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Please forgive me if this is a naive question, but I haven't been able to find an answer in my stats books or online. I'm working on a fish tracking dataset that consists of detections of tagged fish in various locations. Each row of my dataframe is a detection (with a date/time, fish ID, location, and swimming depth). I'd like to test whether there is a different in swimming depth during the day and night, so I've created a column using the maptools package to classify each detection as "night" or "day". There are >8000 detections of 46 different fish, at 40 different locations.

    > head(data)
      Date.and.Time..UTC. Fish.code   Location Detection.depth sqrtdepth daynight
    1 2011-06-26 04:54:58        01         04          1.7589  1.326235    Night
    2 2011-06-26 04:56:00        01         04          1.3192  1.148564    Night
    3 2011-06-26 04:56:45        01         05          1.7589  1.326235    Night
    4 2011-06-27 08:49:02        01         04         36.4952  6.041126      Day
    5 2011-07-06 18:33:14        01         09         56.2817  7.502113      Day
    6 2011-07-07 01:40:59        01         08          3.0780  1.754423    Night

I'm having trouble deciding which statistical test to use to compare daytime depths to nighttime depths. The measured swimming depth data is normally distributed when it is square root-transformed, and the variances of the day and night swimming depths are approximately the same, but my data is not independent. The detections are autocorrelated temporally and spatially; each fish has many depth measurements that occur at night and during the day.

I've used a linear mixed effects model from the lme4 package to show that day/night is a significant predictor for depth, but now I want to know what the effect of each significant predictor is on depth (i.e. "are swimming depths during the day deeper than at night, and is this pattern statistically significant?"). Is my only option to go with a non-parametric test of some sort, even though I have normally distributed data?

Any advice or informative links would be very helpful.

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  • $\begingroup$ The answer might depend on how you are detecting fish. Could you elaborate on the mechanism? $\endgroup$
    – whuber ♦
    Commented Apr 15, 2015 at 20:25
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    $\begingroup$ I should have anticipated that question! It's an acoustic telemetry system. Each fish has a transmitter that sends out an acoustic signal about once a minute. The transmissions are detected by hydrophone receivers ("Location" in the dataframe above) that are deployed strategically in the study area. Each row of the dataframe corresponds to a detection of a transmission by a particular receiver. $\endgroup$
    – Maryanne
    Commented Apr 15, 2015 at 20:37
  • $\begingroup$ Can you clarify/expand on what you mean by "now I want to know what the effect of each significant predictor is on depth" ? $\endgroup$
    – Ben Bolker
    Commented Apr 15, 2015 at 21:42
  • $\begingroup$ Edited post accordingly. Data visualization suggests that the tagged fish swam deeper during the day than at night, so I want to test the statistical significance of this pattern. Sorry for the confusion. $\endgroup$
    – Maryanne
    Commented Apr 16, 2015 at 12:45
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    $\begingroup$ Are you sure you need a formal test? Perhaps the results are so clear that a simple, appropriate graphic would settle the issue. Indeed, such a graphic would likely provide far more information than a test, because it could show you more precisely how the fish behaviors differ over the course of a day. $\endgroup$
    – whuber ♦
    Commented Apr 16, 2015 at 15:05

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