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First of all, I’m new to statistics and this is the first time I am trying to apply it to a real world problem.

I am doing analysis of a series of observations of a variable over all weeks of a year. During certain weeks an event happened that I believe has impacted the variable and I want to check for this.

The values are technically a time series, however I only need to know that the event has an impact so I did an uncorrelated t-test. My reasoning is that, if I split the series of observations into a group of observations when the event happened and one where it didn’t happen, then I can compare the mean of each group using a t-test.

Is this reasoning valid?

Many thanks, David

@GaBorgulya, I only have ONE value for each week.

@Gavin Simpson No, I don't think that the values are autocorrelated. I am working with human behaviour and I believe that the event has an effect but it is not as deterministic as what it would be if the data were autocorrelated.

@Wayne, the event is random.

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  • $\begingroup$ Do you have two values for each week, (1) a continuous outcome measure and (2) a yes/no predictor? $\endgroup$
    – GaBorgulya
    Commented Apr 19, 2011 at 16:03
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    $\begingroup$ But aren't the values within each group autocorrelated and hence you have less information over the entire sample than you would if the data were independent? $\endgroup$ Commented Apr 19, 2011 at 17:07
  • $\begingroup$ I'm not good enough to know the t-test answer to your question, but one thing to think about is: is the event "random" or scheduled? If it's scheduled, all kinds of interaction possibilities come to mind, including things that happen in the same week or things that happen the week before or after. $\endgroup$
    – Wayne
    Commented Apr 19, 2011 at 17:25

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Your reasoning sounds reasonable to me, although I have the feeling you are stretching the independence assumptions of t tests a little. Therefore, you should keep two things in mind.

First, the size of both groups (weeks with event versus weeks without event) should be comparable. E.g., 20 versus 30. would be fine I guess.

Second, your observations are not independent but follow a rule (weeks follow deterministically each other). Therefore, the occurrence of the events should be uncorrelated with the this rule (i.e., order of the weeks). This would be especially important if the dv (your measured variable) is influenced by the order of the week. But if you can negate both of these issues (correlation of event with order of weeks and of order with dv) you are good to go.

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  • $\begingroup$ Thanks for your quick reply. The relation between the sequence of weeks and my event is a good point. $\endgroup$
    – DavidA
    Commented Apr 20, 2011 at 8:27

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