Test correlation of Group size, Turn duration, and Gaze duration

[Christoph Ruehlemann]

Hi All,

I'm working on Gaze in Turns in conversation. The kind of data is illustrated here:

    df <- data.frame(
      Gaze_dur = c(25,35,75,55,
                   150,120,170,190),
      N_p = c(3,3,3,3,
              2,2,2,2),
      Turn_dur = c(100,120,150,110,
                   200,230,210,250)
    )

I know that Turns in Dyads (2 ppl talking) are on average longer than Turns in Triads (3 ppl talking). I also know that Gaze durations are longer in Dyads than in Triads:

    library(tidyverse)

    df %>%
      group_by(N_p) %>%
      summarise(Turn_dur_mean = mean(Turn_dur),
                Gaze_dur_mean = mean(Gaze_dur))
    # A tibble: 2 × 3
        N_p Turn_dur_mean Gaze_dur_mean
      <dbl>         <dbl>         <dbl>
    1     2          222.         158.
    2     3          120           47.5

How can I test the hypothesis that ***Gazes* are shorter in Triads than Dyads because *Turns* are shorter in Triads than Dyads**?

I would think that one step forward toward answering that question might be by computing the **porportional duration** of `Gaze_dur` against `Turn_dur`:

    df %>%
      mutate(Gaze_dur_prop = Gaze_dur / Turn_dur)
      Gaze_dur N_p Turn_dur Gaze_dur_prop
    1       25   3      100     0.2500000
    2       35   3      120     0.2916667
    3       75   3      150     0.5000000
    4       55   3      110     0.5000000
    5      150   2      200     0.7500000
    6      120   2      230     0.5217391
    7      170   2      210     0.8095238
    8      190   2      250     0.7600000

But to proceed from there (if that's the right first step at all)? What's the approriate statistical test? Help is much appreciated!

Best wishes

Christoph

--

Albert-Ludwigs-Universität Freiburg

Projekt-Leiter DFG-Forschungsprojekt "Multimodale Turn-Abschlusssignale"

(https://gepris.dfg.de/gepris/projekt/497779797)

Homepage: http://paul.igl.uni-freiburg.de/ruehlemann/?Home

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