check your calculation for the sums of squares. They _cannot_ be negative.
the computational form appears to allow a negative value, but if you transform it mathematically into the definitional form (or the reverse) you will see that: the definition form cannot be negative, therefore the computational form cannot. Jay Ronny Richardson wrote: > Several people wrote to tell me that my results from Excel were correct and > the Bluman textbook had the wrong answer. I'm continuing to experiment with > ANOVA and I'm hoping that the list can help me answer two additional > questions I have. > > First, in experimenting around with a 3x3 ANOVA without replication, I > filled the cells with =RAND() to generate random numbers and I happened to > get the following: > > SS df MS F > Rows -2.105562167 2 -1.052781083 -1.336268078 > Columns -0.226230909 2 -0.113115455 -0.143574551 > Error 3.151406819 4 0.787851705 > Total 0.819613743 8 > > Unfortunately, I did not convert the random number functions to numbers so > the specific data I used to generate this table was lost when the worksheet > recalculated. > > I've repeated this experiment several times and sometimes the sums of > squares are positive and sometimes one or more of them are negative. Is > this a bug in Excel? I don't see how a sum of *square* can be negative even > though I am using random numbers so all of the SS should be in error. > > Second, Excel offers a two-factor ANOVA with and without replication. None > of the examples of two-way ANOVA in any of the textbooks that I own shows a > two-way ANOVA without replication. It seems counter intuitive to me to > perform ANOVA with a sample size of one in each cell. Am I missing > something here? > > The output from with and without replication is significantly different as > well. Using made up data, without replication, I get the following: > > SS df MS F P-value F crit > Rows 56.25 1 56.25 25 0.1257 161.4462 > Columns 110.25 1 110.25 49 0.0903 161.4462 > Error 2.25 1 2.25 > Total 168.75 3 > > Using made up data, with replication, I get the following > > SS df MS F P-value F crit > Sample 234.38 1 234.38 130.8140 0.0000 4.3513 > Columns 693.38 1 693.38 387.0000 0.0000 4.3513 > Interaction 0.38 1 0.38 0.2093 0.6522 4.3513 > Within 35.83 20 1.79 > Total 963.96 23 > > It makes no sense to me to call them "rows and columns" without replication > and "sample and columns" with replication. It sort of makes sense not to > get interaction without replication. I am assuming that with a sample size > of one in each cell that there is not enough information to compute > interactions. > > Ronny Richardson > .. > .. > ================================================================= > Instructions for joining and leaving this list, remarks about the > problem of INAPPROPRIATE MESSAGES, and archives are available at: > .. http://jse.stat.ncsu.edu/ . > ================================================================= -- Jay Warner Principal Scientist Warner Consulting, Inc. 4444 North Green Bay Road Racine, WI 53404-1216 USA Ph: (262) 634-9100 FAX: (262) 681-1133 email: [EMAIL PROTECTED] web: http://www.a2q.com The A2Q Method (tm) -- What do you want to improve today? . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
