Analysis of variance for circular data

Harrison, David K.; Kanji, Gopal K.; Gadsden, R. J.

doi:10.1080/02664768600000021

Cited by 32 publications

(19 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The circular mean of the MRVs of animals within a session was then taken to get a group response for the session. The Harrison–Kanji test (Harrison, Kanji, & Gadsden, ), an analog of a two‐way anova for circular statistics, was used to determine whether the MRV changed significantly over sessions and between groups.…”

Section: Methodsmentioning

confidence: 99%

Differential responsivity of neurons in perirhinal cortex, lateral entorhinal cortex, and dentate gyrus during time‐bridging learning

2018

View full text Add to dashboard Cite

Many studies have focused on the function of hippocampal region CA1 as a critical site for associative memory, but much less is known about changes in the afferents to CA1. Here we report the activity of multiple single neurons from perirhinal and entorhinal cortex and from dentate gyrus during trace eyeblink conditioning as well as consolidated recall, and in pseudo‐conditioned control rabbits. We also report an analysis of theta activity filtered from the local field potential (LFP). Our results show early associative changes in single‐neuron firing rate as well as theta oscillations in lateral entorhinal cortex (EC) and dentate gyrus (DG), and increases in the number of responsive neurons in perirhinal cortex. In both EC and DG, a subset of neurons from conditioned animals exhibited an elevated baseline firing rate and large responses to the conditioned stimulus and trace period. A similar population of cells has been seen in DG and in medial, but not lateral, EC during spatial tasks, suggesting that lateral EC contains cells responsive to a temporal associative task. In contrast to recent studies in our laboratory that found significant CA1 contributions to long‐term memory, the activity profiles of neurons within EC and DG were similar for conditioned and pseudoconditioned rabbits during post‐consolidation sessions. Collectively these results demonstrate that individual subregions of medial temporal lobe differentially support new and remotely acquired memories. Neuron firing profiles were similar on training trials when conditioned responses were and were not exhibited, demonstrating that these temporal lobe regions represent the CS–US association and do not control the behavioral response. The analysis of theta activity revealed that theta power was modulated by the conditioning stimuli in both the conditioned and pseudoconditioned groups and that although both groups exhibited a resetting of phase to the corneal airpuff, only the conditioned group exhibited a resetting of phase to the whisker conditioned stimulus.

show abstract

Section: Methodsmentioning

confidence: 99%

Differential responsivity of neurons in perirhinal cortex, lateral entorhinal cortex, and dentate gyrus during time‐bridging learning

2018

View full text Add to dashboard Cite

show abstract

“…For the circular variable `phase offset' we used a variance decomposition method based on the mean resultant length (Harrison et al, 1986):

r = \frac{1}{N \overset{false‒}{T}} \sum_{n = 1}^{N} \sum_{t = 1}^{T_{n}} c o s (ϕ_{n, t} - \overset{ϕ}{true})

with the phase offset ϕ n,t in cell n and trial t , and the circular population mean

\overset{ϕ}{true}

of the phase offset. The weighted average of cell-specific variation measures is given by

{\overset{r}{true}}^{2} = (1 ∕ N) \sum_{n = 1}^{N} (T_{n} ∕ \overset{T}{true}) r_{n}^{2}

with the cell-specific mean resultant length

r_{n} = (1 ∕ T_{n}) \sum_{t = 1}^{T_{n}} C O S (ϕ_{n, t} - {\overset{false‒}{ϕ}}_{n})

and the cell-specific circular mean

{\overset{ϕ}{true}}_{n}

The measure of the population variance was decomposed into between and within variance through

1 - r^{2} = [{\overset{false‒}{r}}^{2} - r^{2}] + [1 - {\overset{false‒}{r}}^{2}]

where

[{\overset{r}{true}}^{2} - r^{2}]

is the measure for the circular between-cell variance and

[1 - {\overset{r}{true}}^{2}]

the measure for the circular within-cell variance.…”

Section: Methodsmentioning

confidence: 99%

Single-Trial Phase Precession in the Hippocampus

Schmidt¹,

Diba²,

Leibold³

et al. 2009

J. Neurosci.

127

148

View full text Add to dashboard Cite

During the crossing of the place field of a pyramidal cell in the rat hippocampus, the firing phase of the cell decreases with respect to the local theta rhythm. This phase precession is usually studied on the basis of data in which many place field traversals are pooled together. Here we study properties of phase precession in single trials. We found that single-trial and pooled-trial phase precession were different with respect to phase-position correlation, phase-time correlation, and phase range. Whereas pooled-trial phase precession may span 360°, the most frequent single-trial phase range was only ϳ180°. In pooled trials, the correlation between phase and position (r ϭ Ϫ0.58) was stronger than the correlation between phase and time (r ϭ Ϫ0.27), whereas in single trials these correlations (r ϭ Ϫ0.61 for both) were not significantly different. Next, we demonstrated that phase precession exhibited a large trial-to-trial variability. Overall, only a small fraction of the trial-to-trial variability in measures of phase precession (e.g., slope or offset) could be explained by other single-trial properties (such as running speed or firing rate), whereas the larger part of the variability remains to be explained. Finally, we found that surrogate single trials, created by randomly drawing spikes from the pooled data, are not equivalent to experimental single trials: pooling over trials therefore changes basic measures of phase precession. These findings indicate that single trials may be better suited for encoding temporally structured events than is suggested by the pooled data.

show abstract

“…Two-factor ANOVA or Harrison-Kanji test In a similar fashion to the one-factor ANOVA, we can also test for the influence of two factors simultaneously. Such a two-factor ANOVA method for circular data has been introduced by (Harrison, Kanji, and Gadsden 1986;Harrison and Kanji 1988). In addition to potential effects of the two factors, we can also study the impact of their interactions on the population means.…”

Section: Paired and Multisample Testsmentioning

confidence: 99%

CircStat: AMATLABToolbox for Circular Statistics

Berens¹

2009

J. Stat. Soft.

2,653

2,380

View full text Add to dashboard Cite

Directional data is ubiquitious in science. Due to its circular nature such data cannot be analyzed with commonly used statistical techniques. Despite the rapid development of specialized methods for directional statistics over the last fifty years, there is only little software available that makes such methods easy to use for practioners. Most importantly, one of the most commonly used programming languages in biosciences, MATLAB, is currently not supporting directional statistics. To remedy this situation, we have implemented the CircStat toolbox for MATLAB which provides methods for the descriptive and inferential statistical analysis of directional data. We cover the statistical background of the available methods and describe how to apply them to data. Finally, we analyze a dataset from neurophysiology to demonstrate the capabilities of the CircStat toolbox.

show abstract

Analysis of variance for circular data

Cited by 32 publications

References 10 publications

Differential responsivity of neurons in perirhinal cortex, lateral entorhinal cortex, and dentate gyrus during time‐bridging learning

Differential responsivity of neurons in perirhinal cortex, lateral entorhinal cortex, and dentate gyrus during time‐bridging learning

Single-Trial Phase Precession in the Hippocampus

CircStat: AMATLABToolbox for Circular Statistics

Contact Info

Product

Resources

About