I have some data on successive bets made by customers. I want to see whether there is a statistically significant change in bet stake with each subsequent bet.
The data is skewed, so I have equalized all initial bets to 1. Thereafter, I calculate the proportional change in bet stake. So if someone had a first bet of 15 and a third bet of 30, the value for the stake in the third bet shows 2.00.
For a series of groups, I'm showing the mean standardized stake at the second, third and fourth round of betting. Although the data is quite skewed, I've used a t-test to test whether there is a statistically significant difference between this mean and 1 (i.e. no change in bet size since the initial bet).
Given the data is skewed, I also want to perform a non-parametric test, but I'm having an issue with the median and a one-sample median test. Although for many groups the median is 1, the median test shows a statistically significant difference from 1. For example, one groups has approximately 4000 observations, of which 1800 are
ties/zero or equal to exactly 1.
When performing a
signrank test, 1800 observations are showing us as zero, while of the remaining 2200 observations, there are 200 more positive counts than negative, so the result of the one-sample median test is highly significant. It doesn't seem right.
Should I be using the signrank test for this at all? Would another test be more appropriate?