# **One-way ANOVA Demonstration

Tutorial on the ANOVA test in statistics and probability, with a description, formulas, example, and a calculator applet. This is part of the larger site Virtual Statistician at http://web.mst.edu/~psyworld/virtualstat.htm
Rating:
Author Name:
Richard Hall
Content Quality Concerns:
The assumptions underlying the procedure are not stated. The pages and calculator do not discuss what happens when the data set sizes change. The formulas given for the Sum Squares are not intuitive; therefore it will be difficult for students to understand the meaning of these statistics. In paragraph 5 of the description, the author states "analysis of variance and the F score it yields is a ratio of explained variance versus error." It does not explain that it is the ratio of the Mean Square Treatment (Between) and the Mean Square Error (Within). Students might not pick this up, unless they try to calculate F from what is given. Some terms are not defined. For instance, the formulas for Sum Squares and Mean Squares are given on the Steps page, but they are not discussed on the description page. Students will be able to calculate each one without knowing what it means. On the example page, the statistics M1, M2, and M3 are given in the calculations, but it is not stated that these are the means of the three groups. ***While a note at the top of the calculator page tells the user to be careful to press the calculator buttons in order, it is possible to press them out of order. If this happens, the results obtained are wrong. There are typographical errors throughout the tutorial. For instance, the second formula given on the steps page and the calculator page should be SS(among), not SS(total).
Content Quality Strengths:
This tutorial is a good, well written, and factually correct introduction to ANOVA. The discussion of ANOVA stresses the variance decomposition, and develops intuitive understanding of "Between" versus "Within" group variability. The example is fully worked out and easy to follow. The calculator is well-labeled with the appropriate steps.
Ease of Use Concerns:
While the description, steps, and example pages each have links to each other and to the calculator, the calculator page doesn't have a link to any of the other three. The formulas on the steps page and the calculator page are so small that the subscripts are hard to read. If the user enters fewer than eight data points in a set on the calculator page, the buttons for the sum of the data, the square of the sum, and the mean yield "NaN". Students cannot use the "Tab" key to go from one box to another in calculator because, on this page, "Tab" takes you to a completely different column. Users can type into boxes that are supposed to be populated by the calculator. ***While a note at the top of the calculator page tells the user to be careful to press the buttons in order, it is possible to press them out of order. If this happens, the results obtained are wrong.
Ease of Use Strengths:
The interface is easy to follow. Steps in sequence are labeled, and links are clearly marked. The text is easy to read, and the calculator has well labeled instructions making it easy to operate. A novice would have no problem using this resource. The information is provided all in one place. Spacing of the steps on the page reinforces the order in which to perform them.
Potential Effectiveness Concerns:
There is no flexibility with respect to the number of groups or the number of observations in each group because the calculator requires the user to have three sets of eight data points each. Unbalanced designs are not available. The fact that the user is led to press the calculator buttons in order does not require him or her to understand the steps or even to read the numbers obtained. The description page is several paragraphs of text. Often, students who encounter a lot of text on a web page tend to skip reading it and go directly to the applet, calculator, or chart. Because the formula given for calculating Sum Squares is not intuitive, students may have a hard time remembering it without the formula in front of them.
Potential Effectiveness Strengths:
The tutorial has a natural flow: discussion, then steps, then an example, then application (calculator). Formulas are displayed beside the computations. The calculator is set up as a table and has numbered buttons to lead the user through the process of performing an ANOVA calculation, which is helpful for remembering and computing the formula. The description is written in easy to understand terms and provides connections to other statistical topics.
Content Quality Rating:
4
Ease of Use Rating:
4
Potential Effectiveness Rating:
4
Source Code Available:
Source Code Available
Intended User Role:
Learner, Teacher
Material Type:
Resource Type:
Statistical Topic: