# Math Help - How to set up this T-test

1. ## How to set up this T-test

Need some help setting up a statistical analysis for a project. I'm going to try to just give an example similar to my project rather than take the time to explain it (not that it's that complicated. it would just require a lengthy explanation). Here goes.

Let's say I have an instrument that's measuring the distance from itself to an object that is in motion. The instrument takes measurements every second and records it. I run the exact same test four times with the object following exactly the same path every time. Unfortunately, I wind up with four slightly different sets of data. I want to evaluate the performance of the instrument by comparing these four sets.

My professor told me I should use a T-Test. I'm fairly certain that I have to pick two sets of data at a time and acquire the difference between the two at each point in time in order to eliminate one of the variables (instead of time and the actual location of the object, the only variable will be time). I want to see if the difference between two (or more) of these sets is significant and use either a 90% or 95% confidence interval. Can anybody help me set this up? I haven't done this kind of stuff in a long time and I can't quite figure it out.

My data is all in excel and ready to go. I just need some guidance. Btw, there are about 1500 points in each set so I wouldn't be able to post my info.

Thanks!

2. You can only check two sets of data against each other at a time. You need to have a parameter in mind, are the data sets matched (would a point on one data set correspond to a point on another set)? You might want to check the data, to see if it's normally distributed, it doesn't need to be perfect or even remotely symmetric, just so long as it's single peaked and doesn't have any outliers. For a matched pairs T-Test you find T using the formula: $\bar{x}$/( $s$/ $\sqrt{n}$) where $\bar{x}$ is the mean difference between the sets. You would have 1499 degrees of freedom, I don't think there are any tables that can precisely match your t-value to a precise p value when you have that many degrees of freedom. If unmatched you want a two sample T-test, to calculate T: ( $\bar{x}$1- $\bar{x}$2)/squarerootof(s1/n1 + s2/n2) where s1 and s2 are the standard deviations of the data sets. I can explain the rest when I know if the data sets are matched.