The results of the t-Test are below. The p-value is .0004 which the formal interpretation should be …

Imagine if you collected infinite samples from the simulator with and without the center displayed. This infinite sample would be the population data set. From this we took n=30 random samples from each population. The mean from my n=30 sample from “With Center” is equal to -1.3 mm. The mean of my “Without Center” sample is equal to 10.133 mm. If the population variances of “With Center” and “Without Center” were equal, we would expect to see this big of a difference in sample means in .0004 or .04% of the time. This is very unlikely so I will conclude the means are different.

However, an easier interpretation is that we are 99.96% confident the means are different. Based on this, we are very confident that my performance in placing the lens is closer to the center when a the center line is in place. A few other interesting observations from the data. Note that the mean location error for “Without Center” is equal to 10.133. This indicates my average error is 10.133 mm to the right of center (recall positive error is to the right of center and negative is to the left). The 95% confidence interval of the mean for “Without Center” is from 4.7135 to 15.553. Since this interval does not include zero, we are greater than 95% confident that I am biased to the right side of the target when placing the lens. The 95% confidence interval for the mean for “With Center” goes from -3.926 to 1.326 which does include zero. Therefore, I may tend to place the lens to the left or right, we don’t know yet. If I have a bias for left vs right when using the center target, it would take more samples to determine that.