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I have a list of epoch/unix times at which an event happened. My hypothesis is that there are certain times during the week when this event might happen more frequently. How can I visualize/determine which times are most probable for this event to happen? I'd like to know both time and day of week. I'm working with excel.

1353951487
1353950051
1353948443
1353919982
1353882762
1353724050
1353693717
1353505109
1353474394
1353415614
1353415429
1353397809
1353383231
1353375862
1353342807
1353298391
1353298644
1353295194
1353250737
etc...

Since epoch time starts on a Thursday morning at 0:00 UTC, I subtracted three days from each time, to shift all times to seconds since Sunday Jan 4th 1970. (since the values listed are epoch seconds)

I then found the time modulo (seconds in a week) to find the remainder of seconds which took place after the most recent Sunday.

For the times listed above, here are the seconds since the most recent Sunday at 0:00 UTC.

Time        Seconds since most recent Sunday 0:00 UTC
1353951487  149887
1353950051  148451
1353948443  406043
1353919982  377582
1353882762  340362
1353724050  181650
1353693717  151317
1353505109  567509
1353474394  536794
1353415614  478014
1353415429  477829
1353397809  460209
1353383231  445631
1353375862  438262
1353342807  405207
1353298391  360791
1353298644  361044
1353295194  357594
1353250737  313137
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  • $\begingroup$ Could you explain what these data mean? They don't look like times at all. $\endgroup$ – whuber Jul 25 '13 at 18:48
  • $\begingroup$ It's epoch, or unix time en.wikipedia.org/wiki/Unix_time. The way computers keep time is by counting milliseconds since Jan 1, 1970 UTC. 1,353,951,487 = Mon, 26 Nov 2012 17:38:07 GMT. $\endgroup$ – John Jul 25 '13 at 22:48
  • $\begingroup$ Computers keep time in myriad ways. By default, when numbers appear separated by commas, they would be interpreted as four separate fields. One could guess that these are milliseconds (or whatever), but it's not a good idea to make people guess what your data mean. $\endgroup$ – whuber Jul 26 '13 at 1:10
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    $\begingroup$ Thanks for clarifying. It's impossible to know in advance that a term like "epoch time" (a) has multiple meanings (depending on the operating system) and (b) may have completely different meanings for different people (such as an epoch time for a geographer). So to avoid confusion, multiple conflicting answers, or lack of answers, it's best to explain yourself whenever you can. $\endgroup$ – whuber Jul 28 '13 at 21:19
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    $\begingroup$ If you want to identify peaks in the distribution across the week, possibilities include a periodic-kernel- or periodic-spline- density estimate or as an exploratory tool, perhaps even a histogram. $\endgroup$ – Glen_b Jul 29 '13 at 4:44
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Visualization options include circular histograms and circular kernel density plots. Basically, these are histograms or KDE visualizations wrapped around a circle, better to stress the cyclical nature of the variable, in your case that Sunday is much nearer to Monday than Wednesday.

To the question of which times are more likely to produce the event, you may want to look into harmonic regression (try this handout) or regression on circular statistics (see this question).

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