Lets say I have 2 treatments: Vehicle and tmt A and 3 replicates each
for expt 1: My read outs for assay X are vehicle: 123, 125, 124, Avg 124
for ttmt A are 60 62 64, Avg 62.
Treatment A causes 50% reduction from vehicle. However, n=3 is too few n to do a regular t-test so, I repeat the expt and readouts for expt 2 are Vehicle: 440, 442, 444, avg 442; ttmt A: 218 219 220 avg 219, 49.5% reduction
Now, if I were to divide each data point with the vehicle average of the respective experiments the data (and expressed as percent of vehicle) would look like this: Expt 1: Vehicle 99.1, 100.8, 100 AVg 100; ttmt A 48.4, 50, 51.6 Avg 50%
Expt 2: Vehicle 99.5, 100, 100.4 avg 100, ttmt A 49.3, 49.5, 49.7 avg 49.5%
Now, my question is, after I do this conversion, can I combine the data and compare combined vehicle to combined ttmt A for statistical purpose?
Why can I or why can I not?
You can use a 2-way ANOVA and use "DAY" as a variable. Have you replicated the experiment a third time?
Andrew is right you should compute a Multiway ANOVA.
With a right table it's easy to compute with R :
anova(lm(Response~Factor1*Factor2,data=yourtable))
Please see attach file for script and results of your example.
Thanks for your answers.
No I havent replicated it a third time, but if I were to and got similar results, I still want to know if I can combine the data, From Cyril's answer, it looks like I can combine just the raw data and run a Multiway ANOVA. I will try this with my real data and let you know.
What you are doing is officially called meta-analysis (the subject-level version of this rather than the summary-level version). The previous suggestions deal with the maths, but you need to be sure that the two experiments are sufficiently similar to make it sensible to combine their results. There is a huge literature on this area! Another closely allied area is multicentre trials, which can be analysed in virtually the same way
I strongly agree with Peter that you will have to be careful about which corrections you would have to make to your critical values when combining data of two experiments.
Moreover, in your initial question you said that your concern was the small number of observations in Exp. 1. Please note that if you conduct a multi-way ANOVA, this will NOT increase the number of cases you have, as you will also have to consider the interaction of Exp. number with treatment. In general, the number of observations you have will usually not be regarded sufficient for an ANOVA in any case. There is a bunch of literature on this topic, too (at least in psychology), and usually at least 20 observations per cell are recommended
Dear Aenne,
Mathematically speaking, there is no exigence of more than 3 observation in ANOVA.
I think that the question is more on the type I error made by computing ANOVA with only three observation than the 'legitimacy' of the analysis.
Combining samples and analyzing them as if they were the same single sample is not appropriate and not desirable. The replication is a strength of the work you describe. I am in agreement with Peter and Aenne's suggestion that you approach the problem with meta analysis. You might also look at Robert Rosenthal's contrast analysis.
Harini,
Are you familiar with an area of statistics called Design of Experiments? The blocking you did with your data, by replicating it on different days, is a staple of good design. U of Wisc-Madison was home to one of the most prolific statisticians of the last 50 years, George Box. If you can look through his work, I'm sure you will see similar issues to what you see.
There is an assumption among scientists that things work the same way, day after day. Your data proves this wrong. You don't need to use meta-analysis. You need to use blocking. Blocking acts like a correction factor for your data. Since your block is "Day", it will be a random effect. A Multiway ANOVA will work well. You will have to use good stats software, no calculators or Excel.
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