If you have prior programming experience, R is simple for basic analysis. I don't know of any online tools. The following would be close to sufficient for what you seem to want:
mydata <- read.table("c:/sleepdata.csv", header=TRUE, sep=",") # Read in data w/ variable names in header
fit <- lm(ZQ ~ guess + placebo, data=mydata) # Compute linear regression
summary(fit) # Get estimated coefficients with t-statistics and p-values
For cookbook code, see Quick R. If you do use R, the RStudio IDE is very useful.
I've finished my experiment; if you want to check my R interpreter usage, I put it in the footnotes in http://www.gwern.net/Zeo#vitamin-d-analysis
Quite a few of us are working on interesting projects; many of those are solo, but some could maybe use some help. So here's the place to ask!