In an split plot experiment, 4 methods of Nitrogen(N) application was assigned in main plot and 3 doses of N in subplots and replicated thrice. Along with it, in the same field, No N control was done outside the split plot design and replicated thrice. How to compare No N control with those treatments inside split plot design?
If you take data from something not in the experimental design it is not part of the experiment but might in some way be treated as a covariate or covariates. The classical paper on such things (in this case rainfall) is by R A Fisher referenced here:Chapter The Yields of Wheat on the Broadbalk Fields at Rothamsted
and can be downnloaded from the Fisher archives at this link: https://scholar.google.com/scholar_lookup?title=The%20influence%20of%20rainfall%20on%20the%20yield%20of%20wheat%20at%20Rothamsted&author=RA.%20Fisher&journal=Phil.%20Trans.%20Roy.%20Soc.%2C%20London&volume=213&pages=89-142&publication_year=1924I am sure some clever searching from Google or Google scholar will yield many more such references. You might also check this link which may be easier reading: Montgomery, Design and Analysis of Experiments: https://www.google.com/search?q=montgomery+d.c.+design+and+analysis+of+experiments&rlz=1C1CHBF_enUS915US915&oq=Montgomery+D+C+&aqs=chrome.1.69i57j0l6j69i60.19204j1j15&sourceid=chrome&ie=UTF-8 Start with ANCOVA. Best wishes, David Booth
I agree with Prof David Eugene Booth , being outside the design implies you've discovered/acknowledge a covariate. Yes, re-examine the design, try ANCOVA, and good luck. The past decade has seen advances in the development of new methods for the design and analysis of split-plot experiments with covariates/control. 1. https://www.google.com/url?sa=t&source=web&rct=j&url=https://www.researchgate.net/publication/243102736_Split-Plot_Model_With_Covariate&ved=2ahUKEwirq675-4PsAhVQTBUIHQmoBcgQFjAJegQIAxAB&usg=AOvVaw2TlFHk_aPCyKISJxc_efoW 2. https://www.google.com/url?sa=t&source=web&rct=j&url=https://www.researchgate.net/publication/228534962_SPLIT-PLOT_SPLIT-BLOCK_ANALYSIS_WITH_CONTROL_A_TREATMENTS&ved=2ahUKEwjq757M-4PsAhXVVRUIHfQ_D9UQFjAAegQIDhAC&usg=AOvVaw3tMJr3JjO5BHJSTBB4UH0N
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