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I have a data set that looks like so:

+------+------------+------------+
| Time | Brad Event | Gary Event |
+------+------------+------------+
|    1 | N          | Y          |
|    2 | N          | Y          |
|    3 | y          | N          |
|    4 | N          | Y          |
|    5 | N          | N          |
|    6 | Y          | N          |
|    7 | N          | N          |
|    8 | N          | N          |
|  ... | ...        | ...        |
+------+------------+------------+

I have found out that for n=400 time intervals:

  • Brad has an event in 18% of them
  • Gary has an event in 6% of them

My NULL hypothesis is that the probability of an event in these two series' are the same. My ALTERNATIVE hypothesis is that the the probability of an event in these two series' are different.

Normally this wouldn't be a problem to test, but my data breaks the independence assumption. Brad and Gary levels are independent of each other, but the occurrence of an event within a level may be influenced by a previous occurrence.

From a subjective look at the data, multiple events happen close together, then there is a pause and then multiple events again. When I looked at the duration between occurrences, these were not normally distributed (Histogram was all over the place). I may have time series dependence within the series.

Is there a statistical test that can be used to test for my NULL hypothesis even if it violates the independence assumption?

BigAl
  • 111
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  • First, try to get your concepts right. DATA is not "significant" or "not significant", some HYPOTHESIS may be. I think your null hypothesis is that the probability of event in tose two series are the same, but you have time series dependence within the series. Did yoy try to see at the autocorrelation function? Maybe you coud use a markov chain model, maybe some other timeseries model. Have a look at http://stats.stackexchange.com/questions/197084/binary-time-series , search this site for "binary time series" (without the quotes). – kjetil b halvorsen Sep 24 '16 at 15:56
  • Hello, sorry for my poor explanation. Yes that NULL hypothesis is correct. My alternative hypothesis is that the two series' probability of events are different. I will read up on binary time series. – BigAl Sep 24 '16 at 16:33
  • Can you please edit this corrections into the post? – kjetil b halvorsen Sep 24 '16 at 16:58

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