Linear Models

  • 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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  • This graduate level course offers an introduction into regression analysis. A researcher is often interested in using sample data to investigate relationships, with an ultimate goal of creating a model to predict a future value for some dependent variable. The process of finding this mathematical model that best fits the data involves regression analysis.  STAT 501 is an applied linear regression course that emphasizes data analysis and interpretation and is perfect for both students and teachers of statistics courses.

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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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  • When two variables are related, it is possible to predict a person's score on one variable from their score on the second variable with better than chance accuracy. This section describes how these predictions are made and what can be learned about the relationship between the variables by developing a prediction equation.

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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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  • R is a language and environment for statistical computing and graphics. It is a GNU project which is similar to the S language and environment which was developed at Bell Laboratories (formerly AT&T, now Lucent Technologies) by John Chambers and colleagues. R can be considered as a different implementation of S. There are some important differences, but much code written for S runs unaltered under R.

    R provides a wide variety of statistical (linear and nonlinear modelling, classical statistical tests, time-series analysis, classification, clustering, …) and graphical techniques, and is highly extensible. The S language is often the vehicle of choice for research in statistical methodology, and R provides an Open Source route to participation in that activity.

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