Board :Community
Author :Astrael
Subject :Re. Stats (via stats)
Date :2/26

The right thing to do here is to conduct a t-test.  The sample sizes and variances are likely similar, so we can use a simple pooled two-sample t-test.

1. Calculate sample mean and sample variance of both samples
2. Calculate degrees of freedom: size_1 + size_2 - 2
3. Calculate pooled variance: ((size_1 - 1) * variance_1 + (size_2 - 1) * variance_2) / DoF
4. Calculate the standard error: sqrt(pooled_variance * (1/size_1 + 1/size_2))
5. Calculate the difference between means: mean_1 - mean_2
6. Look up the critical t-value from the t-distribution based on your desired confidence level (typically 95%) and your degrees of freedom
7. Calculate the margin of error: critical_t_value * std_error
8. Calculate the confidence interval: mean_diff +/- margin_of_error

This gives you 95% confidence that the true difference between the two populations means lies between those two boundaries.  If your confidence interval is reasonably narrow and points at a menaingful value, congratulations, you've found something!

If your confidence interval is too huge to be useful, you need to get back in the bear mines and gather more data with both setups.

(Any spreadsheet software will have a function to do this for you, or there are online calculators, etc)

As for what could really be going on here, I can't really guess.  It's safe to say that you shouldn't be missing anything in ATG4, even unscourged, so I can't see 4 hit making a difference.  

It is true that a flamespear has a pretty huge damage range, and so some unlucky swings could realistically result in the occasional mob requiring an additional hit to die.  Extra flat damage from DAM could help make up for this a tiny bit, but I have a hard time believing that this effect from 4 dam could ever add up to ~an additional 10%.  Still, neat if true.