What kind of statistical test can be used for my data?

Question

Let's say hypothetically I need to compare samples taken from group of humans at the day and at the night. I would like to see if there are any significant changes in the samples between those two time points. There are different samples (18 in total), for example blood, urine, spit, etc... I have four replicates for each time point. Each team/group is a composition of different people (male, female, young, old, etc) and the number in each group may be different as well. That means Sample 1 (blood) was taken from 5 people and I calculated a mean. So I used the easiest approach and I just took a mean of the results for each group/team but I am not sure if it should be done like that. Anyway, the results are shown below:

Day:

> dput(data1)
structure(list(Sample = 1:18, `Replicate 1` = c(483139957.466999, 
18419484.8793012, 6323582.65012894, 4835513.9449211, 18825930.9961964, 
3345329.29658372, 10991207.7733899, 11543788.4022557, 37433260.659815, 
52656998.4104276, 4630965.58466113, 7989791.52375088, 5869587.5844277, 
4851157.10912223, 8319804.52469405, 26480159.0093267, 14312197.2102269, 
2622934.76077158), `Replicate 2` = c(430115690.772298, 21746370.57802, 
5117948.43432065, 900198.599477471, 18036003.7406036, 2613255.31600864, 
12628842.5152089, 16829082.1454364, 20833464.069239, 41704022.4059303, 
3224551.81607163, 9531731.20650826, 4622904.13493909, 4594932.39864943, 
8237590.6183486, 24161835.5144514, 22254270.0518872, 2493331.3326573
), `Replicate 3` = c(367285858.792061, 17505038.9708625, 9115997.19573197, 
3017212.56266055, 18737371.5138656, 3235286.82979338, 11851406.2728674, 
8355830.47176874, 13394694.3199866, 47309374.9965771, 4945726.7939656, 
8778605.82132967, 5550794.63124474, 7339020.02097186, 8402907.89430717, 
37094084.0472019, 23193128.0376071, 1112871.90011314), `Replicate 4` = c(413568675.025335, 
20064022.1599402, 7773013.05600225, 4254021.07399388, 24150780.1134545, 
4101556.77813632, 8378739.17697561, 12711332.3613856, 32092851.1380528, 
21539261.3107248, 3432039.98399363, 7802961.67410367, 6561871.72983466, 
5875588.43914924, 11466196.1253827, 33427822.1313595, 33166052.5207409, 
4788465.84362014)), .Names = c("Sample", "Replicate 1", "Replicate 2", 
"Replicate 3", "Replicate 4"), row.names = 2:19, class = "data.frame")

Night:

> dput(data2)
structure(list(Sample = 1:18, `Replicate 1` = c(353623172.869356, 
11571655.7857434, 8104862.69916794, 3799746.12789339, 21085349.9524958, 
2387774.69393264, 12213154.0833913, 10918319.9666355, 29408897.8409511, 
56173957.7386867, 4025995.93106508, 7293493.20054593, 4814461.17385978, 
7142677.49114559, 8293092.20154457, 32394546.169772, 15099008.2859653, 
1821668.51961212), `Replicate 2` = c(424954138.16318, 22047234.918163, 
3991307.57211047, 686033.835602487, 19175437.5284624, 2579579.45862803, 
7805661.23361268, 14880672.2135273, 20106717.6877472, 56120888.9344651, 
3594835.93740008, 9005342.77715287, 5072612.73581937, 6282840.2470555, 
8095341.84525128, 40915897.2583209, 20942848.6480902, 1532641.25411947
), `Replicate 3` = c(341343891.665324, 23343840.5736713, 4784478.52343266, 
3794454.787824, 19608611.2296076, 1812322.82994808, 8500655.49282534, 
7449578.76682836, 30177450.6772738, 38022069.3055181, 3752212.94125585, 
8461228.01641203, 4294351.62196396, 3792939.77566062, 8561121.77342389, 
23677730.1782989, 32512066.4606989, 1547156.89308365), `Replicate 4` = c(524410338.96904, 
12087790.894342, 6440340.32357233, 2825622.25610684, 25733703.0907116, 
1967066.96054326, 5898461.97653573, 10954022.0570318, 26916007.3958975, 
18512737.6244699, 3214702.78720154, 7174077.63370964, 6155566.585692, 
5070975.61705348, 7824657.48924661, 36340170.8005276, 20648969.5206572, 
2102068.53223516)), .Names = c("Sample", "Replicate 1", "Replicate 2", 
"Replicate 3", "Replicate 4"), row.names = 2:19, class = "data.frame")

Of course the composition of directly compared teams is the same (for replicates and time points). That means for example in Sample 1 the group was formed by the same 5 people.

I did a t-test to compare those results but... I can't see any significance there but I am sure that there should be some. The question is if I should change the significance test or change the whole approach ...

Answer 1

From your description it sounds like this is a paired samples situation, so you should do a paired samples t test. You should clarify (as an edit to OP), you got little response so far because your question is somewhat uninformative. Anyhow, I think you should start with more data exploaration before asking about which test to use!

So, a little start of this data exploration, I show how you can make some interesting plots. I started with reading your data into R using dput.

Then I made a paired data plot for Replication 1 only. The code is:

names(Night)  <- names(Day)  <- c("sample","rep_1","rep_2","rep_3","rep_4")
png(filename="WhichTest.png")
plot(c(Day$sample,Night$sample) ~ c(Day$rep_1,Night$rep_1), type="n",
     xlab="Replicate 1",ylab="Sample")  # Setting up axes
points(Day$sample ~ Day$rep_1, col="red")
points(Night$sample ~ Night$rep_1, col="blue")
# Preparing points for plotting horizontal lines:
xx  <-  c(rbind(Day$rep_1, Night$rep_1, rep(NA,18)))
yy  <-  c(rbind(Day$sample,Night$sample,rep(NA,18)))
lines(xx,yy)
dev.off()

resulting in the following graph:

The most distinguished feature of that plot is that the first sample is very different from all the other ones! You could start by asking yourself why that is the case, what is happening? We cannot answer that for you. And make similar plots for the other variables.