Yes, you are just inputing the data wrong. ANOVA in mathematica needs to labeled.
I assume you are just placing the list
list ={{2.749, 2.649, 2.689, 2.679, 2.679, 2.699, 2.699, 2.699, 2.749,
2.749, 2.779, 2.799, 2.799, 2.799, 2.799, 2.799, 2.799, 2.799,
2.799}, {2.849, 2.9465, 2.899, 2.899, 2.899, 2.849, 2.824, 2.859,
2.899, 2.897, 2.899, 2.849, 2.824, 2.8485, 2.899, 2.8485, 2.92,
2.874, 2.859, 2.891, 2.899, 2.899, 2.899, 2.899, 2.899, 2.899,
2.899, 2.899, 2.899, 2.899, 2.949, 2.899, 2.899, 2.899,
2.979}, {2.998, 2.998, 2.999, 2.999, 2.999, 2.999, 2.999, 2.999,
2.999, 3.097, 3.099, 3.099, 3.099, 3.299, 3.199, 3.199, 3.399}}
ANOVA[list]
You need to label the data. Assuming each of the sublists is from a separate factor (i.e. "Treatement") then this should do the trick,
labeledlist=Flatten[MapIndexed[{First@#2, #1} &,
{{2.749, 2.649, 2.689, 2.679,
2.679, 2.699, 2.699, 2.699, 2.749, 2.749, 2.779, 2.799, 2.799,
2.799, 2.799, 2.799, 2.799, 2.799, 2.799}, {2.849, 2.9465, 2.899,
2.899, 2.899, 2.849, 2.824, 2.859, 2.899, 2.897, 2.899, 2.849,
2.824, 2.8485, 2.899, 2.8485, 2.92, 2.874, 2.859, 2.891, 2.899,
2.899, 2.899, 2.899, 2.899, 2.899, 2.899, 2.899, 2.899, 2.899,
2.949, 2.899, 2.899, 2.899, 2.979}, {2.998, 2.998, 2.999, 2.999,
2.999, 2.999, 2.999, 2.999, 2.999, 3.097, 3.099, 3.099, 3.099,
3.299, 3.199, 3.199, 3.399}}, {2}], 1]]
{{1, 2.749}, {1, 2.649}, {1, 2.689}, {1, 2.679}, {1, 2.679}, {1,
2.699}, {1, 2.699}, {1, 2.699}, {1, 2.749}, {1, 2.749}, {1,
2.779}, {1, 2.799}, {1, 2.799}, {1, 2.799}, {1, 2.799}, {1,
2.799}, {1, 2.799}, {1, 2.799}, {1, 2.799}, {2, 2.849}, {2,
2.9465}, {2, 2.899}, {2, 2.899}, {2, 2.899}, {2, 2.849}, {2,
2.824}, {2, 2.859}, {2, 2.899}, {2, 2.897}, {2, 2.899}, {2,
2.849}, {2, 2.824}, {2, 2.8485}, {2, 2.899}, {2, 2.8485}, {2,
2.92}, {2, 2.874}, {2, 2.859}, {2, 2.891}, {2, 2.899}, {2,
2.899}, {2, 2.899}, {2, 2.899}, {2, 2.899}, {2, 2.899}, {2,
2.899}, {2, 2.899}, {2, 2.899}, {2, 2.899}, {2, 2.949}, {2,
2.899}, {2, 2.899}, {2, 2.899}, {2, 2.979}, {3, 2.998}, {3,
2.998}, {3, 2.999}, {3, 2.999}, {3, 2.999}, {3, 2.999}, {3,
2.999}, {3, 2.999}, {3, 2.999}, {3, 3.097}, {3, 3.099}, {3,
3.099}, {3, 3.099}, {3, 3.299}, {3, 3.199}, {3, 3.199}, {3, 3.399}}
Then putting this in ANOVA gives you the one-way analysis.
ANOVA[labeledlist]
If you want to make sure it is doing it correctly you can check with LinearModelFit[]
test=LinearModelFit[labeledlsit, x, x, NominalVariables -> x]
test["ANOVATable"]
Note that if you do not use NominalVariables, it treats the labels as continuous variables and therefore the statistics are a bit different (However it shouldn't change too much) But this should allow you more control over the model you want to check against.