# 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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### 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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### Sphericity assumption in a 2X2X2 within subjects repeated measures anova

My study design has three factors each with 2 levels for a 2X2X2 within subjects repeated measures anova. When using the car package Anova function or the ezAnova function in R my output does not ...
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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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### 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 ...
1 vote
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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/...
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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 ...
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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.)...
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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, ...
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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 ...
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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 ...
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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 ...
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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? ...
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### 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 ...
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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?

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 ...
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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 ...
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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. ...
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### 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 "...
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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 ...
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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 ...
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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: ...
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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)' ...
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### 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 ...
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### 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 ...