# ANCOVA Test

An ANCOVA Test is a statistical hypothesis test based on a regressed ANCOVA model (produced by ANCOVA regression).

**Context:**- It can be used for Continuous Outcome Experiments, especially Non-Normal Continuous Outcome Experiments.
- It can be suited for three or more groups.
- It can cope with the existence of other Continuous Explanatory Variable that also has an effect on the Continuous Experiment Outcome.
- It can (typically) assume that
- The Residual Error Terms are Normally Distributed.
- The Error Variances are equal for different Treatment Classes.
- The Slopes of the different Regression Lines are equal.
- The Regression Relationship between the Dependent Variable and Concomitant Variables are Linear Relationship.
- The Error Terms are Uncorrelated.

**Counter-Example(s):****See:**ANCOVA Algorithm, One-Way ANCOVA, Two-Way ANCOVA.

## References

### 2005

- (Vickers, 2005) ⇒ Andrew J Vickers. (2005). “Parametric versus Non-parametric Statistics in the Analysis of Randomized Trials with Non-normally Distributed Data." BioMed Central Ltd. doi:10.1186/1471-2288-5-35
- QUOTE: It has generally been argued that parametric statistics should not be applied to data with non-normal distributions. Empirical research has demonstrated that Mann-Whitney generally has greater power than the t-test unless data are sampled from the normal. In the case of randomized trials, we are typically interested in how an endpoint, such as blood pressure or pain, changes following treatment. … Change between skewed baseline and post-treatment data tended towards a normal distribution. ANCOVA was generally superior to Mann-Whitney in most situations, especially where log-transformed data were entered into the model. The estimate of the treatment effect from ANCOVA was not importantly biased.

### 2004

- http://people.uncw.edu/pricej/teaching/statistics/ancova.htm
- This is a multivariate means test. It is just like the ANOVA you learned in the last section. But it enables you to add a control variable. Used when:
- DV = continuous.
- IV = categorical with 2 or more categories (nominal or ordinal)
- CV = continuous.

- You write the same hypotheses as with ANOVA, do the test the same way, and interpret the results the same way.
- Null: There is no relationship between the IV and the DV, controlling for the CV. The means are equal. Mean 1 = mean 2 = mean 3 ..... F = 0.
- Research: There is a relationship between the IV and the DV, controlling for the CV. The means are not equal. Mean 1 ≠ mean 2 ≠ mean 3 .... F ≠ 0.

- This is a multivariate means test. It is just like the ANOVA you learned in the last section. But it enables you to add a control variable. Used when: