Heteroscedastic T-test and Homoscedastic T-test

Return the P-value for the hypothesis test. These two functions are used to determine the level of variance between the means of paired samples, assuming both samples have different arguments. For example, they may be used when a given group is to be tested before and after an experiment.

Decision	Reality: H0 is correct	Reality: H1 is correct
Accept H0	No problem	Type 1 error
Reject H0	Type 2 error	No problem

Definition

P-value is a probability of making a Type 2 error.

HeteroscedasticTTest or HomoscedasticTTest returns the p-value for the hypothesis test in the following form:

• For H0:

  

• For H1:

  

  

  

  

Syntax

HeteroscedasticTTest or HomoscedasticTTest <Hypothesis type, offset> (Argument1, Argument2)

Usage Notes

Heteroscedastic t-tests are based on the assumption that variances between two sample data ranges are unequal [σ²(Argument1) ¹ σ²(Argument2)].

Homoscedastic t-tests are based on the assumption that variances between two sample data ranges are equal [σ²(Argument1) = σ²(Argument2)].

The following conditions are invalid:

• Argument1 and Argument2 have a different number of data points, and Hypothesis type = 1 (paired).
• Offset or Hypothesis type is nonnumeric.

Example

For an example using both Heteroscedastic T-test and Homoscedastic T-test, see Hypothesis Testing example.