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This simulation applet is designed to demonstrate the sampling distributions of the F statistic, Mean Square Error (MSE), and Mean Square Treatment (MSTR) for one-way Analysis of Variance (ANOVA). Users determine the mean and size for six factor levels as well as the overall standard deviation and number of samples under 'Change Settings'. By clicking 'Step', 'Walk', or 'Run', users can simulate drawing the specified number of samples. For each simulation, the applet displays boxplot-like graphs of the results (highlighting the true means in pink), and histograms of the MSTR, MSE, and F-statistic. At the conclusion, the observed/empirical sampling distributions (in blue) are compared against the theoretical null distributions (in pink). Users can also run multiple simulations at the same time by opening new windows of the applet; this allows users to compare the results of various simulations. Statistical background on ANOVA is given under the help menu.
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Date Of Record Creation 2007-07-24 16:17:00
Date Last Modified 2013-01-19 16:01:00
Date Of Record Release 2007-07-24 16:17:00
Email Address
Resource Type
Typical Learning Time 10 minutes
Author Name Stefan Michiels, Bert Raeymaekers.
Author Organization Katholieke Universiteit Leuven.
Comments This is an attractive simulation demonstration that can help students understand the one-way ANOVA model and how the distribution of the test statistic is affected by changes in the parameters of the model. Students (and perhaps instructors) will need to spend some effort in understanding what is happening visually.
Content Quality (Concerns) Because there are so many options and visual effects, this applet seems complicated and somewhat confusing. Students can get lost in the process of navigating the applet and will need guidance to understand what is happening. It could be challenging for the instructor to get the students engaged intellectually with the simulation. No information on ANOVA is given directly on the applet screen. The notation given towards the end of the statistical background is complicated and hard to decipher.
Content Quality (Strengths) The content of the applet is technically sound. The applet helps students see how group size, standard deviation, and factor mean affect the results of the ANOVA. The ability to add new windows allows for comparison of various ANOVA simulations, simultaneously. The statistical background found under the help menu is very helpful for understanding the ANOVA procedure and its components. This document is factually correct and helps users understand what is happening in the applet.
Ease of Use (Concerns) The applet instructions link under the help menu is dead, leaving no documentation, instructions, or methods of assessment. Although, instructors will be able to figure out the applet, students will need explanations of how to interact with the applet and how to interpret what they are seeing. Teachers will have to create their own materials to accompany the applet. The grey bars in the upper left graph are the locations of the means (they might be medians) from earlier repetitions. This gives the students an idea of the variation of the sample group means about the true group means, but this might be too much clutter and too much information. Using all four graphs simultaneously could be complicated for students.
Ease of Use (Strengths) The boxplot-like graph for the factor means is especially helpful for students who are learning ANOVA the first time. The graphics are well-designed and, with some explanation, easy to follow.
Potential Effectiveness (Concerns) This applet could be enhanced by having an option to change the equal-variance assumption or to violate the assumption of normality. Instructors could find it difficult to get their students to engage in the applet fully enough to follow what is going on. Hands-on simulations or a discussion about how the student would design the simulation would be useful before using the applet.
Potential Effectiveness (Strengths) This applet utilizes effective visual comparison by allowing users to see the effects of changing the standard deviation and factor means graphically. The upper left graphic displays the results of a single repetition of the simulation which helps students understand the basic assumptions of the one-way model (observations within groups are chosen randomly from a population with that group's fixed mean). By placing the observed distribution for F, MSE, and MSTR on the same graph as the theoretical distributions, students can easily see when the null hypothesis (that the factor means are equal) should be rejected. This applet will be useful for helping students understand the F-distribution more concretely.
Content Quality (Rating) 4
Ease of Use (Rating) 2
Potential Effectiveness (Rating) 4
Source Code Available On
Material Type
Statistical Topic
Intended User Role
Math Level

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