Test for gaze time ~ addressee status

[Christoph Ruehlemann]

Dear All,

I'm not sure which test to use for some multimodal data and would be most grateful for suggestions.

The data are gaze durations in 3-party storytelling sequences from a single-case study. The focus is on how the storyteller uses her gaze to address the two story recipients during storytellings. Specifically, what I'm interested in is to examine whether the amount of time the storyteller gazes at a participant depends on that participant's addressee status as either (i) a primary addressee, (ii) or a secondary addressee, or (iii) an equal addressee.

There are 5 storytelling sequences in the data. In 2 of them (let's call these cases A), one story recipient is the primary addressee and the other the secondary addressee. In 3 of them (let's call them B), there is no observable difference in the recipients' addressee status.

As might be expected, in A the storyteller gazes longer at the primary addressee than at the secondary addressee (the proportions are 0.7 v 0.3 and 0.6 v 0.4). But: in B, there are marked differences too: 0.6 v 0.4 and 0.4 v 0.6. Only in one story in B does the storyteller spend as much time gazing at one equal addressee as on the other. (Attached is a graph showing the proportions for all five stories.)

Any suggestions as to how one can test whether gaze time depends on addressee status are highly appreciated (and will, of course, be acknowledged in the paper reporting on this study!)

Best

Chris

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https://www.uni-marburg.de/fb10/iaa/institut/personal/ruehlemann

ἰχθύς

[Alex Perrone]

I’m trying to understand. You have 5 triads of people, where in each triad, the same 5 stories are told? The storyteller is the same in each triad for all 5 stories, and the addressee status is randomly assigned to the participants per story (it may switch, as it appears in the graph)? Are all triads are unique (no person is in multiple triads)?

I could just say “use ANOVA” but I think there are some issues to be dealt with before that. The main thing is I’m wondering if you really have more than 5 data points, since it probably does not make much sense to lump different stories together — although a hierarchical model could deal with this. Per story, it seems you have only 5 independent observations. If that is the case, will be very hard to conclude much from 5 data points.

I’d be interested to hear other people’s reactions to this, too. 

Alex

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<Gaze-fixation time per story.tiff>

[Stefan Th. Gries]

If these are 5 proportions, I am assuming each blue and each red bar
represents multiple observations, correct? That means you do have more
than 5 data points and a linear mixed model with a hierarchical
structure might indeed work.

[Christoph Ruehlemann]

Yes, there are 5 stories in the data (it's a single case study based on strictly conversational data). The teller is gazing alternatingly at recipient R and recipient L while telling the stories. Altogether there are 102 gazes, as it happens 51 each to each recipient (i.e. 102 observations). The gaze durations are measured and added up for each recipient in each story to obtain the proportions.

Hope this clarifies the scenario.

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ἰχθύς

[Alex Perrone]

How many "tellers" are there?

[Christoph Ruehlemann]

Just 1.

[Alex Perrone]

Well there is not too much to analyze here, statistically. You just have the proportion of results from that "single case study" with one group of three people. It's only 5 data points, and 1 per story. 

I don't think you can fit a frequentist hierarchical model, and even if you could, there's no way you'd be able to reject a null hypothesis test. You definitely can forget a (non-hierarchical) linear model because you have no variance in x or variance in y, so you can't compute CIs at all -- it's like fitting a line of best fit to a single point. 

You could always fit a Bayesian hierarchical model, with a parameter for the family of proportions from which each story is drawn from, but with just one update (one per story, at least, five for the family-wise parameter), I'd doubt you could learn much in a Bayesian sense... meaning, I'd doubt your parameters would change much after updating with so little data. So if you start with a flat prior (like a uniform [0-1] for the proportion directed at primary addressee) then it would stay really flat.