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I have weather stations collecting data (temperature, humidity, solar radiation, wind, etc.) inside and outside low-tech greenhouses. Four of the weather stations are inside, and one is outside. I am testing to see if the differences between inside and outside are statistically significant.

I have taken hourly data and averaged it to monthly. I want to test each monthly average: inside vs. outside. Temperature and humidity are close to normal. The other variables are not.

A: Can I test statistical significance?

B: What approach would I use?

Please let me know if I am missing any details from my study. As I am new to statistics, I don't always know what's important to provide.

Thanks.

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    $\begingroup$ Why did you average your hourly data to monthly? You could keep it as is for more statistical power. Either way, with a small sample you could use a t test or anova. $\endgroup$
    – Estimate the estimators
    Commented Jun 25, 2017 at 3:33
  • $\begingroup$ I averaged it because I am interested in monthly patterns and I am want to avoid correlation between time steps. $\endgroup$
    – phaser
    Commented Jun 25, 2017 at 3:45

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I agree with the comment that your power to detect significant differences will increase if you use hourly data.

It sounds like you don't care about any comparisons between the four different indoor stations, and instead are interested in the possibility of differences existing between each of the four indoor stations and the sole outdoor station.

If that is right then, a series of independent sample t-tests would be a good place to start. More sophisticated modeling approaches could be employed to consider differences in readings that may occur during certain times of day or in certain seasons, but such techniques wouldn't be necessary to address your primary research aim.

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  • $\begingroup$ Yes, that is my primary aim. I didn't think t-tests would work because of the small sample. I also didn't think t-tests would work for the non-normal data. Am I wrong about the assumptions behind the t-test? $\endgroup$
    – phaser
    Commented Jun 25, 2017 at 3:48
  • $\begingroup$ I would expect a few things to happen if you use hourly data. First, with the larger sample of data points you may start to see a more normal distribution emerge. That is if sample size is your concern right now, I would imagine that it is a small sample that is preventing your data from appearing normal. T-tests do assume a normal distribution, and if normality is sufficiently violated there are ways to transform the scores to better meet this assumption. $\endgroup$
    – Matt Barstead
    Commented Jun 25, 2017 at 13:39
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    $\begingroup$ That all being said, if distributional assumptions underlying frequentist statistics like t-tests remain a concern, you could always move the problem into a Bayesian world. Still, it seems to me that temperature at least should be approximately normally distributed. Humidity I could see having either a right or left skew depending on where you live/work. In either case t-tests on the original hourly scores or transformed scores should get you a reasonable answer. $\endgroup$
    – Matt Barstead
    Commented Jun 25, 2017 at 13:44

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