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Just a note

If you prefer this expressed algebraically, if all values of P are the same, and all values of T are the same, then:
  • 1,2 = 1,1 +P+T
  • 2,1 = 1,1 +T
  • 2,2 = 1,1 +T+PT

  • so   1,1+1,2 = 21,1+P+T
  • and 2,1+2,2 = 21,1+P+T
Therefore (on average) we would expect the mean of group 1 minus the mean of group 2 will equal zero.