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{"sheet":"ANOVA calculations","index":0,"n_rows":93,"n_cols":6,"rows_kept":93,"flags":["formulas_cached_only"]}
[null,"Treatment Groups"]
[null,1,2,3,4]
[null,"Unop Control","Inj Control","High dose","Low dose","N"]
["ENTER Æ",{"$nulls":4},1]
["DATA Æ",{"$nulls":4},2]
["HERE Æ",{"$nulls":4},3]
["Æ",{"$nulls":4},4]
["Æ",{"$nulls":4},5]
["ENTER Æ",{"$nulls":4},6]
["DATA Æ",{"$nulls":4},7]
["HERE Æ",{"$nulls":4},8]
["Æ",{"$nulls":4},9]
["Æ",{"$nulls":4},10]
["ENTER Æ",{"$nulls":4},11]
["DATA Æ",{"$nulls":4},12]
["HERE Æ",{"$nulls":4},13]
["Æ",{"$nulls":4},14]
["Æ",{"$nulls":4},15]
["ENTER Æ",{"$nulls":4},16]
["DATA Æ",{"$nulls":4},17]
["HERE Æ",{"$nulls":4},18]
["Æ",{"$nulls":4},19]
["Æ",{"$nulls":4},20]
["ENTER Æ",{"$nulls":4},21]
["DATA Æ",{"$nulls":4},22]
["HERE Æ",{"$nulls":4},23]
["Æ",{"$nulls":4},24]
["Æ",{"$nulls":4},25]
["ENTER Æ",{"$nulls":4},26]
["DATA Æ",{"$nulls":4},27]
["HERE Æ",{"$nulls":4},28]
["Æ",{"$nulls":4},29]
["Æ",{"$nulls":4},29]
["ENTER Æ",{"$nulls":4},30]
["DATA Æ",{"$nulls":4},31]
["HERE Æ",{"$nulls":4},32]
["Æ",{"$nulls":4},33]
["Æ",{"$nulls":4},34]
["ENTER Æ",{"$nulls":4},35]
["DATA Æ",{"$nulls":4},36]
["HERE Æ",{"$nulls":4},37]
[]
["          DO NOT Enter Data or Modify Anything Below This Line"]
[]
["Basic Stats",1,2,3,4]
["Mean",{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"}]
["St Dev",{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"}]
[]
[null,null,"number of groups/treatments (a):",4]
[null,null,"Total samples/individuals (n):",0]
[]
["ANOVA calculations:",{"$nulls":4},"Grand Sums"]
["Sum Y",0,0,0,0,0]
["n",0,0,0,0,0]
["Sum Y-sq",0,0,0,0,0]
["Variance",{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"}]
[]
[null,{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"}]
[]
["4. Correction term",{"$nulls":4},{"$error":"#DIV/0!"}]
["5. SS total",{"$nulls":4},{"$error":"#DIV/0!"}]
["6. SS groups",{"$nulls":4},{"$error":"#DIV/0!"}]
["7. SS within",{"$nulls":4},{"$error":"#DIV/0!"}]
[]
["ANOVA table"]
["Source of variation",null,"df","SS","MS","Fs"]
["Ybar-Ydblbar, Among groups",null,3,{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"}]
["Y-Ybar, Within groups",null,-4,{"$error":"#DIV/0!"},{"$error":"#DIV/0!"}]
["Y-Ydblbar, Total",null,-1,{"$error":"#DIV/0!"}]
[]
["Summary:",null,"Fs","df (a-1)","df (n-a)","P"]
[null,null,{"$error":"#DIV/0!"},3,-4,{"$error":"#DIV/0!"}]
[]
["Planned pairwise comparisons"]
["Groups "]
["compared"]
[null,"SS (1 vs. 2)","Fs","df (a-1)","df (n-a)","P"]
["1 vs. 2",{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},1,-2,{"$error":"#DIV/0!"}]
[]
[null,"SS (1 vs. 3)","Fs","df (a-1)","df (n-a)","P"]
["1 vs. 3",{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},1,-2,{"$error":"#DIV/0!"}]
[]
[null,"SS (1 vs. 4)","Fs","df (a-1)","df (n-a)","P"]
["1 vs. 4",{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},1,-2,{"$error":"#DIV/0!"}]
[]
[null,"SS (2 vs. 3)","Fs","df (a-1)","df (n-a)","P"]
["2 vs. 3",{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},1,-2,{"$error":"#DIV/0!"}]
[]
[null,"SS (2 vs. 4)","Fs","df (a-1)","df (n-a)","P"]
["2 vs. 4",{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},1,-2,{"$error":"#DIV/0!"}]
[]
[null,"SS (3 vs. 4)","Fs","df (a-1)","df (n-a)","P"]
["3 vs. 4",{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},1,-2,{"$error":"#DIV/0!"}]

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["Abbreviated table of F values for (df) degrees of freedom (a-1) vs (n-a)"]
[]
["Values taken from Table 16, \"Critical values of the F-distribution,\" pp 108-130, "]
["in \"Statistical Tables,\"  by Rohlf & Sokal, 2nd Edition, ©1981 W.H. Freeman & Co., New York"]
[]
["For P ≤ 0.05",{"$nulls":8},"For P ≤ 0.01"]
[null,"a-1",1,2,3,4,5,6,null,null,"a-1",1,2,3,4,5,6]
["n-a",{"$nulls":8},"n-a"]
[1,null,161,199,216,225,230,234,null,1,null,4050,5000,5400,5620,5760,5860]
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[3,null,10.1,9.55,9.28,9.12,9.01,8.94,null,3,null,34.1,30.8,29.5,28.7,28.2,27.9]
[4,null,7.71,6.94,6.59,6.39,6.26,6.16,null,4,null,21.2,{"v":18,"d":"18.0"},16.7,{"v":16,"d":"16.0"},15.5,15.2]
[5,null,6.61,5.79,5.41,5.19,5.05,4.95,null,5,null,16.3,13.3,12.1,11.4,{"v":11,"d":"11.0"},10.7]
[6,null,5.99,5.14,4.76,4.53,4.39,4.28,null,6,null,13.7,10.9,9.78,9.15,8.75,8.47]
[7,null,5.59,4.74,4.35,4.12,3.97,3.87,null,7,null,12.2,9.55,8.45,7.85,7.46,7.19]
[8,null,5.32,4.46,4.07,3.84,3.69,3.58,null,8,null,11.3,8.65,7.59,7.01,6.63,6.37]
[9,null,5.12,4.26,3.86,3.63,3.48,3.37,null,9,null,10.6,8.02,6.99,6.42,6.06,{"v":5.8,"d":"5.80"}]
[10,null,4.96,{"v":4.1,"d":"4.10"},3.71,3.48,3.33,3.22,null,10,null,{"v":10,"d":"10.0"},7.56,6.55,5.99,5.64,5.39]
[15,null,4.54,3.68,3.29,3.06,{"v":2.9,"d":"2.90"},2.79,null,15,null,8.68,6.36,5.42,4.89,4.56,4.32]
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[25,null,4.24,3.39,2.99,2.76,{"v":2.6,"d":"2.60"},2.49,null,25,null,7.77,5.57,4.68,4.18,3.86,3.63]
[30,null,4.17,3.32,2.92,2.69,2.53,2.42,null,30,null,7.56,5.39,4.51,4.02,{"v":3.7,"d":"3.70"},3.47]
[40,null,4.08,3.23,2.84,2.61,2.45,2.34,null,40,null,7.31,5.18,4.31,3.83,3.51,3.29]
[60,null,{"v":4,"d":"4.00"},3.15,2.76,2.53,2.37,2.25,null,60,null,7.08,4.98,4.13,3.65,3.34,3.12]
[120,null,3.92,3.07,2.68,2.45,2.29,2.17,null,120,null,6.85,4.79,3.95,3.48,3.17,2.96]
["•",null,3.84,{"v":3,"d":"3.00"},{"v":2.6,"d":"2.60"},2.37,2.21,{"v":2.1,"d":"2.10"},null,"•",null,6.63,4.61,3.78,3.32,3.02,{"v":2.8,"d":"2.80"}]
[]
["a = number of groups (or treatments)"]
["n = number of samples/individuals from all groups"]

{"sheet":"Hartley's F-max test","index":2,"n_rows":20,"n_cols":6,"rows_kept":20,"flags":["formulas_cached_only"]}
["Hartley's F-max test is a \"quick and dirty\" way of testing whether"]
["the variances among groups are homogeneous (\"the same\"). "]
["If so, then ANOVA is an appropriate way to analyze the data."]
[]
["Take the ratio of the highest group and lowest group variances"]
[]
["Fmax = ","Varmax/Varmin"]
[]
[]
[null,1,2,3,4]
["Variances",{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},{"$error":"#DIV/0!"},"from previous sheet"]
["n",0,0,0,0,"from previous sheet"]
["df (n-1)",-1,-1,-1,-1,"from previous sheet"]
[]
[null,"Var-max",{"$error":"#DIV/0!"}]
[null,"Var-min",{"$error":"#DIV/0!"}]
[null,"Ratio",{"$error":"#DIV/0!"},"Using this ratio, the a value and the minimum"]
[{"$nulls":3}," degrees of freedom (n-1) [C19], use the Fmax table"]
["min df used in calculation",null,-1,"to determine whether the Fmax value indicates the "]
["number of groups (a)",null,4,"variances among the groups are non-homogeneous."]

{"sheet":"Fmax table","index":3,"n_rows":34,"n_cols":15,"rows_kept":34,"flags":["formulas_cached_only"]}
["Critical values of F max"]
[]
[null,null,"a",2,3,4,5,6,7,8,9,10,11,12]
[null,"n-1"]
[null,2,null,{"v":39,"d":"39.0"},87.5,142,202,266,333,403,475,550,626,704," ¨  0.05"]
[{"$nulls":3},199,448,729,1036,1362,1705,2063,2432,2813,3204,3605," ¨  0.01"]
[null,3,null,15.4,27.8,39.2,50.7,{"v":62,"d":"62.0"},72.9,83.5,93.9,104,114,124]
[{"$nulls":3},47.5,85,120,151,184,216,249,281,310,337,361]
[null,4,null,{"v":9.6,"d":"9.60"},15.5,20.6,25.2,29.5,33.6,37.5,41.1,44.6,{"v":48,"d":"48.0"},51.4]
[{"$nulls":3},23.2,37,49,59,69,79,89,97,106,113,120]
[null,5,null,7.15,10.8,13.7,16.3,18.7,20.8,22.9,24.7,26.5,28.2,29.9]
[{"$nulls":3},14.9,22,28,33,38,42,46,50,54,57,60]
[null,6,null,5.82,8.38,10.4,12.1,13.7,{"v":15,"d":"15.0"},16.3,17.5,18.6,19.7,20.7]
[{"$nulls":3},11.1,15.5,19.1,22,25,27,30,32,34,36,37]
[null,7,null,4.99,6.94,8.44,{"v":9.7,"d":"9.70"},10.8,11.8,12.7,13.5,14.3,15.1,15.8]
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