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By definition, standard deviation is the square root of variance.
The standard deviation reported by ARM is the square root of the Error
Mean Square (EMS) from the AOV table. When trial data is analyzed as a
randomized complete block (RCB), ARM performs a two way analysis of
variance (AOV). As a result, both the treatment and the replicate sum of
squares are partitioned from the error sum of squares.
Sometimes a user attempts to verify the standard deviation calculated
in ARM by using a spreadsheet or a scientific calculator. It is
important to note that the standard deviation calculated by a
spreadsheet or a scientific calculator is typically based on a one way
AOV. The EMS (and thus the standard deviation) calculated for a one way
ANOVA is different than that calculated for a two way AOV, so standard
deviation calculated by ARM for a RCB experimental design will almost
always be different than the standard deviation calculated using a
spreadsheet or scientific calculator. In other words, the variance (EMS)
is not the same when calculated for a two way ANOVA as a one way ANOVA.
ARM performs a one way AOV only when analyzing trial data as a
completely random experimental design. For a completely random design,
the standard deviation calculated by Excel or a scientific calculator
will match the one calculated by ARM. |
