# Student t-test

The t-test tests if there is a significant difference in Mean between two data sets (2 sample t-test) or one data set and a specific value (one sample t-test). The t-test also called "student's t-test" and follows the t distribution. This distribution is based on the normal distribution and whit a high sample size the shape is the same.

## 1 sample t-test

If Diff mean is selected and one of the comparing column contains 1 value the 1 sample t-test is calculated. To calculate the if there is a significant difference in Mean between a data-set and a Hypothesized value. ### Colors of the cells

• Red
Data-set is not normally distributed
• Green
No significant difference
• Yellow
Significant difference
• Orange
Sample size to small

### Formula With the t value and the degrees of freedom the program calculate p value.

### Sample size

The result is the minimum sample size of the data-set.

#### not equal #### bigger smaller ### Example 1 sample t-test (not equal)

To use the 1 sample t-test test first unselect "non normal distributed" when the box is selected the 1 sample Wilcoxon median test is calculated. Then select Diff mean.
• E is significant not equal with the data-set A and the sample size is big enough (Row t-test p <0.05). Data file

## 2 sample t-test

If Diff mean is selected the 2 sample t-test is calculated between this column, and the comparing column, if this column and the comparing column contains more than 1 value. To calculate if there is a significant difference in Mean between the two data-sets. ### Colors of the cells

• Red
Data-set is not normally distributed
• Green
No significant difference
• Yellow
Significant difference
• Orange
Sample size to small

### Formula Calculating t value #### Formula Calculating the amount of degrees of freedom With the t value and the degrees of freedom the program can interpolate the p value out of the t table.

### Sample size is the biggest one of the two comparing data sets. The result is the minimum sample size for both data sets.

#### not equal #### bigger smaller ### Example 2 sample t-test (not equal)

To use the 2 sample t-test test first unselect "non normal distributed" when the box is selected the 2 sample Mann-Whitney median test is calculated. Then select Diff mean.
• The difference between data set A and B is not significant and the sample size is to small (Row t-test p >0.05).
• The difference between data set A and C is significant and the sample size is big enough (Row t-test p <0.05).
• The difference between data set A and D is not significant and the sample size is big enough (Row t-test p >0.05). Data file

## Paired t test

The paired t test is a modified version of the 1 sample t test. To conduct a Paired t-test subtract the two comparing data stets and run a 1 sample t test on this resulting data set. By comparing this data set with a column with as only input 0.

### Example

To conduct a Paired t-test between data-set A and B First subtract the difference between the columns and store the data in Column C. Then compare the column C with the comparing value in this case 0. Data file
In this example the difference between A and B is not significant difference with 0 and the sample size is to small for this difference.

## Legend

n = Amount of smamples
s = STDEV = Mean = Hypothesized value = Mean difference between to data sets