SOCR EduMaterials AnalysisActivities ANOVA 2

Jump to: navigation, search

SOCR Analyses Example on Two-Way Analysis of Variance


The 2-Way Analysis of Variance (ANOVA) is a statistical technique for analyzing study designs with one numerical outcome (response/dependent) variable and two categorical explanatory (predictor/independent) variables. For instance, in a completely randomized design we want to compare the response/outcome of a test by various subject-demographics (e.g., age, gender, disease severity, etc.) Subjects are grouped by one demographic-factor and then randomly assigned one treatment-factor (hence two-way!)

The methodological details about the 2-Way ANOVA may be found at Wolfram Research, Wikipedia and elsewhere. A motivational example demonstrating the need and utilization of 2-Way designs and analyses can be found here.

2-way ANOVA is based on decomposing the variance of the response/dependent variable (total sum of squares) into within and between sum of squares. Sum of Squares between is then itself partitioned by intervention (blocking and interaction).

Typical hypotheses being tested in 2-way ANOVA are:

  • Presense of significant main effects (within each of the 2 factors);
  • Presense of an interaction between the two factors.


Go to the SOCR 2-Way ANOVA Applet. This really simple SOCR built-in example, EXAMPLE 1 uses a dataset from An Introduction to Computational Statistics: Regression Analyses" by Robert Jennrich, Prentice Hall, 1995 (Page 207). The data are about the time taken for coins to drop into different water fountain. Here, the dependent variable is time taken. And the two independent variables are: I for coin type, where "1" denotes for quarters and "2" for dimes; J for three different fountains. Our interest is to see if time is significantly related to these two independent factors. This example demonstrates a general two-way additive ANOVA model.

Here are the steps of the activities:

  • Click on "Anova Two Way" at the left panel's combo box.

SOCR AnalysisActivities AnovaTwoWay Chu 051707 Fig1.gif

SOCR AnalysisActivities AnovaTwoWay Chu 051707 Fig2.gif

On the right panel, first click on "EXAMPLE 1" and next click on "Data" to retreive the demonstrating example. The column X is time, the response variable, which is treated as a quantitative variable. The columns I and J are the independent variables.

SOCR AnalysisActivities AnovaTwoWay Chu 051707 Fig1B.gif

  • Click on the "Mapping" button to get to the "Mapping" panel. Click on "ADD" under Dependent to add X, and click on "ADD" under Independent to add I and J.

SOCR AnalysisActivities AnovaTwoWay Chu 051707 Fig3.gif

  • Next, click on "Calculate" to let the computer do the calculation. Then click on "Result" to see the results.

SOCR AnalysisActivities AnovaTwoWay Chu 051707 Fig3A.gif

  • Plots are available for vewing and checking regression dignostics. Click on "Graph" to see plots.

SOCR AnalysisActivities AnovaTwoWay Chu 051707 Fig4.gif

SOCR AnalysisActivities AnovaTwoWay Chu 051707 Fig5.gif

SOCR AnalysisActivities AnovaTwoWay Chu 051707 Fig6.gif

SOCR AnalysisActivities AnovaTwoWay Chu 051707 Fig7.gif

SOCR AnalysisActivities AnovaTwoWay Chu 051707 Fig8.gif

SOCR AnalysisActivities AnovaTwoWay Chu 051707 Fig9.gif

Technical Notes

SOCR vs. R and SAS 2-Way ANOVA

SOCR 2-Way ANOVA handles repeated measures and some of the default examples cover this situation (e.g., Example 2). There is a difference between the R-based and SAS-based approaches to repeated measures. In SOCR 2-Way ANOVA, we follow the SAS model and apply the dummy variable method described in Jennrich's book. Thus, the SOCR results format is the same as the output of SAS, in terms of degrees of freedom, sum of squares, etc. R's output is a little different from SAS's, and therefore it's not the same as the results reported by SOCR. In R, the order of the two factors (J and K) matters in the input. That is, if you put factor J first or K first, then the 2-way Anova results will be different. When the second factor is evaluated, the first one is considered fixed in R.

See also

Translate this page:

Uk flag.gif

De flag.gif

Es flag.gif

Fr flag.gif

It flag.gif

Pt flag.gif

Jp flag.gif

Bg flag.gif

الامارات العربية المتحدة
Ae flag.gif

Fi flag.gif

इस भाषा में
In flag.gif

No flag.png

Kr flag.gif

Cn flag.gif

Cn flag.gif

Ru flag.gif

Nl flag.gif

Gr flag.gif

Hr flag.gif

Česká republika
Cz flag.gif

Dk flag.gif

Pl flag.png

Ro flag.png

Se flag.gif