Author: Will
Linear Mixed Models in SPSS
This tutorial includes the explanation of what a linear mixed model is, how to structure its statistical model, data example, as well as steps for linear mixed models in SPSS. Definition of Linear Mixed Models Linear mixed models (LMMs) are...
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Linear Regression and Orthogonal Projection
This tutorial explains why and how linear regression can be viewed as an orthogonal projection on 2 and 3-dimensional spaces. Projection with 2 Dimensions Suppose that both X0 and Y have 2 dimensions (e.g., 2 observations from 2 participants). It...
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Interaction in Linear Regression
This tutorial focuses on interaction between a categorial variable and a continuous variable in linear regression. Note that, in this tutorial, we limit the the categorical variable to be 2 levels. (For a categrocial variable with 3 levels, please refer...
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Dummy and Contrast Codings in Linear Regression (IV has 3 levels)
This tutorial explains the differences between dummy coding and contrast coding in linear regression using R code examples. It is worth pointing out that, this tutorial focuses on the categorical independent variable has 3 levels. Short Note Note that, in...
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Sample Variance Formula and Calculation by Hand
Sample variance is the measure of the variability in a given sample. A sample is a set of observations that are a subset of a population. Sample Variance Formula The following is the formula for sample variance. where, Data Example...
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Calculate Standard Deviation in Excel
STDEV(), STDEV.S(), and STDEV.P() can be used to calculate standard deviation in Excel. It depends on if you are calculating sample or population standard deviation. Sample Standard Deviation: Use either STDEV() or STDEV.S(). Population Standard Deviation: Use STDEV.P(). Example 1 The following...
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Conduct Paired Samples t-test in Excel
This tutorial shows detailed steps of how to do paired-sample t-test in Excel with a data example. Data Example The data table shown below has 3 columns, name, math, and English. We are going to compare if Math and English...
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How to Calculate Two-Factor ANOVA without Replication
ANOVA Two-Factor without Replication is used for a design of two factors (e.g., Factor A and Factor B) and only 1 observation in each cell. For instance, both Factor A and Factor B have two levels, leading to 4 cells...
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Difference between ANOVA Two-Factor with Replication and without Replication
You use ANOVA: Two-Factor without Replication when each cell only has 1 observation, but use Two-Factor with Replication when each cell has more than 1 observation. For instance, there are two factors, City and Chain Brand. Each has 2 levels,...
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Two-Way ANOVA: Formulas and Calculation by Hand
This tutorial will first show the formulas for Two-way ANOVA and then use an example to show how you can calculate two-way ANOVA by hand. The following depicts the conceptual framework of the variance breaking down for two-way ANOVA. Typically,...
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