Statistical Difference from Zero

Question

I have a set of data that represents periodic readings. The data shows an upward trend but I need to test for a statistical difference from zero. I believe I should use the t test, two tailed but what should I use for the second set of data? Zeros, the starting value?

0.2245
0.243
0.2312
0.1795
0.1923
0.17
0.2025
0.2059
0.2394
0.205
0.2201
0.2261
0.1817
0.2143
0.2126
0.237
0.1984
0.228
0.2292
0.2236
0.2096
0.2258
0.2155

Answer 1

A t-test would be able to test if the average of all the values is different from 0. There is no second set of data, you want a one-sample t-test. In R:

x <- c(1,2,3,4) #PUT YOUR DATA HERE
t.test(x)

would do.

But if you want to test whether the trend is different from 0, that's a different question. How to do that would depend on whether the time intervals in your data are equal, whether you want to look at possible seasonality and so on. A simple (but possibly incorrect) method would be:

x <- c(1,2,3,4) #PUT YOUR DATA HERE
time <- seq(1,length(x))
model1 <- lm(x~time)

before that, though, I would make some plots, e.g

plot(x~time)

and perhaps look at some smoothers.

Answer 2

No, don't use 0s, use the one sample t-test and test whether the mean differs from 0 (it does).
In R it goes as follows:

x <- c(0.2245, 0.243, 0.2312, 0.1795, 0.1923, 0.17, 0.2025, 0.2059, 
0.2394, 0.205, 0.2201, 0.2261, 0.1817, 0.2143, 0.2126, 0.237, 
0.1984, 0.228, 0.2292, 0.2236, 0.2096, 0.2258, 0.2155)
> t.test(x)

        One Sample t-test

data:  x 
t = 52.3, df = 22, p-value < 0.00000000000000022
alternative hypothesis: true mean is not equal to 0 
95 percent confidence interval:
 0.2052 0.2222 
sample estimates:
mean of x 
   0.2137