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Quantitative ANOVA

  • A Cartoon to illustrate the idea of interaction (cell means) plots for a two factor ANOVA.  The cartoon was created in October 2018 by Larry Lesser from The University of Texas at El Paso.  

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  • Statistics is often taught as though the design of the data collection and the data cleaning have already been done in advance.  However, as most practicing statisticians quickly learn, typically problems that arise at the analysis stage, could have been avoided if the experimenter had consulted a statistician before the experiment was done and the data were conducted.  This course is created to provide an understanding of how experiments should be designed so that when the data are collected, these shortcomings are avoided.  Perfect for students and teachers wanting to learn/acquire materials for this topic.

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  • This is a graduate level course/collection of lessons in analysis of variance (ANOVA), including randomization and blocking, single and multiple factor designs, crossed and nested factors, quantitative and qualitative factors, random and fixed effects, split plot and repeated measures designs, crossover designs and analysis of covariance (ANCOVA). Perfect for students and teachers alike looking to learn/acquire materials on ANOVA.

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  • Analysis of variance (ANOVA) is used to test hypotheses about differences between two or more means. The t-test based on the standard error of the difference between two means can only be used to test differences between two means. When there are more than two means, it is possible to compare each mean with each other mean using t-tests. However, conducting multiple t-tests can lead to severe inflation of the Type I error rate. (Click here to see why) Analysis of variance can be used to test differences among several means for significance without increasing the Type I error rate. This chapter covers designs with between-subject variables. 

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  • When an experimenter is interested in the effects of two or more independent variables, it is usually more efficient to manipulate these variables in one experiment than to run a separate experiment for each variable. Moreover, only in experiments with more than one independent variable is it possible to test for interactions among variables.  Experimental designs in which every level of every variable is paired with every level of every other variable are called factorial designs. 

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  • Within-subject designs are designs in which one or more of the independent variables are within-subject variables. Within-subjects designs are often called repeated-measures designs since within-subjects variables always involve taking repeated measurements from each subject. Within-subject designs are extremely common in psychological and biomedical research.

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  • A collection of Java applets and simulations covering a range of topics (descriptive statistics, confidence intervals, regression, effect size, ANOVA, etc.).

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  • This site offers separate webpages about statistical topics relevant to those studying psychology such as research design, representing data with graphs, hypothesis testing, and many more elementary statistics concepts.  Homework problems are provided for each section.

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  • This app allows you to derive an approximation to the difference in Bayesian information criterion and to the probability of the null and the alternative hypothesis from the sum of squares obtained in an ANOVA analysis.

    Required input

    • Number of participants
    • Df ... degrees of freedom of the effect of interest
    • Whether the effect is between or within participants
    • SSEffect ... sum of squares of the effect of interest
    • SSError ... sum of squares of the error, for within-factors the by-subject error, associated with this effect
    • SSTotal ... total sum of squares, only required for within-participant designs when using effective sample size (strongly recommended, Nathoo & Masson, 2007)
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  • A song for use in helping students to recognize, in context, the idea of ANOVA as comparing variance between groups to variance within groups.  Music & Lyrics © 2016 by Monty Harper.  This song is part of an NSF-funded library of interactive songs that involved students creating responses to prompts that are then included in the lyrics (see www.causeweb.org/smiles for the interactive version of the song, a short reading covering the topic, and an assessment item).

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