How this calculation works
Subtract within each matched pair before summarizing the differences. Report the mean and median change, sample standard deviation of changes and counts by direction. The sign convention is always after minus before.
dᵢ = afterᵢ − beforeᵢ; mean change = Σdᵢ/n; sample SD = √[Σ(dᵢ−d̄)²/(n−1)]A worked example
Before values 10,20,30 and matching after values 12,18,33 give changes 2,−2,3. Mean change is 1, median 2, and sample SD is √7 ≈ 2.645751.
Good to know
At least two complete pairs using a common measurement unit. No hypothesis test, interval, percentage improvement, independent-group comparison or causal conclusion. Higher values are not automatically better.
A pair is a relationship between observations
Each position must identify the same item before and after the change. For example, rows could represent the same three machines measured in matching units on two occasions. Sorting either list separately destroys that matching and can change the spread and median of the differences, even if the average difference happens to stay the same.
The default changes are 2, −2 and 3. Their total is 3, so the mean change is 1. The sorted changes are −2, 2 and 3, giving median 2. This is a useful small example where the mean and median answer different summary questions.
The statistics calculator summarizes one list. A paired change calculator first derives an aligned list of within-item changes before summarizing that different quantity.
Variation belongs to the changes being summarized
Relative to the mean change of 1, the three deviations are 1, −3 and 2. Their squared deviations sum to 14; dividing by n−1 = 2 gives sample variance 7 and sample standard deviation √7. Calculating the standard deviation of just the before values would describe a different quantity.
An increase is a sign, not a judgment of success. A larger wait time and a larger output quantity need different interpretations. The result keeps increased, decreased and unchanged counts separate and does not relabel them as improved or worsened.
Complete pairs and measurement units matter
A missing after value cannot be fixed by deleting one number from only that list: every subsequent observation would be paired with the wrong item. Prepare complete pairs first, keep the same row order and use matching measurement units. Entering a dash or a missing-value marker produces an error rather than silently dropping data.
For an independent single dataset, the statistics calculator summarizes its spread. The forecast error calculator instead compares predictions against actuals with absolute and squared errors. Neither substitute makes before-and-after measurements causal evidence; this page supplies no hypothesis test or confidence interval.
A few questions, answered
Does this perform a paired t test?
No. It summarizes differences and their sample standard deviation without a p-value, test statistic or confidence interval.
Can I mix seconds and minutes between lists?
Convert them to a common unit first. This page subtracts the entered numbers directly.
Why require two pairs?
The displayed sample standard deviation uses n−1, which is zero for one observation.