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{"sheet":"Sample Size","index":0,"n_rows":29,"n_cols":23,"rows_kept":29,"cut":false,"hidden":false,"merged":[[20,6,20,8],[16,16,16,17],[14,10,14,11],[15,10,15,11],[16,10,16,11],[14,13,14,14],[15,13,15,14],[16,13,16,14],[28,14,28,16],[28,18,28,20],[28,22,28,24],[2,1,2,6],[3,1,3,3],[20,22,20,24],[20,14,20,16],[20,18,20,20],[3,12,3,13],[3,4,3,5],[3,8,3,11],[3,18,3,20],[3,21,3,24],[12,2,12,20],[11,2,11,20],[14,16,14,17],[13,16,13,17],[26,22,26,24],[27,10,27,12],[27,14,27,16],[27,18,27,20],[27,22,27,24],[26,10,26,12],[26,14,26,16],[26,18,26,20],[24,14,24,16],[24,18,24,20],[24,22,24,24],[25,10,25,12],[25,18,25,20],[25,22,25,24],[25,14,25,16],[22,22,22,24],[22,14,22,16],[22,18,22,20],[23,10,23,12],[23,14,23,16],[23,18,23,20],[23,22,23,24],[22,10,22,12],[30,10,30,11],[27,1,27,4],[28,1,28,4],[22,6,22,8],[23,6,23,8],[24,6,24,8],[25,6,25,8],[26,6,26,8],[24,10,24,12],[27,6,27,8],[28,6,28,8],[13,7,13,8],[28,10,28,12],[26,1,26,4],[22,1,22,4],[7,2,7,3],[7,6,7,7],[23,1,23,4],[24,1,24,4],[25,1,25,4],[15,4,15,5],[16,4,16,5],[14,7,14,8],[15,7,15,8],[21,6,21,8],[14,4,14,5],[16,7,16,8],[21,22,21,24],[8,10,8,11],[7,10,7,11],[2,16,2,24],[7,14,7,15],[7,18,7,19],[3,16,3,17],[2,8,2,14],[21,10,21,12],[21,14,21,16],[21,18,21,20],[6,1,6,17],[20,10,20,12],[13,13,13,14],[13,10,13,11],[15,16,15,17]]}
[null,"Sample Size for Linear Models with Fixed Predictors and Uncorrelated, Balanced Data a "]
[]
[null,"Step 1: Enter Alpha Error Rate",null,null,null,null,null,null,"Step 2: Enter Power Level",null,null,null,null,null,null,null,"Step 3: Enter Model Degrees of Freedom"]
[null,"alpha (a) =",null,null,0.05,null,null,null,"power (1-b) =",null,null,null,0.8,null,null,null,"df 1 = ",null,3,null,null,"(Must be integer)"]
[]
[]
[null,"Step 4: Enter One Effect Size Value and Click the Corresponding \"Find n\" Button"]
[null,"d = ",0.75,null,null,"r =",-0.47,null,null,"r2 = ",9.35E-2,null,null,"f =",0.42499999999999999,null,null,"f2 =",6.2399999999999997E-2]
[]
[]
[]
[null,null,"In the absence of prior research to estimate effect sizes, Cohen b offers"]
[null,null,"the following guidelines for effect sizes:"]
[null,null,null,null,null,null,null,"d",null,null,"r",null,null,"f",null,null,"f2"]
[null,null,null,null,"  Small",null,"=",0.2,null,null,0.1,null,null,0.1,null,null,0.02]
[null,null,null,null,"  Medium",null,"=",0.5,null,null,0.3,null,null,0.25,null,null,0.15]
[null,null,null,null,"  Large",null,"=",0.8,null,null,0.5,null,null,0.4,null,null,0.35]
[]
[]
[]
[null,"Results",null,null,null,null,"Non-central",null,null,null,"Laubscher's",null,null,null,"Laubscher's",null,null,null,"Tiku's",null,null,null,"Patnaik's"]
[null,null,null,null,null,null,"F",null,null,null,"Cube Root c ",null,null,null,"Square Root c ",null,null,null,"3-Moment c ",null,null,null,"2-Moment c,d "]
[null,"Total Sample n =",null,null,null,null,110,null,null,null,109,null,null,null,109,null,null,null,111,null,null,null,109]
[null,"power (1-b) =",null,null,null,null,0.80128220902642577,null,null,null,0.80325294922876944,null,null,null,0.80170540335218687,null,null,null,0.80064916026240596,null,null,null,0.80208930554904712]
[null,"noncen. para. (λ) =",null,null,null,null,11.345835631549917,null,null,null,11.242691671263101,null,null,null,11.242691671263101,null,null,null,11.448979591836736,null,null,null,11.242691671263101]
[null,"df 2 =",null,null,null,null,106,null,null,null,105,null,null,null,105,null,null,null,107,null,null,null,105]
[null,"beta (b) =",null,null,null,null,0.19871779097357423,null,null,null,0.19674705077123056,null,null,null,0.19829459664781313,null,null,null,0.19935083973759404,null,null,null,0.19791069445095288]
[null,"F critical =",null,null,null,null,2.690303433823888,null,null,null,2.6911329009270792,null,null,null,2.6911329009270792,null,null,null,2.6894897720052375,null,null,null,2.6911329009270792]
[null,"effect size f2 =",null,null,null,null,0.10314396028681744,null,null,null,0.10314396028681744,null,null,null,0.10314396028681744,null,null,null,0.10314396028681744,null,null,null,0.10314396028681744]

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[null,"Calculate Power for Linear Models with Fixed Predictors and Balanced Designs"]
[]
[null,"Step 1: Enter Alpha Error Rate",null,null,null,null,null,null,"Step 2: Enter Sample Size",null,null,null,null,null,null,"Step 3: Enter Model Degrees of Freedom"]
[null,"alpha (a) =",null,null,0.05,null,null,null,"n =",135,null,null,null,null,null,"df 1 = ",null,2,null,null,"(Must be integer)"]
[]
[]
[null,"Step 4: Enter One Effect Size Value and Click the Corresponding \"Find Power\" Button"]
[null,"d = ",0.32,null,null,"r =",0.19989999999999999,null,null,"r2 = ",0.1173,null,null,"f =",0.16,null,null,"f2 =",0.39285700000000001]
[]
[]
[]
[]
[]
[null,"Results",null,null,null,null,"Non-central",null,null,null,"Laubscher's",null,null,null,"Laubscher's",null,null,null,"Tiku's",null,null,null,"Patnaik's"]
[null,null,null,null,null,null,"F",null,null,null,"Cube Root b ",null,null,null,"Square Root b ",null,null,null,"3-Moment b ",null,null,null,"2-Moment b,c "]
[null,"Power (1-b) =",null,null,null,null,0.35753201594091816,null,null,null,0.34490548396207099,null,null,null,0.36463360418596746,null,null,null,0.3557655500327247,null,null,null,0.34469747074393675]
[null,"alpha =",null,null,null,null,0.05,null,null,null,0.05,null,null,null,0.05,null,null,null,0.05,null,null,null,0.05]
[null,"sample size n =",null,null,null,null,135,null,null,null,135,null,null,null,135,null,null,null,135,null,null,null,135]
[null,"df 1 = ",null,null,null,null,2,null,null,null,2,null,null,null,2,null,null,null,2,null,null,null,2]
[null,"noncen. para. (λ) =",null,null,null,null,3.456,null,null,null,3.456,null,null,null,3.456,null,null,null,3.456,null,null,null,3.456]
[null,"df 2 =",null,null,null,null,132,null,null,null,132,null,null,null,132,null,null,null,132,null,null,null,132]
[null,"beta (b) =",null,null,null,null,0.6424679840590819,null,null,null,0.65509451603792901,null,null,null,0.63536639581403254,null,null,null,0.6442344499672753,null,null,null,0.65530252925606325]
[null,"F critical =",null,null,null,null,3.0647606768696747,null,null,null,3.0647606768696747,null,null,null,3.0647606768696747,null,null,null,3.0647606768696747,null,null,null,3.0647606768696747]
[null,"effect size f2 =",null,null,null,null,2.5600000000000001E-2,null,null,null,2.5600000000000001E-2,null,null,null,2.5600000000000001E-2,null,null,null,2.5600000000000001E-2,null,null,null,2.5600000000000001E-2]

{"sheet":"ES Conversion","index":2,"n_rows":17,"n_cols":16,"rows_kept":17,"cut":false,"hidden":false,"merged":[]}
[null,"Convert Among Effect Size Measures"]
[]
[]
[]
[null,"Effect Size Type",null,"Enter Effect Size Below",null,"d",null,"r",null,"r2 ",null,"f",null,"f2  ",null,"h2= r2 "]
[]
[null,"d ",null,0.47,"=","---",null,{"$f":"IF(SIGN(D7)-1,-1*SQRT(D7^2/(D7^2+4)),SQRT(D7^2/(D7^2+4)))","v":0.22876802685600006},null,{"$f":"H7^2","v":5.2334810111587568E-2},null,{"$f":"SQRT(N7)","v":0.23499999999999999},null,{"$f":"J7/(1-J7)","v":5.5224999999999989E-2},null,{"$f":"($L$7^2)/(1+$L$7^2)","v":5.2334810111587568E-2}]
[]
[null,"r ",null,0.23,"=",{"$f":"D9*2 / SQRT(1-D9^2)","v":0.472672040177118},null,"---",null,{"$f":"IF(D9>1, \"error\", IF(D9<-1, \"error\",D9^2))","v":5.2900000000000003E-2},null,{"$f":"SQRT(N9)","v":0.23633602008855897},null,{"$f":"J9/(1-J9)","v":5.5854714391299756E-2},null,{"$f":"$J$9","v":5.2900000000000003E-2}]
[]
[null,"r2",null,0.09,"=",{"$f":"H11*2 / SQRT(1-H11^2)","v":0.62897090203315098},null,{"$f":"SQRT(P11)","v":0.3},null,"---",null,{"$f":"SQRT(N11)","v":0.31448545101657549},null,{"$f":"P11/(1-P11)","v":9.8901098901098897E-2},null,{"$f":"IF(SIGN($D$11)=-1, \"error\",IF($D$11>1,\"error\",$D$11))","v":0.09}]
[]
[null,"f ",null,0.25,"=",{"$f":"IF(SIGN(D13)=-1, \"error\", D13*2)","v":0.5},null,{"$f":"SQRT(F13^2/(F13^2+4))","v":0.24253562503633297},null,{"$f":"H13^2","v":5.8823529411764705E-2},null,"---",null,{"$f":"J13/(1-J13)","v":6.25E-2},null,{"$f":"$J$13","v":5.8823529411764705E-2}]
[]
[null,"f2",null,5.357E-2,"=",{"$f":"L15*2","v":0.46290387771112912},null,{"$f":"SQRT(F15^2/(F15^2+4))","v":0.22549095467196781},null,{"$f":"H15^2","v":5.0846170638875442E-2},null,{"$f":"SQRT(D15)","v":0.23145193885556456},null,"---",null,{"$f":"$J$15","v":5.0846170638875442E-2}]
[]
[null,"h2= r2",null,0.04,"=",{"$f":"H17*2 / SQRT(1-H17^2)","v":0.40824829046386307},null,{"$f":"IF(D17>1, \"error\", IF(D17<0, \"error\",SQRT(D17)))","v":0.2},null,{"$f":"H17^2","v":4.0000000000000008E-2},null,{"$f":"SQRT(N17)","v":0.20412414523193154},null,{"$f":"J17/(1-J17)","v":4.1666666666666678E-2},null,"---"]

{"sheet":"ES Calculations","index":3,"n_rows":121,"n_cols":13,"rows_kept":121,"cut":false,"hidden":false,"merged":[]}
["Rule of thumb I have discovered - for random IV models (non-fixed predictors), sample size can be determined"]
["by find n for fixed model, then adding number of predictors to that n for the adjusted n."]
["Gatsonis and Sampson (1989) seem to say same thing, n + p + 1. See commend in NCSS manual about formula, they note N+ (or -) predictors."]
["Liu 2013 book discusses formula (pages not identified in Google view) - looks like n + predictors tested + 1, this differs a bit"]
[]
["Example: adjusted r for one predictor based on t-ratio is .33426, calls for n of 65; total of 9 predictors."]
["Empirical power from three tests (all predictors have same correlation with Y) is .728, .732, .774 with 500 replications."]
["Empircal power from three tests with n = 65 + 9 = 74 (with 1500 replications) were .797, .804, .791"]
["Gatsonis and Sampson would be n = 65 + 9 + 1 = 75 (tested with 1500 rep) power were .792 .806 .808"]
[]
["Redoing this with 50,000 reps:  Looks like correct n is fixed n + all predictors + 1"]
["n = 74",null,null,null,"n = 75"]
["empircal power = .7899, .7971, .7933",null,null,null,".8036, .8001, .8003"]
[]
[null,null,null,null,null,{"$f":"(1427.57*2)/9993","v":0.2857139997998599}]
[null,null,null,null,null,null,null,null,null,"r2","r",null,"Cohen p. 411"]
[null,"f2 = (df variable *F) / df error",null,null,null,null,"delta R2",null,1,0.03,{"$f":"J17^0.5","v":0.17320508075688773},null,"R2 = f2 / (1+f2)"]
[null,"F","df","error df","f2","r_sp","r_sp2",null,2,0.03,{"$f":"J18^0.5","v":0.17320508075688773}]
["x",20.963000000000001,12,307,{"$f":"(B19*C19)/D19","v":0.8194006514657981},null,{"$f":"E19/(12+E19)","v":6.3918795717809632E-2},"<correct?",3,0.08,0.28284271247461901]
["horse",10.212,1,387,{"$f":"(B20*C20)/D20","v":2.6387596899224805E-2},null,null,"not for",4,0.08,0.28284271247461901]
["weight",55.005000000000003,1,387,{"$f":"(B21*C21)/D21","v":0.14213178294573645},null,null,"df > 1",5,0.11,0.33166247903553997]
["origin",16.309999999999999,2,379,8.6068601583113455E-2,null,null,"works only with df1",6,0.11,0.33166247903553997]
[null,"f2 = (t^2 * df) / df error",null,null,null,null,null,"tests?",7,null,0]
[null,"t","df","error df","f2",null,null,null,8,null,0]
["displace",-12.664,1,325,{"$f":"(B25^2*C25)/D25","v":0.49346737230769228},null,null,null,9,null,0]
["horse",-3.1960000000000002,1,387,{"$f":"(B26^2*C26)/D26","v":2.6393839793281658E-2},null,null,null,"Sum 1-9",{"$f":"SUM(J17:J25)","v":0.44},"divided by 8"]
["weight",-7.4169999999999998,1,387,0.14214958397932817,null,null,null,"Left",{"$f":"J26-J20","v":0.36},{"$f":"J27/8","v":4.4999999999999998E-2}]
[]
["corr_data_50k_4predictors.dta",null,null,"R2 =",0.3286,null,"f2 ",null,"delta R2","f2",null,{"$f":"0.6025-0.05","v":0.55249999999999999}]
[null,"b","se","t","df","error df","from t","r_sp","r_sp2","from r_sp2"]
["z1",0.1732051,7.4859000000000002E-3,{"$f":"B31/C31","v":23.137511855621902},1,9993,{"$f":"(D31^2*E31)/F31","v":5.3571945848998707E-2},{"$f":"(D31*(1-$E$29)^0.5) / (F31^0.5)","v":0.18965285245157198},{"$f":"H31^2","v":3.5968204443017737E-2},{"$f":"I31/(1-$E$29)","v":5.3571945848998714E-2}]
["z2",7.4773099999999995E-2,3.8078999999999999E-3,{"$f":"B32/C32","v":19.636308726594709},1,49995,{"$f":"(D32^2*E32)/F32","v":7.7124636544882398E-3},{"$f":"(D32*(1-$E$29)^0.5) / (F32^0.5)","v":7.1959350314072482E-2},{"$f":"H32^2","v":5.1781480976234038E-3},{"$f":"I32/(1-$E$29)","v":7.7124636544882389E-3}]
["z3",0.15426770000000001,3.7750000000000001E-3,40.865615894039735,1,49995,3.3403311579141774E-2,0.14975641353289609,2.2426983394235784E-2,3.3403311579141767E-2]
["z4",0.27191480000000001,3.7750000000000001E-3,72.030410596026485,1,49995,0.10377797881052434,0.26396313184493408,6.9676534973386051E-2,0.10377797881052435]
["z5 z6",null,null,null,null,null,null,"delta R2 of Iv drop from above equation =",null,null,null,6.9677000000000003E-2]
[null,null,null,null,null,null,null," Model R2 from dropping IV =",null,null,null,{"$f":"E26-L35","v":-4.3283160206718345E-2}]
[null,null,null,null,null,null,"backwards"]
["Total Model R2 =",null,null,null,null,5.8799999999999998E-2,"r",null,null,"Partial r is the adjusted ES after controlling for"]
["Model R2 without predictors =",null,null,null,null,0,{"$f":"F39^0.5","v":0},null,null,"predicted variance in model. E.g. f -> r is original r"]
["Change in R2 adding predictor = ",null,null,null,null,{"$f":"F38-F39","v":5.8799999999999998E-2},"d","r (partial r)","r2","and adjusted f to r is partial r."]
["f2 from change in R2 and total R2 =",null,null,null,null,{"$f":"F40/(1-F38)","v":6.2473438164045894E-2},{"$f":"((F41)^0.5)*2","v":0.49989374136528614},{"$f":"G41/((G41^2+4)^0.5)","v":0.24248711305964279},{"$f":"H41^2","v":5.8799999999999984E-2}]
["Adjusted f2 due to model R2 without predictors =",null,null,null,null,{"$f":"F41 / (1-F38)^0.5","v":6.4395341149730112E-2},null,"Use d or f for adjustments, not f2 since it is non-linear."]
["Original f",null,null,null,null,{"$f":"F41^0.5","v":0.24994687068264307}]
["adjusted f",null,null,null,null,{"$f":"F43 / (1-F38)^0.5","v":0.25763611672295239},"Related among r, partial r, semipartial r, etc."]
[null,null,null,null,null,null,"r = semipartial r if all IV are uncorrelated"]
["adjusted f2 to enter in power calculations as added IV =",null,null,null,null,{"$f":"F42","v":6.4395341149730112E-2},"partial r = adjusted r taking into account other predictors"]
[null,null,null,null,null,null,"E.g., original r y.z4 = .4330, z4 uncorrleated with other Z, model R2 = .4375, "]
[null,null,null,null,null,null,"then partial r is .50"]
["Thoughts about adjusted ES - examples Cohen provides (I think, need to study all examples), has the "]
["covariates as unrelated to the variable added. In that case, we can adjust (inflate) the expected ES. However,"]
["if the covariates are correlated with added IV, then adjusting the ES may lead to an underpowered study since colinearity might not result in enlarged ES. "]
["Check math here. If correct, better to calculate ES from t or F ratio, and then do not adjust since this represents"]
["the ES that is likely to be realisitically observed. "]
["Example - use corr2data to calculate two files, one with correlated Ivs and one without, maintain same r between IV and DV in both - "]
["do the actual effect sizes increase or decrease? What happens when IV correlations are negative or positive?"]
[]
[]
[]
[]
[]
[]
["Example 1: data files with correlations",null,null,null,null,null,null,"Example 2: data files with correlations"]
[null,"Y","Z1","Z2","Z3","Z4",null,null,"Y","Z1","Z2","Z3","Z4"]
["Y",1,0.1,0.3,0.1,0.3,null,"Y",1,0.1,0.3,0.1,0.3]
["Z1",0.1,1,0,0,0,null,"Z1",0.1,1,0.2,0.2,0.2]
["Z2",0.3,0,1,0,0,null,"Z2",0.3,0.2,1,0.2,0.2]
["Z3",0.1,0,0,1,0,null,"Z3",0.1,0.2,0.2,1,0.2]
["Z4",0.3,0,0,0,1,null,"Z4",0.3,0.2,0.2,0.2,1]
[]
["Partial and semipartial correlations of y with",null,null,null,null,null,null,"Partial and semipartial correlations of y with"]
[]
["               Partial   Semipartial      Partial   Semipartial   Significance",null,null,null,null,null,null,"               Partial   Semipartial      Partial   Semipartial   Significance"]
["   Variable |    Corr.         Corr.      Corr.^2       Corr.^2          Value",null,null,null,null,null,null,"   Variable |    Corr.         Corr.      Corr.^2       Corr.^2          Value"]
["------------+-----------------------------------------------------------------",null,null,null,null,null,null,"------------+-----------------------------------------------------------------"]
["         z1 |   0.1111        0.1000       0.0123        0.0100         0.0000",null,null,null,null,null,null,"         z1 |   0.0000        0.0000       0.0000        0.0000         1.0000"]
["         z2 |   0.3180        0.3000       0.1011        0.0900         0.0000",null,null,null,null,null,null,"         z2 |   0.2510        0.2390       0.0630        0.0571         0.0000"]
["         z3 |   0.1111        0.1000       0.0123        0.0100         0.0000",null,null,null,null,null,null,"         z3 |   0.0000        0.0000       0.0000        0.0000         1.0000"]
["         z4 |   0.3180        0.3000       0.1011        0.0900         0.0000",null,null,null,null,null,null,"         z4 |   0.2510        0.2390       0.0630        0.0571         0.0000"]
[]
[null,null,null,null,null,null,null,"Note the delta-R2 is now 0.00 for Z1 and Z2; effect size is 0.00."]
[null,null,null,null,null,null,null,"For Z2 and Z4, the ES has decreased from .09 to .057"]
[]
["Example 3: data files with correlations",null,null,null,null,null,null,"Example 4: data files with correlations"]
[null,"Y","Z1","Z2","Z3","Z4",null,null,"Y","Z1","Z2","Z3","Z4"]
["Y",1,0.4,0.3,0.4,0.3,null,"Y",1,0.1,0.3,0.1,0.3]
["Z1",0.4,1,0.2,0.2,0.2,null,"Z1",0.1,1,-0.2,0.2,0.2]
["Z2",0.3,0.2,1,0.2,0.2,null,"Z2",0.3,-0.2,1,-0.2,-0.2]
["Z3",0.4,0.2,0.2,1,0.2,null,"Z3",0.1,0.2,-0.2,1,0.2]
["Z4",0.3,0.2,0.2,0.2,1,null,"Z4",0.3,0.2,-0.2,0.2,1]
[]
["Partial and semipartial correlations of y with",null,null,null,null,null,null,"Partial and semipartial correlations of y with"]
[]
["               Partial   Semipartial      Partial   Semipartial   Significance",null,null,null,null,null,null,"               Partial   Semipartial      Partial   Semipartial   Significance"]
["   Variable |    Corr.         Corr.      Corr.^2       Corr.^2          Value",null,null,null,null,null,null,"   Variable |    Corr.         Corr.      Corr.^2       Corr.^2          Value"]
["------------+-----------------------------------------------------------------",null,null,null,null,null,null,"------------+-----------------------------------------------------------------"]
["         z1 |   0.3098        0.2689       0.0960        0.0723         0.0000",null,null,null,null,null,null,"         z1 |   0.1025        0.0896       0.0105        0.0080         0.0000"]
["         z2 |   0.1781        0.1494       0.0317        0.0223         0.0000",null,null,null,null,null,null,"         z2 |   0.4078        0.3884       0.1663        0.1509         0.0000"]
["         z3 |   0.3098        0.2689       0.0960        0.0723         0.0000",null,null,null,null,null,null,"         z3 |   0.1025        0.0896       0.0105        0.0080         0.0000"]
["         z4 |   0.1781        0.1494       0.0317        0.0223         0.0000",null,null,null,null,null,null,"         z4 |   0.3536        0.3287       0.1250        0.1080         0.0000"]
[]
[null,null,null,null,null,null,null,"Note negative correlation increaes some ES and weakens others."]
[]
["Example 5: data files with correlations"]
[null,"Y","Z1","Z2","Z3","Z4"]
["Y",1,0.1,-0.3,0.1,0.3]
["Z1",0.1,1,-0.2,0.2,0.2]
["Z2",-0.3,-0.2,1,-0.2,-0.2]
["Z3",0.1,0.2,-0.2,1,0.2]
["Z4",0.3,0.2,-0.2,0.2,1]
[]
["Partial and semipartial correlations of y with"]
[]
["               Partial   Semipartial      Partial   Semipartial   Significance"]
["   Variable |    Corr.         Corr.      Corr.^2       Corr.^2          Value"]
["------------+-----------------------------------------------------------------"]
["         z1 |   0.0000        0.0000       0.0000        0.0000         1.0000"]
["         z2 |  -0.2510       -0.2390       0.0630        0.0571         0.0000"]
["         z3 |   0.0000        0.0000       0.0000        0.0000         1.0000"]
["         z4 |   0.2510        0.2390       0.0630        0.0571         0.0000"]
[]
["Making Z2 negatively correlated with all removes some ES like Example 2."]

{"sheet":"Working Formulas","index":4,"n_rows":59,"n_cols":11,"rows_kept":59,"cut":false,"hidden":false,"merged":[]}
[]
[null,"es r =",-0.431004,null,null,null,"num =",{"$f":"0.461-0.618*0.683","v":3.8905999999999996E-2}]
[null,"d =",{"$f":"C2*2 / SQRT(1-C2^2)","v":-0.95529227505188019},null,null,null,"dnom=",{"$f":"(1-0.683^2)^0.5","v":0.73041837326288539}]
[]
[null,"covar r =",0.34252700000000003,null,null,null,"sr2 =",{"$f":"H2/H3","v":5.3265363282417474E-2}]
[null,"adj d =",{"$f":"C3 /( (1-C5^2)^0.5)","v":-1.0168005914708917}]
[null,"adj r =",{"$f":"IF(SIGN(C6)-1,-1*SQRT(C6^2/(C6^2+4)),SQRT(C6^2/(C6^2+4)))","v":-0.4531940636590619}]
[]
[]
[null,"r2 =",0.17419999999999999]
[null,"r =",{"$f":"C10^0.5","v":0.4173727350941841}]
[]
[]
["My two-way ANCOVA"]
[null,null,"R2","R","Model "]
[null,null,0.4773,{"$f":"C16^0.5","v":0.69086901797663502},"factor1 factor2 b1 b2"]
[null,null,0.29160000000000003,{"$f":"C17^0.5","v":0.54},"factor1 b1 b2"]
[null,null,0.36,{"$f":"C18^0.5","v":0.6},"factor2 b1 b2"]
[null,null,0.17419999999999999,{"$f":"C19^0.5","v":0.4173727350941841},"b1 b2"]
[]
[null,null,"Delta R2","delta R"]
[null,null,{"$f":"C16-C18","v":0.11730000000000002},{"$f":"C22^0.5","v":0.34249087579087417},"factor1"]
[null,null,{"$f":"C16-C17","v":0.18569999999999998},{"$f":"C23^0.5","v":0.43092922852830484},"factor2"]
[]
[null,null,null,null,null,"Covariate+factor adjusted ES (covariate+factor r=.54 or .60)"]
[null,null,"Zero order R2","Zero order R",null,null,"adj ES","Pre Power","empirical power"]
[null,null,0.1173,{"$f":"C27^0.5","v":0.34249087579087417},"factor1",null,0.41465000000000002,0.628,0.63939999999999997," NA - no covariates in factorialsim"]
[null,null,0.18579999999999999,{"$f":"C28^0.5","v":0.43104524124504612},"factor2",null,0.49354999999999999,0.86299999999999999,0.88329999999999997]
[null,null,null,null,null,null,null,null,"   ^","   ^"]
[null,null,null,"Sample size per cell =",null,6,null,null,"15000 reps","factorial sim"]
[]
[null,null,null,null,"total n =",{"$f":"9*F30","v":54}]
[]
["*","The estimates of pre-power were estimated using the same procedure as used in ancova -- leave n as total n and just "]
[null,"adjust the effect size to account for the other model predictors. "]
["*","These estimates likely disagree with Cohen's 1988 since he adjusts sample size based on denominator df"]
[null,"and number of groups."]
["*","factorialsim (to use, must locate simdat.dta file in ado directory) reports values noted above. "]
[null,"Factorial sim does not estimate effects of covariates"]
[]
[]
["My two-way ANOVA (NO COVARIATES!)"]
[]
[null,null,"R2","R"]
[null,null,0.1173,{"$f":"C45^0.5","v":0.34249087579087417},"factor1"]
[null,null,0.1857,{"$f":"C46^0.5","v":0.4309292285283049},"factor2"]
[]
[null,null,null,null,null,"Covariate+factor adjusted ES (covariate+factor r=.54 or .60)"]
[null,null,"Zero order R2","Zero order R",null,null,"adj ES","Pre Power","empirical power"]
[null,null,0.117325,{"$f":"C50^0.5","v":0.342527371169079},"factor1",null,0.37461,0.4904,0.48309999999999997,0.49149999999999999,0.49199999999999999]
[null,null,0.1857645,{"$f":"C51^0.5","v":0.4310040603057006},"factor2",null,0.45319399999999999,0.75429999999999997,0.76400000000000001,0.76910000000000001,0.75409999999999999]
[null,null,null,null,null,null,null,null,null,null,"   ^"]
[null,null,null,"Sample size per cell =",null,6,null,null,"  ^","   ^","factorial sim"]
[null,null,null,null,null,null,null,null,"1500 reps","15000 reps"]
[null,null,null,null,"total n =",{"$f":"9*F53","v":54},null,null,"with ","no","with"]
[null,null,null,null,null,null,null,null,"interactions","interactions","interactions"]
[]
[null,null,null,null,null,null,null,null,"Note interactions F ratio is 0.00, no"]
[null,null,null,null,null,null,null,null,"effect at all, no correlation at all."]

{"sheet":"Cohen d","index":5,"n_rows":33,"n_cols":8,"rows_kept":33,"cut":false,"hidden":false,"merged":[]}
["Comparison of d values for unequal sample sizes"]
[]
["ANOVA of Cars data, MPG for US and Japanese cars"]
[null,null,null,"M","sd","VAR","n"]
[null,null,"American",20.13,6.3769999999999998,{"$f":"E5^2","v":40.666128999999998},248]
[null,null,"Japanese",30.45,6.09,{"$f":"E6^2","v":37.088099999999997},79]
[]
[]
[null,"t test results"]
[null,null,"t","df",null,"f2 from t","d from f2"]
[null,null,-12.664,325,null,{"$f":"(C11^2)/D11","v":0.49346737230769228},{"$f":"(F11^0.5)*2","v":1.4049446569992603}]
[]
[null,"ANOVA"]
[null,null,"F","dfb","df e","f2 from F","d from f2","d from F"]
[null,null,160.37899999999999,1,325,{"$f":"(C15*D15)/E15","v":0.49347384615384615},{"$f":"(F15^0.5)*2","v":1.4049538727714104},{"$f":"(E15*D15/C15)^0.5","v":1.4235342802072228}]
[]
[null,"d = (M1 - M2) / pooled SD",null,null,null,"Pooled SD = "]
[]
[null,null,null,null,"Num",{"$f":"(G5-1)*F5+(G6-1)*F6","v":12937.405662999998}]
[null,null,null,null,"Denom",{"$f":"G5+G6-2","v":325}]
[null,null,null,null,"Ratio",{"$f":"F19/F20","v":39.807402039999992}]
[null,null,null,null,"SQRT ",{"$f":"F21^0.5","v":6.3093107420700081}," = Pooled SD"]
[]
[null,null,null,null,"Mean Diff",{"$f":"D6-D5","v":10.32}]
[null,null,null,null,"d",{"$f":"F24/F22","v":1.6356778770123048}]
[]
[]
[null,"d unequal n"]
[null,null,"n_h",null,{"$f":"(2*G5*G6)/(G5+G6)","v":119.82874617737004}]
[null,null,"Mean n",null,{"$f":"(G5+G6)/2","v":163.5}]
[null,null,"2t/SQRT(df)",null,{"$f":"C11*2/(D11^0.5)","v":-1.4049446569992603},null,null,"So d from t underestimates ES in absolute value."]
[null,null,"SQRT(n_h/Mean n)",null,{"$f":"(E30/E29)^0.5","v":1.1680955540350593}]
[null,null,"t =",null,{"$f":"E31*E32","v":-1.6411096075061473}]