# Student t-test

The **student t-test** is an analysis of variance that is found in many radiology studies.

To use the test on the data, the data must:

- be a comparison of only two groups
- must not be "matched data" (e.g. before and after results for the same group)
- must be from a normally distributed population
- must be continuous data (e.g. interval or ratio data)

The sample groups in a student t test are both drawn randomly from the same population. An intervention is performed on one group and the other is a control. The researcher then looks for a difference between the groups (a difference in their mean values). The problem with this (and the reason for the test) is that he or she doesn't know what the population mean or standard deviation is.

The difference between the groups is the difference in their means:

###### |(mean of group 1 - mean of group 2)|

The standard error of each group is added together to get the standard error of the difference between the groups:

###### SE_{d} = **√**(s_{12}/n_{1} + **s**_{22}**/****n**_{2})

So the t-score becomes:

###### t = **|(mean of group 1 - mean of group 2)| / √****(s**_{12}**/****n**_{1}** + ****s**_{22}**/****n**_{2}**)**

There's only one wrinkle, before you can determine if your result is statistically significant, you need to determine how many degrees of freedom you are using (which is n_{1} + n_{2} - 2).

There are many computer programs that will automate the above steps for you and provide you with a t-score for your data.

#### Other statistical options

- if the sample groups are unequal, the t-test can still be performed, but the standard errors are weighted by their sample sizes
- if the data is matched, consider a paired t-test
- if testing more than two groups consider a one-way ANOVA
- for low n data from a non-normal distribution, consider a nonparametric test

#### Related articles

##### Research

- clinical trials
- descriptive studies
- statistics
- concepts
- analyses of variance
- regression
- nonparametric statistics
- bias