Dapresy supports a Z-test, a T-Test and a norm/population test. Below you can find all details regarding the T-Test.

A T-test can be applied on numeric variables when using the numeric mean calculation in the StoryTeller, Cross Table, and the StoryCreator. It can be applied categorical means in the StoryTeller and StoryCreator.

**T test formula: Means**

Note: all input values above are unweighted if the result is unweighted. If the result is weighted the x̅_{1}, x̅_{2} , s_{1} and s_{2} are weighted always but n_{1} and n_{2} are either weighted, unweighted or based on the effective base size.

**T test formula: Proportions**

This is the T-Test formula applied to the proportions:

Note: all input values above are unweighted if the result is unweighted. If the result is weighted the n_{1} and n_{2} in the T-value formula are either weighted, unweighted or based on the effective base size.

**Standard deviation formula**

Standard deviation formula used when result is unweighted:

Standard deviation formula used when result is weighted:

**Critical value **The critical values used when determining if the result is significant or not is based on the Degrees of freedoms which is calculated as below.

Note, n_{1} and n_{2} are always the unweighted base sizes, even if the result is weighted.

If degrees of freedom > 1500 the following critical values are used:

- Confidence Interval 90% = 1.64485362695147
- Confidence Interval 95% = 1.95996398454005
- Confidence Interval 99% = 2.57582930354890

If degrees of freedom ≤ 1500 the “critical value” table is referenced.

All input values in the T-test formula are unweighted if the result is unweighted, if the result is weighted the x̅_{1}, x̅_{2} , s_{1} and s_{2} are weighted always but base sizes (n_{1} and n_{2}) are either weighted, unweighted or based on the effective base size.

*Here we see the base size in the formula which can be either weighted, unweighted or the effective base size.*

Which base size to be used is specified by the user when setting up a chart/table.

Note: when applying a Z test on categorical variables you choose between the following base sizes to be used in the formula when result is weighted: Weighted, Weighted - effective base, Unweighted - Option A, Unweighted - Option B. The Unweighted - Option B in the Z test is the same as the Unweighted option in the T-test. The Unweighted Option A is not available when applying a T-test on numeric means.