# One-tail tests in QPSMR

This document explains how to get one-tailed significance levels for statistics applied to tables in QPSMR.

## One-tail vs two-tail tests

The formulae for one-tail and two-tail tests are the same; the difference is whether the result lies outside the “not significant” area (in the tails).

Two-tailed tests look at both sides of the area (both tails) and a “significant” result means that the statistic lies either side of the “not significant” area. Two-tailed tests show the probability that the samples differ without regard to which one is higher.

One-tailed tests look at only one side of the area
(single tail) and a “significant” result means that the
statistic lies this side of the “not significant” area.
One-tailed tests show the probability that one sample is
higher than the other. One-tailed tests are not
concerned with* how much higher*
one sample is than the other; just that it is likely to be
higher.

## Probability levels

When setting probability levels the one-tailed test ignores one of the tails and so the other tail can be double the size for the same level of probability.

- To get a one-tailed test at .01 probability (99%) you can set the two-tailed test to .02 probability (98%).
- To get a one-tailed test at .05 probability (95%) you can set the two-tailed test to .10 probability (90%).
- To get a one-tailed test at .10 probability (90%)you can set the two-tailed test to .20 probability (80%).
- To get a one-tailed test at .50 probability (50%) you would have to set the two-tailed test to 1.00 probability (0%).

The last example shows that it is absolutely certain that one of one of the samples will be higher than the other (or both are equal); which means that a one-tailed test below 50% cannot be done.

## How to set in QPSMR

QPSMR does not have any one-tailed tests but these can be done by using the two-tailed tests and adjusting the significance levels.

You should set format SLA and possibly SLB, SLC and SLD to the equivalent two-tailed percentages as shown above.

You should change the footnote to show the equivalent one-tailed level and state clearly that this level is a one-tailed test level.

When using column markers, QPSMR will only mark the higher of values being tested. You cannot decide beforehand which of the tails to ignore: which of the samples you are going to assume is higher than the other. This absence of a decision about the direction of testing is the reason that one-tailed test are not used very often.