# I'm Confused Between Independent T-Test, Mann-Whitney And Chi Square Test?

#### plethoraldork

##### New Member
hello everyone, i need your help regarding these statistical tests since i'm not really big on stats. i want to know if there are any significant difference between the two groups in my study. i'm confused which statistical treatment i will be using.
here's a little background on my study. i grouped the respondents in my study into two groups. respondents with successful outcome and respondents with unsuccessful outcome. i have several independent variables in my study which include: age, gender, place of residence, marital status, income, employment status, substance use and co-morbidities. i want to know if there are significant difference between respondents with successful outcome and respondents with unsuccessful outcome with regards to the variables listed or if any of the variables can affect the outcome of the respodents.
age and income are the only continuous variables in my study while the rest are categorical variables.

which among these statistical treatment is better to analyze my data?

#### Karabiner

##### TS Contributor
t-test is for the comparison of 2 groups with regard to an interval scaled measure (total sample size should preferably be > 30). Mann-Whitney is for the comparison of 2 groups regarding ordinal/ranked data, or interval data which have been transformed into ranks (something which usually the software does for the user). Chi2 can be used for comparison of 2 groups regarding a categorical variable. So you have to figure out first which scale level (interval, ordinal, categorical) your respective variables have.

With kind regards

k.

#### plethoraldork

##### New Member
t-test is for the comparison of 2 groups with regard to an interval scaled measure (total sample size should preferably be > 30). Mann-Whitney is for the comparison of 2 groups regarding ordinal/ranked data, or interval data which have been transformed into ranks (something which usually the software does for the user). Chi2 can be used for comparison of 2 groups regarding a categorical variable. So you have to figure out first which scale level (interval, ordinal, categorical) your respective variables have.

With kind regards

k.

thank you very much. so i have to use t-test for my continuous variables and chi square for my categorical variables?

#### GretaGarbo

##### Human
t-test is for the comparison of 2 groups with regard to an interval scaled measure (total sample size should preferably be > 30).
The t-test is a small sample test, so it is OK to use even if the sample size is as small as n=4 as in the original publication by "Student" in 1908. It is valid provided that it is known that the measured variable is normally distributed with constant variance.

i want to know if there are significant difference between respondents with successful outcome and respondents with unsuccessful outcome with regards to the variables listed
It seems to me that the original poster need to use logistic regression with successful or unsuccessful outcome as dependent variable and age, gender, place of residence as explanatory variables.

#### Karabiner

##### TS Contributor
The t-test is a small sample test, so it is OK to use even if the sample size is as small as n=4 as in the original publication by "Student" in 1908. It is valid provided that it is known that the measured variable is normally distributed with constant variance.
Agreed. Because of this I wrote "preferably", not "necessarily". Unfortunately,
whether it is safe to assume that the underlying distributions are normal,
one often doesn't know. In my own domain of research (medicine, psychiatry,
psychology, sociology), one often can safely assume that they are markedly
non-normal.

It seems to me that the original poster need to use logistic regression with successful or unsuccessful outcome as dependent variable and age, gender, place of residence as explanatory variables.
I supposed that since he doesn't want to build a model with multiple
predictors, the robust approach would well meet a beginner's needs.
BTW, is a simple logistic regression superior to t-test, U-test or Chi²
in terms of power? That could be a strong argument in favour of logistic
regression.

With kind regards

K.

#### GretaGarbo

##### Human
Agreed. Because of this I wrote "preferably", not "necessarily". Unfortunately,
whether it is safe to assume that the underlying distributions are normal,
one often doesn't know. In my own domain of research (medicine, psychiatry,
psychology, sociology), one often can safely assume that they are markedly
non-normal.
Agreed!
I am sorry if what I said sounds like nitpicking. But I just wanted to point out to beginner stats student that even when the sample size is small, and the underlying distribution is normal, then the test-statistic will be exactly t-distributed. So it is "allowed" to use the t-test even then. In contrast the logistic regression relies on large sample statistics. So when the sample is "large" the test statistic will be approximately chi-squared distributed. But we don't know how it works when the sample size is small.

I believe that when Karabiner says something it has a lot authority. I just don't want beginner student to believe that it is "not allowed" to use t-tests on small samples. But of course, the larger the sample the better.

I supposed that since he doesn't want to build a model with multiple
predictors, the robust approach would well meet a beginner's needs.
BTW, is a simple logistic regression superior to t-test, U-test or Chi²
in terms of power? That could be a strong argument in favour of logistic
regression.
Maybe we have a slight dis-agreement here. I don't think that it would be a "robust" method to use single variable methods, like Pearsons chi-squared test, when there really are several variables that have an influence. I think it can be quite sensitive, especially if there is multi-colinearity among the explanatory variables.

About power: Isn't the likelihood ratio test one often can see in 2x2 tables exactly the same a the Wald test one get in logistic regression?