# Biological and technical replicates - mixed model?

I'm trying to make sure I use the correct statistical tests on a group of experiments. Suppose I perform 5 experiments. In each experiment a single batch of cells is partitioned into 6 batches of equal size, 3 receive one treatment, and 3 receive another. After a period of time I take a measurement. So I have 5 experiments (biological replicates) x 2 treatments x 3 technical replicates each.

Here is the data:

structure(list(Experiment = c("a", "a", "a", "a", "a", "a", "b",
"b", "b", "b", "b", "b", "c", "c", "c", "c", "c", "c", "a", "a",
"a", "a", "a", "a", "b", "b", "b", "b", "b", "b", "c", "c", "c",
"c", "c", "c", "d", "d", "d", "d", "d", "d", "e", "e", "e", "e",
"e", "e"), Replicate = structure(c(1L, 2L, 3L, 1L, 2L, 3L, 1L,
2L, 3L, 1L, 2L, 3L, 1L, 2L, 3L, 1L, 2L, 3L, 1L, 2L, 3L, 1L, 2L,
3L, 1L, 2L, 3L, 1L, 2L, 3L, 1L, 2L, 3L, 1L, 2L, 3L, 1L, 2L, 3L,
1L, 2L, 3L, 1L, 2L, 3L, 1L, 2L, 3L), .Label = c("1", "2", "3"
), class = "factor"), Condition = c("Control", "Control", "Control",
"Treatment", "Treatment", "Treatment", "Control", "Control",
"Control", "Treatment", "Treatment", "Treatment", "Control",
"Control", "Control", "Treatment", "Treatment", "Treatment",
"Control", "Control", "Control", "Treatment", "Treatment", "Treatment",
"Control", "Control", "Control", "Treatment", "Treatment", "Treatment",
"Control", "Control", "Control", "Treatment", "Treatment", "Treatment",
"Control", "Control", "Control", "Treatment", "Treatment", "Treatment",
"Control", "Control", "Control", "Treatment", "Treatment", "Treatment"
), Outcome = c(4.587, 4.317, 2.701, 5.293, 6.341, 4.222, 1.922,
2, 1.815, 1.515, 2.435, 2.408, 2.741, 3.1, 4.832, 3.851, 5.251,
4.796, 4.587, 4.317, 2.701, 5.293, 6.341, 4.222, 1.922, 2, 1.815,
1.515, 2.435, 2.408, 2.741, 3.1, 4.832, 3.851, 5.251, 4.796,
4.34262726045549, 5.07005370965656, 3.023745836476, 5.23437121243791,
6.38505931216395, 3.72020626149008, 1.8174210928025, 2.03374053072335,
2.24793604273508, 1.43128735459152, 1.96194778022775, 3.2230322670882
)), row.names = c("7", "8", "9", "10", "11", "12", "24", "25",
"26", "30", "31", "32", "36", "37", "38", "42", "43", "44", "71",
"81", "91", "101", "111", "121", "241", "251", "261", "301",
"311", "321", "361", "371", "381", "421", "431", "441", "72",
"82", "92", "102", "112", "122", "242", "252", "262", "302",
"312", "322"), .Names = c("Experiment", "Replicate", "Condition",
"Outcome"), class = "data.frame")


My question is, would it be appropriate to model this with a mixed model? If so, would this model be proper:

lmer(data = experiment_data, Outcome~Condition + (1|Experiment/Replicate))


Or do I even need to include replicate in here? Can I just do:

lmer(data = experiment_data, Outcome~Condition + (1|Experiment))


I know one safe way to analyze the data would be to pool the technical replicates into a single mean value, but this seems like a waste of data. Furthermore, I'm interested in looking at how much variability is induced by technical and biological replication.

Thank you for the help!