# How much better are you with your main? (prove it!)

#### immortalchaos29

##### Member
I was curious whether my main (Zhanchi) was actually faster than other cubes. In fact, it seems like every week I change my mind about what my favorite cube is. In order to prove it, I took an average of 20 for each cube and these were the results:

 Cube Average St. Dev. S_pooled T_exp T_99.9% T_75% T_25% Zhanchi 16.70 1.01 1.57 3.622 3.566 1.168 0.321 Lunhui 16.71 1.02 1.47 1.311 MoYu 16.85 1.89 1.52 0.313 Guhong 17.31 1.82 SS Wind 18.50 1.98

Sure enough, it seems like there is no real difference between my top 3 (maybe even 4) favorite cubes, other than I seem to be less consistent with the MoYu and Guhong. Hmmm.

After performing a paired t test, I found with over 99.5% certainty that there is a difference between my times with Zhanchi and ShengShou. Also I can say with over 75% confidence that my Zhanchi is better than my Guhong. (with more trials I could increase certainty.) Finally, and most interestingly, I can be at least 75% confident that there is NO difference between my performance with Zhanchi and with MoYu.

These calculations are really easy to perform in excel. If you want to know how to do it I show how below:
First put your averages in column B and corresponding deviations in column C (if you want them in order, you can highlight all values and right click, then tell excel to "sort: low to high," then select the "expand current selection" option).

Then you must pool the variances between the two cubes you wish to compare. Say you are comparing the cubes in rows 2 and 3. This is done by using the following equation:

S_pooled = sqrt((( #trials_A - 1 ) * S_A + ( #trials_B - 1 ) * S_B )/( #trials_A + #trials_B - 2 ))

If you are doing 20 trials like I did you can type it in excel like so:

=SQRT((19*C2^2+19*C3^2)/38)

Then you must calculate a t value with:

T_exp = abs(average_A - average_B)/(S_pooled * sqrt(1/#trials_A + 1/#trials_B))

=ABS(B2-B3)/(E2*SQRT(1/10))

Then compare it to the corresponding value in a t table or type into excel:

=TINV(0.001,38)

Where the first number is 1 - p_value (99.9% confidence shown above) and the second number is degrees of freedom (#trials_A + #trials_B - 2)

If T_exp > T_table, you reject the null hypothesis (the values are different). Otherwise, your cubes show no statistical difference at the corresponding level of confidence.

This experiment is fun to try and prove which cube(s) are really best for you. For me at least, it was also an exploration on how little hardware can actually effect your times

What cubes are your fastest? Are they significantly different? Which cubes surprised you when you discovered how good or how bad you are with them?

#### jayefbe

##### Member
20 solves is a pretty small sample size. ~100 plus per cube would probably start to show more realistic results, and honestly even that would be small. After doing lots of ao100s, I still see variation I wouldn't attribute to differences in abilities. At those numbers you run into the problem of doing the solves over multiple days, and I see a significant difference in my day to day times.

I'm slightly better with my Zhanchi (main) and Moyu than other cubes, but I would wager it's entirely due to familiarity with those cubes. I'm sure I could do just as well with any decent cube after a day of practicing with it. My potential as a cuber is nowhere near the limit that these cubes can achieve.

#### immortalchaos29

##### Member
20 solves is a pretty small sample size. ~100 plus per cube would probably start to show more realistic results, and honestly even that would be small. After doing lots of ao100s, I still see variation I wouldn't attribute to differences in abilities. At those numbers you run into the problem of doing the solves over multiple days, and I see a significant difference in my day to day times.

I'm slightly better with my Zhanchi (main) and Moyu than other cubes, but I would wager it's entirely due to familiarity with those cubes. I'm sure I could do just as well with any decent cube after a day of practicing with it. My potential as a cuber is nowhere near the limit that these cubes can achieve.
Yes sample size is important especially for something like this, but t test takes sample size into account. But for sure in order to improve accuracy we would need to do x muber of solves with each cube, every day (for, say, a week). That limits error due to day-to-day consistency, "warmed-up" solves, and gives a larger sample size.

And yes I am best with the cubes I am most used to. But it doesn't take long to get used to a cube's feel (I've only had my MoYu for a week). The test certainly tells me nothing about how good I COULD be with each cube.

#### Ross The Boss

##### Member
AAAHHHHHHHH, math! im getting out of here!