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 numerical means, categorical means and percentages in the StoryTeller, Cross Table, and the 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 (see attachment at the bottom of this article).

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.