# How to Calculate ANCOVA

Save

Analysis of covariance (ANCOVA) is a more sophisticated form of analysis of variance. It accounts for a shared variable between populations that may be explaining variation. For example, three groups may receive three treatments. Variations between group survivals may be driven by age differences; therefore, controlling for the effect of age by including it as a variable could improve the model's explanatory power.

### Things You'll Need

• ANCOVA Formulas
• Statistical Software
• Statistical Calculator

## Graphical Explanation

• Determine the independent and dependent variables, including the covariate.
In the above example, the two dependent variables are the covariate, age and which treatment the group received. The covariate should be continuous. Beyond avoiding empty cells, the benefit of this will become clear in the following steps.

• Determine the linear regression for each group. In our example, age is an independent variable, survival time is an independent variable and each group has its own line of regression. Age has therefore been accounted for.

• Reject the null hypothesis (that the treatments are the same, i.e., that the treatment coefficient is zero) if the difference between slopes is statistically significant.

• Determine whether the intercepts are the same if the slopes were not found to be statistically different.

• Reject the null hypothesis if the intercepts are significantly different. If the three lines of regression have the same slope but their intercepts are significantly different, then their parallel nature means they won't meet anywhere and the treatments are different.

## Tips & Warnings

• ANCOVA is a blend of discrete (i.e., categorical) and continuous variables. In the example above, age is the continuous variable and whether one is in a group or not is a (binary) discrete variable. SAS handles such regression problems easily, sidestepping the above complication.
• If bias can be removed by better randomizing the populations, this would be preferable to compensating for such bias mathematically. In the above example, age should be distributed randomly before the experiment is begun, if possible.
• The assumptions of the ANCOVA model must be met by the data to a significant extent for the model's predictions to be valid. These assumptions, as in ANOVA (analysis of variance), are that the variance of the errors are not a function of the independent variables, that the errors are normally distributed and that the relation between the independent and dependent variables is linear.
• Two-way ANOVA is more appropriate if the covariate (time, in the above example) is categorical/discrete, thus avoiding the problem of empty cells and therefore a need for more test subjects.

## References

Promoted By Zergnet

## Resources

### You May Also Like

• How to Calculate ANOVA on a Table

The type of statistical test used to analyze the results from designs with one independent variable and more than two levels or...

• How to Perform an Analysis of Variance in SPSS

How to Calculate ANCOVA. Analysis of covariance (ANCOVA) is a more sophisticated form of analysis of variance.

• Definition of Control Variable

SAS Code for ANCOVA: Intuitive Explanation; Richard Suen: Introduction to Optimal Control Theory; US Dept. of Justice Glossary; Resources. Statistics.com: Statistical Glossary;

• How to Interpret an SPSS ANOVA Output

Statistical Package for the Social Sciences (SPSS) is a program for analyzing data collected by researchers in the social sciences. An ANOVA...

• How to Calculate a One-Way ANOVA Test on a TI-84

A One-Way ANOVA, or analysis of variance, is a test used primarily in market research studies to compare the means of a...

• How to Understand Anova

How to Write a Results Statement for a T-Test or an ANOVA. Recap the results in easy-to-understand language.

• How to Calculate Variance

How to Calculate Variance With a Calculator. Variance is a term in statistics used to measure how much variation there is in...

• How to Use Excel for ANOVA

Statistics classes teach the Analysis of Variance (ANOVA) as a type of test to determine statistical correlation. Normally statistics used specialized software...

• How to Calculate the Root MSE in ANOVA

In statistics, the analysis of variance (ANOVA) is a way of analyzing different groups of data together to see if they are...

• How to Calculate Variance Analysis

Management accounting helps top leadership analyze operating expenses. accounting calculator over the hundred dollar bank notes ... Analysis of variance, ...

• How to Interpret Excel ANOVA

ANOVA stands for analysis of variance. The two-way with replication ANOVA test examines data from repeated trials during which both "factors" and...

• How to Adjust for Confounding Variables Using SPSS

Researchers control for confounding variables by using an ANCOVA (Analysis of Covariance). Other People ... (for example, "Crime" and "Level of Violence")...

• How to Calculate Unexplained Variance

Unexplained variance is a term used in analysis of variance (ANOVA). ANOVA is a statistical method of comparing the means of different...
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}