# N needed comparing groups in linear regression with many covariates-do I have to few?

#### kristian

##### New Member
I have two easy, but for me at this point rather devastating, questions I was hoping for one kind hearted or bright individual,or two, to reply on.

I'm doing a study with data from a national representative population study. The design is cross-sectional. I've run into serious troubles with my data, and am doubting if I will be able to complete my thesis with a satisfactory level of quality.

The sample in total consists of over 4000 individulas. But after isolationg a group of individiuals which my research question related to, and exluding observations with missing data, I'm left with only about 240 individuals. The thought of how low this number is makes me shake at this point already, but it gets worse.

Becuase I actually want to compare three subgroups of these 240 individuals, and one of them (the smallest) has only 17 individuals. (Life satisfaction is the outcome.)

In addition i want to control for confounding variables, age, sex, marital status, eduaction and maybe level of physical functioning. How much does my data allow me to? I didn't ever think I would have to worry about this, as my original sample was so large, and noe I'm stuck with this rotten piece of material, and it makes me sick to the bone.

I have two questions I was hoping for a kind hearted individual or two to reply on:

1. Does linear regression allow me two compare the three groups when one group has only 17 individuals? I dummy coded the groups before i implemented them into the regression analysis. Am i right in that it is the t-test assumptions that applies here, and that the smallest group is too small for comparison, since it has only 17 individuals which is less than 30?

2. Do I have to worry about how many coviartes i include in the adjusted analysis when N is so small

Any help, or attempt to help, is highly appreciated!

#### Karabiner

##### TS Contributor
Re: N needed comparing groups in linear regression with many covariates-do I have to

1. Does linear regression allow me two compare the three groups when one group has only 17 individuals?
Yes. Or you could use analysis of covariance, with group as factor
and the several covariates.
Am i right in that it is the t-test assumptions that applies here, and that the smallest group is too small for comparison, since it has only 17 individuals which is less than 30?
There is no assumption that both groups have to be > 30 in a t-test.

Do I have to worry about how many coviartes i include in the adjusted analysis when N is so small
Many people hate rules of thumb, but if you have at least
20 observations per predictor, then IMHO you should not be
worried too much.

With kind regards

K.

#### kristian

##### New Member
Re: N needed comparing groups in linear regression with many covariates-do I have to

Thank you.

There is no assumption that both groups have to be > 30 in a t-test.
K.
I was thinking about the central limit theorem. Since I have dummy coded the groups, I am comparing this group with fewer than 30 people in it with the other two. In the regression output the statistic I get out is a t-value. Therefore I ask if I can rely on this statistic when this one group has less than 30 people in it? Do you know?

Many people hate rules of thumb, but if you have at least
20 observations per predictor, then IMHO you should not be
worried too much.
K.
I'm really confused about this. Does it mean that i should devide my total number of included people in the analysis with number of predictors? E.g. I have 240 individuals included. Divided by e.g. 6 predictors, it gives me 40. Does this mean that i have 40 "observations per predictor"?

Appreciate the help!