too small for the difference to be detected.

#### Karabiner

##### TS Contributor
I agree with CowboyBear that one cannot confirm equivalence
of the groups with regard to age etc. by using a test of significance.
And if the allocation of patients was not by randomization, it
is almost certain that the populations differ to some degree.

But I wouldn't fnd the idea of a significance test too bad, since
statistical power with n=70 looks quite reasonable. Personally
I would consider both approaches, first comparing both groups
using Chi² (sex) and t-test (age, weight, time to contraction)
(or, alternatively, U-test instead of t-test), then performing a
regression with sex (0/1), age, weight, and dosage as predictors
and time to contraction as dependent variable.

With kind regards

K.