I measured two groups of data (samples with Z=1 and Z=2) that are different in number and are plotted according to independent variable X and dependent variable Y measurements. The X measurement is slightly different for each sample but ranges from 0.4 to 0.8.
It is fairly obvious from looking at the data that as X increases, Y decreases and lines may be fit to both Z=1 and Z=2 groups. These lines are more or less parallel, but the Z=2 line is below the Z=1 line.
Is there a simple statistical test I may do to show that Z=2 measurements have significantly lower Y for a given X than Z=1 measurements? In other words, I want to calculate the significance that Z=1 and Z=2 as groups are justified in being treated differently from one another due to their contrasting trend lines.
That's a standard ANCOVA model. Both series are decribed by one (linear) model, which is of the form
Y = b0 + b1*X + b2*G
where G is either 0 (e.g. when Z=1) or 1 (when Z=2), and b0, b1 and b2 are the coefficients that are fitted to the data. b0 is the intercept for the line where G=0, b1 is the slope of that line, and b2 is the difference in the intercept from the line for G=0 to the line for G=1 (since the lines are parallel, this is the vertical distance between the lines - that's what you are looking for). Any stats software will give you the estimates of these coefficients together with confidence intervals and p-vaues testing the hypotheses that their values are zero.
NB: when the lines are not (neccesarily) parallel, the model can include an interaction term (+ b3*X*G), and the coefficient b3 now gives the difference in the slopes of the lines. The coefficient b2 in that model is still the difference in the intercpets, but since the lines are not parallel anymore, it is not anymore a "general offset", and it depends on how the intercept is defined (usually, b2 is required for the math to make sense, but it is often not scientifically interesting, so to say).
For a particular x value let y1 be the value of y when Z=1 and y2 when Z=2. Then y1 chi-square (n-1, alpha). I suggest that y1 and y2 be interchanged and the test repeated since the choice of the expected line was arbitrary. If both tests are nonsignificant then the lines are the same.
- Badges
- Science topic
- Similar topics
- Solid State Physics
- Devices