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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?

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  • $\begingroup$ The signed rank test assumes symmetry about the median. You might be able to adapt the sign test, but the effect of discreteness will need to be considered with care (i.e. you'll need to think about what you're actually trying to test and formulate both null and alternative - and from there, test statistic - so that they actually correspond to your question of interest) $\endgroup$ – Glen_b -Reinstate Monica May 21 '14 at 23:19
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You seem to want two things:

1) a test related to the mean

2) a nonparametric test

The obvious thing would be a permutation test, which can certainly use the mean as a test statistic. The two sample case is should be fairly simple, as long as you keep in mind that the observations are paired. Given that you are standardizing by dividing by the first bet, you may want to also consider whether you're better off working on the log-scale.

However, you also refer to "change in bet stake with each subsequent bet" which doesn't suggest a two-sample test, but some kind of test for trend across a variable number of bets -- at least if you expect it to be monotonic in bet-number (first bet, second bet, third bet, ...).

This might involve a variety of possible analyses, depending on what kinds of conclusions you're seeking to draw.

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