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Questions tagged [sphericity]

Sphericity is an assumption of repeated measures ANOVA. It states that the variance of all pairwise differences is constant.

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How to get sphericity results with Anova() function from Car package [closed]

I have an unbalanced dataset. I want to run a mixed ANOVA (type III) with the Car package. My dataset has 3 factors: Day (10 levels, within-subject factor), Sex (2 levels, between-subject factor) and ...
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Is a correction for sphericity violation needed for post-hoc comparisons following repeated-measures ANOVA?

In a repeated-measures ANOVA, there is an assumption of sphericity, so that the variance of differences between groups is similar for all pairs of groups. A violation of this assumption can be ...
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In a repeated measures ANOVA, is the pairwise comparison result still valid if sphericity is not assumed?

For the pairwise comparison, the p value is less than 0.001. However, the p value for Mauchly's test of sphericity is also <0.001. I believe that SPSS automatically applies the Greenhouse-Geisser ...
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Does the sphericity assumption apply to linear mixed models?

I have recently been asked to check the sphericity of my data to confirm it meets the assumptions of the linear mixed models I have generated (using lmerTest in R). I have read conflicting information ...
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The test point’s standard deviation from the origin (ESL’s Exercise)

This is Ex.2.4 from The Elements of Statistical Learning. I don’t understand the sentence that I underline in the image. I know that $\sqrt{10}$ is approximately equal to 3.1, but I don’t know how to ...
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Why is the Treatments P-value halved after a Geisser-Greenhouse correction for sphericity

I have noticed that when Graphpad Prism does a sphericity correction using the Geisser-Greenhouse correction, it halves the P value for this source of variation (typically Treatments). For example, in ...
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Variance-Covariance Matrix (Sphericity): Valid?

I am completing a basic statistics exercise for a graduate-level ANOVA course (for psychology trainees). We've just started on repeated measures (i.e. within-subjects) designs, beginning with the ...
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What is the marginal probability distribution of the surface uniform sphere

I need to complete the following problem Let $~(X_1, X_2)~$ be a continuous random vector, with uniform density on the unit sphere $~\{(x_1,~ x_2,~ x_3) ~∈~ \mathbb R^3 ~:~ x_1^2 + x_2^2 + x_3^2 = 1\}...
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What does it mean "they differ in parameter space" regarding the compound symmetry and random intercept model?

I read discussions on how the random intercept model is not equivalent to the compound symmetry. I understand, that the CS model allows for a case, where the responses are more similar across subjects ...
dasivalana's user avatar
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Mauchly's test of sphericity result interpretation

How to interpret the following result from Mauchly's test conducted in R? Mauchly's test of sphericity Contrasts orthogonal to ~1 data: SSD matrix from lm(formula = Controls3 ~ 1) W = 0, p-value = ...
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Accuracy vs Precision: Can I use the Sphercity Assumption data in a meaningful way?

I understand that when conducting a repeated measures design with say one factor having three levels (Training: None, Standard, New Method), in the analysis you want the sphercity assumption to not be ...
Hubris555's user avatar
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What is the origin of the Winer's compound symmetry test of the variance-covariance matrix?

In his famous book, Winer (Statistical principles in experimental design 1971; reedited Winer, Brown, Michels, 1991, p. 517) introduced a test of compound symmetry. The test expands on the likelihood ...
Denis Cousineau's user avatar
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Reproducing this chi-square probability from published work

So i'm working on a Greenhouse-Geisser correction and i found this "John, Nagao & Sugiura’s test for sphericity" in this publication (https://www.utdallas.edu/~herve/abdi-GreenhouseGeisser2010-...
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estimating sphericity

I have $n$ independent samples from a $p$-dimensional multivariate normal distribution with mean 0 and covariance $\Sigma$. Optimally, the $p$ variables should uncorrelated and of equal variance ($\...
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Post-hoc tukey test after repeated measures ANOVA in R taking into account spherecity

I am trying to do some repeated measure anova in R. Consider the following data. ...
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Mixed-ANOVA Design - Assumption

1) In a Mixed-ANOVA design, with one-between subjects (2 levels) and one within-subjects test (2 levels), do we normally check the Levene's output to ensure that we are not violating the assumption of ...
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Sphericity: Is there an accepted graphical inspection technique?

I was wondering whether there is some accepted graphical way of reporting and inspecting sphericity, i.e. visualizing the pairwise differences and their variances (other than looking at the var-...
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How does sphericity violations affect RM-ANOVA results?

My current understanding is that sphericity violations inflate the F-value and therefore type I error. I'd like to know how exactly this manifests itself mathematically. To follow-up, why does ...
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Are there other alternatives to the Mauchly's sphericity test?

Are there other alternatives to the Mauchly's sphericity test? I am about to run a Repeated Measures ANOVA and a One-Way ANOVA and must perform a pre-requisite check on the dataset. I was wondering ...
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How to you calculate the Mauchly Test by hand

I am creating a web application that is supposed to perform a Mauchly Test but I cannot find hand written or worked examples anywhere. It is imperative that the answer must not provide examples using ...
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Is sphericity violated if my sample size is less than the repeated measurement count?

In SPSS, I find that the Mauchley's test does not provide any result if the sample size is less than the repeated measurement count. I have a sample size of 19 and a repeated measures of 22. My ...
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What does it mean to have sphericity established on a RM-ANOVA?

What does it mean to have sphericity established on a RM-ANOVA? How does it affect the explanatory variables?
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Mauchly Sphericity test conditions

Can a sphericity test be done without doing a RM-ANOVA? My objective is to test whether the variance of the pairwise differencces are equal (by sphericity I mean this:https://en.wikipedia.org/wiki/...
Toney Shields's user avatar
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Can I use RM-ANOVA with unbalanced within-subject design with sphericity violated?

I have data from an EEG experiment. Originally, the design was balanced, but because in EEG you loose a lot of data to noise and malfunctioning equipment, the end-result is unbalanced data. I am ...
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No value or "."returned for Mauchly's Test of Sphericity in SPSS

I am learning how to do a Two-Way Repeated Measures ANOVA in SPSS but when I try to check the Mauchly's Test of Sphericity Significance value it only displays a single decimal point. It is also ...
Deepend's user avatar
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Why is the "sphericity assumption" in RM-ANOVA (constant variance of difference scores) called "sphericity"?

Why is the "sphericity assumption" in RM-ANOVA, i.e. the assumption of constant variance of difference scores, called "sphericity"? (This question was suggested in the comments to a related question.)...
user1205901 - Слава Україні's user avatar
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Generating a dataset satisfying / violating the RM-ANOVA sphericity assumption

I was reading a research paper where they had a 2x3 repeated measures factorial design with a single DV. A suitable approach to this analysis would be a univariate repeated measures ANOVA. However, ...
Simon's user avatar
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ANOVA does not show sphericity test [duplicate]

I have a dataset, df, which I converted to wide format and then used the Anova function (in the ...
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HLM vs. repeated measures ANOVA -- sphericity concerns?

All, Say I have a 2 (between) x 4 (repeated measures) mixed factorial design. I was going to analyze it with ANOVA, but normality issues and sphericity concerns have made that not a good idea. Are ...
Tom Carpenter's user avatar
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Sphericity. Mauchly's W of 1.000, df 0, and Sig of . . Nothing

The question is about sphericity of repeated measures ANOVA (2 within factors)x(3 between factors). When I check for violations of the sphericity assumption Mauchly's test of sphericity gives me a ...
Natalia Giraldo Holguín's user avatar
3 votes
1 answer
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Running Bartlett's sphericity test for PCA, I get $-\infty$ as a chi-squared value; why?

I am using XLStat for a PCA of time-series water chemistry data. I have 23 analytes and 29 samples. I am using a correlation matrix for PCA as I find it more interpretable in the context of ...
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Does sphericity (an RM-ANOVA assumption) require the covariances between difference scores to be the same?

Field's Discovering Statistics Using SPSS (2013, Sage) defines sphericity as follows: Sphericity: a less restrictive form of compound symmetry which assumes that the variances of the differences ...
user1205901 - Слава Україні's user avatar
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1 answer
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Why is compound symmetry sufficient to establish sphericity?

At this website it is stated that "If compound symmetry is met then sphericity is also met." Is it impossible to construct a data set that has perfect compound symmetry but not perfect sphericity? ...
user1205901 - Слава Україні's user avatar
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3 answers
3k views

Why does repeated measures ANOVA assume sphericity?

Why does repeated measures ANOVA assume sphericity? By sphericity I mean the assumption that the variance of all pairwise differences between groups should be the same. In particular, I don't ...
user1205901 - Слава Україні's user avatar
1 vote
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Sphericity assumption in multivariate approach

I read a few texts about the multivariate approach for repeated measures where k repeated measures are transformed to (k-1) "difference scores". All texts say that using this approach, the assumption ...
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Simulating data for repeated measures ANOVA

I am currently working on a simulation study in which I compare two methods for analysing data from a repeated measures design. Let's say there are n subjects, and each subject goes through i ...
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Does Greenhouse-Geisser correction influence the effect size estimation, the statistical significance treshold, or both of them? [duplicate]

I discussed recently with one of my colleagues about the Greenhouse-Geisser correction for non-sphericity. I told him first that this correction is very conservative and that it would be more ...
Psychokwak's user avatar
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Repeated-measures multiple regression that takes care of sphericity in R

I'm looking for a way to run a repeated-measures multiple regression in R, which would take care of sphericity - either by applying some corrections (such as Huynh-Feldt), or by avoiding the problem ...
themeo's user avatar
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1 answer
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Box's test for equal covariances or Mauchly's test of sphericity?

I am writing a report on a 2 x 3 mixed study. There is ONE within IV with TWO levels and there is ONE between subjects IV THREE levels. There are two DVs. Sample sizes for each group is 25, 25, 27. ...
buket dogan's user avatar
1 vote
0 answers
156 views

ANOVA post hoc with concerned about the sphericity

According to this post the best way to do post hoc analysis in ANOVA in R is t-test + ptukey. Because lme + glht "essentially assumes the sphericity assumption holds". How are t-test + ptukey "...
sviter's user avatar
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What are good values to assume for correlation and sphericity when estimating sample size for a within-subjects design

I am planning a within-subjects study with four different conditions and I am using G*Power to calculate my needed sample size. Not being intimately acquainted with the intricacies of statistics in ...
ThomasH's user avatar
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2 answers
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Bonferroni and Greenhouse-Geisser corrections with repeated-measures ANOVA

I guess my question comes in two parts: Following a 1x7 repeated-measures ANOVA, I carried out 3 pre-planned tests. Two were t-tests between 2 of the conditions. The third is a 1x6 ANOVA (to test ...
Eric's user avatar
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1 answer
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Why is ezANOVA not giving me Mauchly´s test of sphericity, even though I belive I have more than 2 levels of within-Ss variables?

I am trying to do learn how to do a repeated measure in R using ezANOVA and I have used the following command: ...
Marja's user avatar
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1 answer
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Issues with the Huynh-Feldt values using either Anova or ezANOVA in R?

Is there an issue with the output of the Huynh-Feldt correction when running an ANOVA for both between and within factors (mixed design) in R? My issue is that when I run a 'within-subject (only)' ...
Sean Estrada's user avatar
3 votes
2 answers
1k views

Whether to use multivariate F test, df adjusted estimate, or sphericity assumed in repeated measures ANOVA?

I have data that involves 2 groups (equal sample size in each) and data for each group over 3 time points (they are actually 3 different monetary reward conditions). I want to investigate within group ...
Short Elizabeth's user avatar
29 votes
3 answers
47k views

Differences between MANOVA and Repeated Measures ANOVA?

What is the difference between a repeated measures ANOVA over some factor (say experimental condition) and a MANOVA? In particular one website I stumbled across suggested that MANOVA does not make the ...
russellpierce's user avatar
8 votes
4 answers
10k views

How to get Sphericity in R for a nested within subject design?

Thank you for reading. I am trying to get sphericity values for a purely within subject design. I have been unable to use ezANOVA, or Anova(). Anova works if I add a between subject factor, but I have ...
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20 votes
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Post-hocs for within subjects tests?

What is the preferred method for for conducting post-hocs for within subjects tests? I've seen published work where Tukey's HSD is employed but a review of Keppel and Maxwell & Delaney suggests ...
russellpierce's user avatar