One-tailed and Two-tailed tests: Part 2

In the previous post we learnt about one-tailed tests.

What about two-tailed tests?

In this case we split the total alpha error equally, so that half the alpha error falls to the left, and the other half falls to the right of the midline (mean).

What does this imply?

It implies that we feel the outcome of the study could go in any direction.

(Recollect that when we were certain that the outcome would be in a particular direction, we kept the entire alpha error to one side of the midline.)

Example: Is Kindness greater than love?

Stating the above in terms of hypotheses, we have:

Null Hypothesis (H0): Kindness = Love (the null hypothesis always states that there is no difference–> both are same)

{Alternate Hypothesis (Ha) [one-tailed]: Kindness < Love


Alternate Hypothesis (Ha) [one-tailed]: Kindness> Love}

Alternate Hypothesis (Ha) [two-tailed]: Kindness is not equal to love (here we are merely stating that the two are not the same- unlike in the case of a one-tailed test where we took sides and declared one to be better than the other).

The above alternate hypothesis is an example of a two-tailed test of hypothesis.

Figure showing the area under the curve for a two-tailed test

Note how the total alpha error of 5% has been equally split on both sides.

The light blue area corresponds to 95% of the total area under the curve.

Let’s recap what we learnt:

Figure showing a series of images depicting one-tailed and two-tailed tests

The following figure shows the value of the z statistic corresponding to the area under the curve also:

Figure showing one-tailed and two-tailed tests with the corresponding values of the z statistic

As can be seen from the above figure, the value of the z statistic in a one-tailed test is 1.65. This means that a test statistic greater than 1.65 will be considered statistically significant, resulting in rejection of the null hypothesis.

The corresponding value of the z statistic for a two-tailed test is 1.96. A test statistic greater than +/-1.96 will result in rejection of the null hypothesis.

Compare the two values of the z statistic. It is obvious that the null hypothesis will be rejected at lower values of the test statistic if a one-tailed test were to be used (as compared to a two-tailed test).

Statisticians believe that this would result in a higher false positive error rate than if a two-tailed test were employed.

Therefore, it is recommended that a two-tailed test be employed in all but the most rare situations (when the use of a one-tailed test can be justified).


2 thoughts on “One-tailed and Two-tailed tests: Part 2

  1. Pingback: Topic requests for the new year | communitymedicine4asses

  2. Pingback: Oversimplification: Common Biostatistical concepts in a few lines | communitymedicine4asses

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