Null hypothesis for Roman dice

#1
I’m museum curator working on a project that’s looking for evidence of bias in Roman dice. This involves me rolling each dice a few hundred times and carrying out a chi-square test on the results.

So far I’ve been working with this null hypothesis: “The die is equally likely to land on any of its faces”. Recently I’ve started to worry that this isn’t the right approach, and I’m wondering if there’s anyone here who can help.

I’m not a statistician, but my understanding is that the null hypothesis should assume that the data is random (as I’ve assumed above). But, given that my Roman dice are handmade and obviously imperfect, it’s actually more likely that they are unbalanced than not – ie, I ought to be surprised if the dice DO produce random results!

Does this mean that my null hypothesis should be: “The die is unlikely to land equally on each face” and that I'm actually trying to prove a lack of bias?

Any thoughts much appreciated.
 

rogojel

TS Contributor
#2
hi,
I do not think you should give up the null hypothesis - just consider how many different alternative hypothesises you have. Large bias for side 1, smaller bias for side 1 ....etc.
Also, your research question is fully compatible with this choice of the null hypothesis.

regards