## One-tail tests

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

## 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 outside the “not significant” area in one direction only. The 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.

• At .01 probability (99%) one-tailed test, you can set the two-tailed test to .02 probability (98%).
• A .05 probability (95%) one-tailed test, you can set the two-tailed test to .10 probability (90%).
• A .10 probability (90%) one-tailed test, you can set the two-tailed test to .20 probability (80%).
• A .50 probability (50%) one-tailed test, you would have to set the two-tailed test to 1.00 probability (0%).

The last example shows that it is absolutely certain 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 Companion

Companion does not have any one-tailed tests but these can be done using the two-tailed tests and adjusting significance levels. You should set format SLA and possibly SLB, and SLC 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, Companion 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 should not used very often.