Dan's Segment 19
To Think About
1. Why are we so interested in t-values? Why do we square them?
We are interested in t-values because they are a way to quantify the deviation of data from the mean. They allow us to quickly evaluate data from a frequentist perspective, for example is something a 2-sigma fit? We square them because that way they fit the chi-squared distribution.
2. Suppose you measure a bunch of quantities xi, each of which is measured with a measurement accuracy σi and has a theoretically expected value μi. Describe in detail how you might use a chi-square test statistic as a p-value test to see if your theory is viable? Should your test be 1 or 2 tailed?
In this case, we can just sum up the chi-square statistics of each data point, and this summation should be chi-squared distributed. At this point we can compute a simple one-sided p-value test by integrating the distribution from zero to the actual value of our statistic.