How to deal with averaging before calculating statistics

[Monique]

I have the following data set: condition A and condition B, with 4 replicates recorded over 3 time periods.

Hypothetically you can think of it as measuring the height of the sun in the sky in winter (A) compared to the summer (B), in 4 nearby villages (independent observations) over 3 days (the assumption is that the height is stable over the consecutive days).

Since I want to know the true behavior of each replicate, I average the data of the three time periods (to take out any irrelevant fluctuations). This is the key, but it is also a problem (I think).

Now I calculate the average and the SD of condition A and condition B (based on the 3-day average of each replicate) and want to do a statistics test on the height at t=12:00.

My question: what is the best way to deal with the data? If I perform a t-test on the average then a condition would have 4 independent replicas, but in fact underneath there are 3 dependent replicas.

Am I over-inflating the significance by doing that and how can it be corrected? Any thoughts are welcome

Example of three days worth of data, averaged into one
A1 ~~~ = ~
A2 ~~~ = ~
A3 ~~~ = ~
A4 ~~~ = ~

B1 ~~~ = ~
B2 ~~~ = ~
B3 ~~~ = ~
B4 ~~~ = ~

 

[DrDu]

I think it's ok but instead of averaging, couldn't you use Anova?

 

[camillio]

What is the zero hypothesis of the test? Is it that the means of variables A and B are equal?

Edit:
If yes, I think that averaging is OK. Also, I think you can use the Hotelling's T2 test of equality of random vectors.

 

[chiro]

Hey Monique.

I would recommend if you are trying to compare means for multiple groups (which is what it sounds like) then use an ANOVA: this is what this technique was designed for.

Also, are there any assumptions for your data that you either know or don't know?

 

[camillio]

I would summarize it a bit...

1) If one needs to test the hypothesis that several random variables (2 and more) with (nearly) normal distribution have the same mean value, one uses anova (alternatively Welch's t test or other tests, depending on assumptions).
2) If one needs to test the hypothesis that two random vectors with a multivariate normal distribution have the same mean value, Hotelling's T2 suits well.

But it depends on what the test is about, which is not clear from the OP.

 

[Monique]

I didn't thank yet for the replies, but I did take the comments along in my evaluation so: thanks! By formulating the question I already came up with the answer without immediately realizing it.

I didn't use ANOVA, since the data needs to be plotted in a graph and there are only 2 conditions. For each time point I averaged the replicate measurement (~~~), calculated the area under the curve for time frames of each independent measurement (1-4) and and used a t-test to compare the two experimental populations (A, B).

I hadn't heard of Hotelling's T2 before, so I'll educate myself some more on that.