Is it harder to reject the null hypothesis when conducting a two-tailed test rather than a one-tailed test? Wh

Question

Is it harder to reject the null hypothesis when conducting a two-tailed test rather than a one-tailed test? Why or why not?

Answer 1

Without the aid of pictures, this will be long-winded...

First off, keep in mind that hypothesis testing is about assuming something is true (the null hypothesis) until there is sufficient evidence (a surprisingly extreme test statistic) that we can reject the null hypothesis. What is 'sufficient evidence' is determined by

1. The level of the test, usually labeled with the Greek letter 'alpha' and often set at 5%.

2. If the test is one-sided or two-sided.

I'll assume this is a Z or T test since this is probably the context in which this question arose. Right now only be concerned with the second aspect above regarding whether the test is one-sided or two-sided. Additionally, I'll refer to the following hypothesis tests as an example:

One-sided:

H_0: mu = 3

H_A: mu > 3

Two-sided:

H_0: mu = 3

H_A: mu not= 3

With a one-sided test, we expect the test statistic to show up only on one side of the value in the null hypothesis. In the example above, we would expect our test statistic (Z or T) to show up above 0*, in which case we put our 'rejection region' only on this one side of 0. (Our 'rejection region' is the range of values our test statistic could take if we were to reject the null hypothesis.)

* the mean is expected to be above 3, and Z or T will then be above 0.

If the test is two sided, then we must split our rejection region between both sides (in the example, half goes above and half goes below). In such a case, the test statistic must be even more extreme since there is less of a chance if we were just looking at one side of 0. That is, Z or T must be even further from 0, but now it can be above or below 0, just further away. That is, our test statistic must be even further from 0.

Since our test statistic must be more extreme in a two-sided test to reject the null hypothesis, it is harder to reject when the test is two-sided.

Answer 2

rejection of the null hypothesis is ususally based on 95% certainty that the null hypothesis is wrong.  if your version of two tailed test means you have to get the same answer twice in two and only two tries, then your not conducting a logical experiment and application of the null hypothesis is wrong.