i want to make hypothesis test for a data for pH values measured for each month of a year. I want to test whether there is any correlation ie: are the values for month of summer having similar values and like that for months of winter and monsoon. which test is most appropriate for this kind of analysis.

This is the seasonal component.

` Jan Feb Mar Apr May Jun Jul 1 -11.500000 -9.916667 7.333333 26.416667 -18.583333 22.750000 1.083333 2 -11.500000 -9.916667 7.333333 26.416667 -18.583333 22.750000 1.083333 Aug Sep Oct Nov Dec 1 -10.916667 -3.583333 -2.083333 -3.750000 2.750000 2 -10.916667 -3.583333 -2.083333 -3.750000 2.750000 `

trend of pH with trend line.

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#### Best Answer

Put a 11 dummies for each month, or 3 dummies for quarters in your model (regression). First, check if any of the dummies are significant. If not, then test that all dummies are zero simultaneously. If the dummies are significant individually or all together, then you have seasonality.

As @RichardHardy noted this will not always work. I'm just suggesting a place to start. You may need to find a better solution taylored for your domain. For instance, in economic data with monthly seasonality X-13 routine from Census Bureau is widely used. It has a ton of diagnostics and not very intuitive to sue at first, but it's very powerful