sum of squares plays an important role in statistical models based on the normal distribution, like ANOVA.
Questions tagged [sums-of-squares]
193 questions
62
votes
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How to interpret type I, type II, and type III ANOVA and MANOVA?
My primary question is how to interpret the output (coefficients, F, P) when conducting a Type I (sequential) ANOVA?
My specific research problem is a bit more complex, so I will break my example into parts. First, if I am interested in the effect…
djhocking
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27
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7 answers
How does one do a Type-III SS ANOVA in R with contrast codes?
Please provide R code which allows one to conduct a between-subjects ANOVA with -3, -1, 1, 3 contrasts. I understand there is a debate regarding the appropriate Sum of Squares (SS) type for such an analysis. However, as the default type of SS used…
russellpierce
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26
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3 answers
Choice between Type-I, Type-II, or Type-III ANOVA
We have a dataset with three variables (dV: self-reported measure on scale 1-5, assumed to be metric; iV1: factor with 4 levels; iV2: factor with 8 levels). We are interested whether the dV differs in regard to both iVs and whether there is an…
phx
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25
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The order of variables in ANOVA matters, doesn't it?
Am I correct to understand that the order in which variables are specified in a multifactorial ANOVA makes a difference but that the order does not matter when doing a multiple linear regression?
So assuming an outcome such as measured blood loss y…
Farrel
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22
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What is the sum of squared t variates?
Let $t_i$ be drawn i.i.d from a Student t distribution with $n$ degrees of freedom, for moderately sized $n$ (say less than 100). Define
$$T = \sum_{1\le i \le k} t_i^2$$
Is $T$ distributed nearly as a chi-square with $k$ degrees of freedom? Is…
shabbychef
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18
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square things in statistics- generalized rationale
Why do you square things in stats? I have run across this a lot, in both data mining and statistics classes, but no one has ever been able to give me an answer. One specific example is when summing the deviation scores in statistics you have to…
Rilcon42
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Should I include an argument to request type-III sums of squares in ezANOVA?
I developed the ez package for R as a means to help folks transition from stats packages like SPSS to R. This is (hopefully) achieved by simplifying the specification of various flavours of ANOVA, and providing SPSS-like output (including effect…
Mike Lawrence
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15
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1 answer
Algebra of LDA. Fisher discrimination power of a variable and Linear Discriminant Analysis
Apparently,
the Fisher analysis aims at simultaneously maximising the
between-class separation, while minimising the within-class
dispersion. A useful measure of the discrimination power of a variable
is hence given by the diagonal quantity:…
category
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15
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Conflicting results of Type III sum of squares in ANOVA in SAS and R
I'm analyzing data from an unbalanced factorial experiment both with SAS and R. Both SAS and R provide similar Type I sum of squares but their Type III sum of squares are different from each other. Below are SAS and R codes and outputs.
DATA…
MYaseen208
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14
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3 answers
Why do we use a one-tailed test F-test in analysis of variance (ANOVA)?
Can you give the reason for using a one tailed test in the analysis of variance test?
Why do we use a one-tail test - the F-test - in ANOVA?
Cynderella
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14
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Distribution of sum of squares error for linear regression?
I know that distribution of sample variance
$$
\sum\frac{(X_i-\bar{X})^2}{\sigma^2}\sim \chi^2_{(n-1)}
$$
$$
\sum\frac{(X_i-\bar{X})^2}{n-1}\sim \frac{\sigma^2}{n-1}\chi^2_{(n-1)}
$$
It's from the fact that $(X-\bar{X})^2$ can be expressed in…
KH Kim
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12
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2 answers
Distribution of sum of squares of T-distributed random variables
I am looking at the distribution of the sum of squares of T-distributed random variables, with tail exponent $\alpha$. Where X is the r.v., the Fourier transform for $X^2$, $\mathscr{F}(t)$ gives me a solution for the square before the convolution…
Nero
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12
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Difference in reported p-values between lm and aov in R
What explains the differences in p-values in the following aov and lm calls ?
Is the difference only due to different types of sums-of-squares calculations…
Remi.b
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12
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2 answers
Collinearity between categorical variables
There's a lot about collinearity with respect to continuous predictors but not so much that I can find on categorical predictors. I have data of this type illustrated below.
The first factor is a genetic variable (allele count), the second factor…
Matt Albrecht
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12
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2 answers
Why is sum of squared residuals non-increasing when adding explanatory variable?
In my econometric textbook(Introductory Econometrics) covering OLS, the author write, "SSR must fall when another explanatory variable is added."
Why is it?
Eric Xu
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