Is there a non-parametric equivalent of the t-test for a small sample size? 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 the weather station data inside and outside is statistically different from zero.
Because I have an unequal number of replicates inside and outside the greenhouses, I calculated the difference for each variable between each weather station inside each greenhouse and the one weather station outside. This gives me a sample size of 4. Sometimes 3 because I lost a replicate for part of the study. I was hoping to test the significance of the differences from zero rather than the original weather station data.
I am looking for a statistical test that works on small sample sizes and non-normal distributed data. I am thinking a non-parametric alternative to the z-test.
I tried the wilcoxon sign test, but I am getting no statistical significance where there should be some. For example, testing if 3 values in the -300 range are statistically different from 0. The test said no.
Please let me know if I provided enough information about my study.
 A: In first place, the difference between t-test and z-test is that for z-test population variance is known. If you are looking for an equivalent non parametric test, variance doesn't matter and therefore "equivalent to z-test" is equal to "equivalent  to t-test".
In general, non parametric tests don't use actual value of data. They just use ranks. Therefore, you will get the same p-value with quite similar samples (like {1} and {1.1,1.3,1.5}) than with very different samples (like {1} and {1000, 1001, 1002}) because the only information the Wilcox test uses is that the three values in the second sample are larger than the only one in the first one. Furthermore, since even this extreme result is likely to happen if the null hypothesis is true, p-values will always be large in your setting (you can see this answer to a similar question).
In any case, if you are taking series of measures (for example, daily), I wouldn't compare data from a single day. I would take in account all days in the same test. Performing a two way unbalanced ANOVA with inside/outside as first factor and day as second factor (or block) may tell you if there is a significant difference between inside and outside. You can check for normality of residuals after the test, but they are likely to be normal enough to keep ANOVA conclusions valid.
