# Exploring Illmo through Experimental Data about Wooden Dice

In order to make sense of the torrent of new information and the use of the new program Ilmo we decided to start with a simple statistical test with rolling dice. Experimenting with real dice and gather data in a real situation. In this part we are exploring if we can rig the dice and if the surface on which you throw has effect on the outcome. By doing the experiment with the dice we can explore the use of discrete data and understand how to draw conclusions about the collected data.

Hypothesis

The layer in between the magnetic dice and a metal surface will influence the outcome of the test significantly.

Method

In this test we made a wooden dice with a magnetic piece in the side of the one. Expecting that the  metal surface underneath and the slight weight imbalance can influence the outcome by throwing more six then 1. To test this we tried different surfaces in between and performed a null test on a wooden surface.

Results

Each dice we throw 49 times and write down what the number is.

Distribution Analysis vs T-Test

When we perform a traditional T-test in Illmo we find that the difference between 1 and 2 is not significant.

(2 – 1) :
Gaussian model : dif = 0.367347
pairwise T-test (assuming equal variance):
se (pooled standard error) = 1.70072
se_dif (standard error of dif) = 0.343596
two-sided T-test:
T(96) = dif/se_dif = 1.0691 (p=0.287695)
|T| < 1.9849 (p=0.05) : not significant
confidence CI(dif) = [-0.314642,1.04934]
effect size – r = sqrt(T*T/(T*T+96)) = 0.108473
effect size – Cohen’s d = dif/se = 0.215996
estimated power is 0.179904
(need 9.33 times as many trials for beta=0.8)

Data Distribution

1. Prob(0) = 0.163265 (95% CI = [0.073225,0.296484])
Prob(1) = 0.081633 (95% CI = [0.022700,0.196066])
Prob(2) = 0.224490 (95% CI = [0.117707,0.366232])
Prob(3) = 0.163265 (95% CI = [0.073225,0.296484])
Prob(4) = 0.142857 (95% CI = [0.059446,0.272461])
Prob(5) = 0.224490 (95% CI = [0.117707,0.366232])

2. Prob(0) = 0.081633 (95% CI = [0.022700,0.196066])
Prob(1) = 0.142857 (95% CI = [0.059446,0.272461])
Prob(2) = 0.122449 (95% CI = [0.046274,0.247708])
Prob(3) = 0.183673 (95% CI = [0.087588,0.320244])
Prob(4) = 0.204082 (95% CI = [0.102427,0.343529])
Prob(5) = 0.265306 (95% CI = [0.149425,0.410763])

3. Prob(0) = 0.142857 (95% CI = [0.059446,0.272461])
Prob(1) = 0.204082 (95% CI = [0.102427,0.343529])
Prob(2) = 0.061224 (95% CI = [0.012807,0.168721])
Prob(3) = 0.244898 (95% CI = [0.133464,0.388658])
Prob(4) = 0.102041 (95% CI = [0.033957,0.222205])
Prob(5) = 0.244898 (95% CI = [0.133464,0.388658])

4. Prob(0) = 0.224490 (95% CI = [0.117707,0.366232])
Prob(1) = 0.183673 (95% CI = [0.087588,0.320244])
Prob(2) = 0.142857 (95% CI = [0.059446,0.272461])
Prob(3) = 0.142857 (95% CI = [0.059446,0.272461])
Prob(4) = 0.163265 (95% CI = [0.073225,0.296484])
Prob(5) = 0.142857 (95% CI = [0.059446,0.272461])

Conclusion

The data distribution shows much more about the way the data is displayed. Compared to the first dice we see that in set 2 the number 6 was thrown much more then in set 1. Even though the amount of data is not sufficient to make significant conclusions about the fairness of the dice we can at least show that the impact of the data distribution can give a lot of valuable insights averages and normal distributions can’t. This insight is important in the data analysis of user studies.

For a full description of the first experiments please click to see the pdf file

Documentation Experimental Data Dice