Which stats tests to use? Bee flight activity quantified during an eclipse

Question

I'm trying to perform a statistical analysis but not sure what test is most appropriate. The experiment and snippet of sample data are below:

Methods: Bee flights from a beehive were recorded, tracked, and quantified using some fancy software. 2 min recordings were made, every 15 min, over a span of 3 hours, on 2 consecutive days from the same hive. On Day 1 there was a solar eclipse peaking at 3:15 pm. Day 2 was a normal day. At each timepoint we calculated only 1 number. Assumptions are that the number of bees flying at each timepoint is variable, and not dependent on earlier/later times. The hypothesis is that during an eclipse bee flight activity will be different.

Time    Day 1       Day 2 
1:45    4.825986975 5.011309825 
2:00    4.76436878  4.944759887 
2:15    4.857806302 4.995020539 
2:30    5.160417753 5.098229915 
2:45    5.151340989 5.123143909 
3:00    5.205157211 5.01482563 
3:15    5.576328277 5.060712789 
3:30    5.499265895 4.767659804 
3:45    5.341123626 4.698898463 
4:00    4.511481755 4.336670549 
4:15    4.454618556 4.540783545 
4:30    4.475789132 4.203964626 
4:45    4.378358091 4.239819416 

Results: Visually we saw more flights during the onset of the eclipse. When plotted the curves qualitatively show a difference during the eclipse.

QUESTIONS:

1. What stats test would be correct to run on the dataset to say whether there was a difference between Day 1 and 2 (in other words, did the eclipse meaningfully influence flight activity on Day 1)? I realize there are caveats to the whole setup but what I'm asking is about stats..

2. Can I use a test to see if there was a meaningful change just during the eclipse Day?

3. I know the sunlight intensity (irradiance) during the eclipse. Can I do a Pearson's to look for a correlation between intensity and flight activity?

Answer 1

Here is a graph of the two days' data (Day 1, gold line with black markers, Day 2 black line with gold markers; I coded time in terms of minutes elapsed since the first measurement of the day):

The trouble with asking "whether there was a difference between Day 1 and 2" is that the answer is Yes. There are many differences:

1. At every time of measurement, the bees' area of flight activity is different (even during the period where there was no eclipse).
2. Within each day, there are differences in bees' area of flight activity: both Day 1 and Day 2 experience a dip and then something like an increase peaking, as it so happens, between 2:45 and 3:15 (90 minutes in), and then dropping in activity thereafter.
3. Bees area of flight activity at any point in time seems to be slightly different than its activity 15 minutes earlier, except from about 3:30 to 4:00 (105 to 120 minutes).
4. The peak measurement of bees' area of flight activity is at 3:15 on Day 1, and different by 30 minutes (earlier) on Day 2.
5. The mean bees' area of flight activity is 4.94 on Day 1, but 4.77 on Day 2; similarly the variance is a good bit different (greater) on Day 1 (0.0131) than Day 2 (0.00874).

There are probably lots more ways to conceive of "differences" between the two days.

So: statistics will be more useful to you when you can more precisely articulate which differences are important to you.

Here's another graphical take, but this time it's Day 1 activity minus Day 2 activity:

If both days were very similar, we might expect the curve to center vertically on 0. If we had the data for eclipse activity (inactivity?) for the same times of bee measurement, we could ask whether the curve of eclipsing over this time looks like the bee difference curve. Your question about the Pearson's correlation coefficient would be one way to do this. Regression would be another, and would give a bit more information. You could perform a test in such a circumstance (e.g., a test that Pearson's $\rho = 0$, or a test that the slope of the line, $\beta = 0$). But again, you might want to think carefully about what difference is meaningful to you.