Instructions

NXV compares two independent groups whose scores come from a short rating scale, such as a 1–7 pain score or a 5-point Likert item. Enter the scores for one group in the S box and the other in the T box, separated by commas or spaces. Each group can hold up to 20 values. If the first group is larger than the second, the site swaps them, tells you it has done so, and gives the same answer either way. Enter the range of the rating scale, r, and λ, the number of tied scores you expect in a sample of this size from this population. If you have no prior view on λ, try a few values and see how much the answer moves.

The top graph and p-value are the NXV result. The graph shows the exact distribution of the Mann–Whitney U statistic under the null hypothesis that both groups come from the same population, allowing for tied scores. The marked region is the tail at or beyond your observed U, and its total is pNXV. The bottom graph is the classical Mann–Whitney test on the same data, blind to tied scores, with its normal approximation overlaid for comparison. If the two disagree, the tied scores are doing real work in your data.

The site counts tied scores the way NXV does: if three people share a score, that is two tied scores, because the second and third each tie to the first. A rating scale with r points can only hold r different scores, so when there are more people in total (n = s + t) than points on the scale, at least n − r of the scores must be tied. If your data contain more different scores than the r you entered, the site raises r to the number of different scores and tells you. If you enter a λ above what the sample can hold, the site uses the largest valid value and tells you. If you enter λ = 0 when tied scores are unavoidable, it uses the smallest possible number and flags that too. If you enter something that is truly impossible, such as more than 20 scores in a group, the site shows an error and wipes both graphs, so an old result can't be mistaken for an answer to the new question. The Greyscale button is for printing, or for screens where the colours don't separate well.

One-tailed or two-tailed?

A two-tailed test asks whether the groups differ at all, in either direction. Its p-value is the chance, if there were no real difference, of a U at least as far from the middle of the distribution as yours, at either end. Every distribution NXV uses is exactly symmetric, so this is exactly twice the smaller tail, and exactly 1 when your U sits in the middle. The site starts on two-tailed, and if in doubt you should use it: it is what most journals expect.

A one-tailed test asks a question with a direction, which you must commit to before you see the data. Choose One-tailed, then “I predict that S is larger overall” or “I predict T is larger overall”; the site won't run until you have chosen. Only results in the predicted direction count as evidence. If your data go the other way, the one-tailed p-value will be large, close to 1. That is correct, not a fault: the data give no support to the prediction you made. Use one-tailed only if you committed to the direction in advance and a difference the other way would genuinely mean nothing to you. The classical comparison below the NXV result follows the same choice.

Significance level, α

α is the threshold you set in advance for calling a result significant. It starts at 0.05, and you can enter any value between 0 and 1. The site reports the result as significant when pNXV ≤ α, and not significant when pNXV > α. The “or equal to” matters here, because NXV's p-values are exact and can land exactly on α: for two groups of three with no tied scores and λ = 0, the most extreme one-tailed result has p = 1/20 = 0.05 exactly, and counts as significant at α = 0.05. The verdict is given for pNXV only; the classical result is there for comparison.