Hypothesis Testing Terminology

When performing a hypothesis test, you are likely to encounter terms with which you may not be familiar. Unfortunately, this could hamper your ability to carry out hypothesis testing in a meaningful way. Likewise, you will find it hard to communicate your results to the stakeholders without the appropriate vocabulary. To avoid these issues, brushing up on your hypothesis-testing terminology is important. Let’s take a look at the most commonly used terms.

Alpha level

Also known as the alpha risk. The risk of committing a Type A error or incorrectly rejecting your null hypothesis is acceptable. An alpha level is always a number between 0 and 1—most commonly, people use a value of 0.05. Once your test is complete and you’ve run the data through statistical software, you’ll have a p-value to compare to your alpha level.

Alternative hypothesis

A hypothesis that disagrees with the null hypothesis; the two are mutually exclusive.

Beta level

Also known as the beta risk. It’s the acceptable risk of committing a Type B error–i.e., not rejecting your null hypothesis when it is, in fact, incorrect.

Conclusion

A statement that depicts the level of evidence (sufficient or insufficient), at what level of significance, and whether you reject (null) or support (alternative) the original claim.

Confidence level

Also known as the confidence interval. This refers to how confident you can be that your conclusion is, in fact, correct. The confidence level is easy to calculate: the alpha and confidence levels always add up to one. ie:

1 – α = confidence level

Critical region

Set of all values which would cause us to reject the null hypothesis H₀. Also known as a rejection region.

Critical value(s)

The value(s) which separate the critical region from the non-critical region. The critical values are determined independently of the sample statistics.

A critical value separates the rejection region from the non-rejection region.

Decision

A statement based upon the null hypothesis. It is either “reject the null hypothesis” or “fail to reject the null hypothesis.” We will never accept the null hypothesis.

A p-value is the probability of getting a test statistic that is at least as extreme as the one found in the sample data.

Error

Two basic error types occur in hypothesis testing: type A errors, where you reject a correct hypothesis, and type B errors, where you accept an incorrect hypothesis. Read more about errors.

H0

Also known as the null hypothesis.

H1

Also known as the alternative hypothesis, or H(a).

Left-tailed test

The hypothesis test is left-tailed if the alternative hypothesis H1 contains the less-than inequality symbol (<).

Null hypothesis

The statement that you’re trying to disprove. Generally, this is the assumption that the experimental results are due to chance alone; nothing else influenced the results.

P-value

A p-value is a crucial element of any hypothesis test results. It’s a number between 0 and 1, and it gauges the probability that random fluctuations caused any data that might cause you to reject the null hypothesis. It’s calculated by running test results through a statistical significance test. If the p-value is lower than your alpha level, then you reject the null hypothesis. If higher, then you do not reject the null hypothesis. Read more about p-values.

Pooled (vs. Unpooled)

Pooling refers to the way in which the standard error is estimated when calculating terms for a hypothesis test.

The two proportions are averaged in the pooled version, and only one proportion is used to estimate the standard error. ASQ, Villanova, and most other organizations favor pooled calculations.

In the unpooled version, the two proportions are used separately. IASSC generally favors unpooled.

(Source)

Here’s a good read on when to use which in practice.

Rejection region

Also known as a critical region.

Right-tailed test

If the alternative hypothesis H1 contains the greater-than-inequality symbol (>), the hypothesis test is right-tailed.

• In hypothesis testing, when performing a right-tailed test, we reject the null hypothesis if the test statistic is larger than the critical value.
• Only when the test statistic is larger than the critical value will we be able to reject the null? Usually (emphasis on “usually”), we hope to reject the null because that means that our efforts are not in vain. If you are testing the null hypothesis and you are hoping that you have not adversely affected the process, you would then be hoping NOT to reject the null.

Significance level

Also known as the alpha level.

The probability of rejecting the null hypothesis when it is true: alpha = 0.05 and alpha = 0.01 are common. If no level of significance is given, use alpha = 0.05. The level of significance is the complement of the level of confidence in estimation.

The significance level (denoted by Alpha) is the probability that the test statistic will fall in the critical region when the null hypothesis is actually true.

Test statistic

A sample statistic is used to decide whether to reject or fail to reject the null hypothesis.

Two-Tailed Test

A two-tailed test is one with two rejection regions. If the null hypothesis has an equal sign, then this is a two-tailed test, and you can use the test statistic to reject the null hypothesis if the test statistic is too large or too small.

H0: µnew = µcurrent

Ha: µnew ≠ µcurrent

H0: µ_new = µ_current   Ha: µ_new is not = µ_current

For example, if the null hypothesis has an equal sign, then this is a two-tailed test, and you can use the test statistic to reject the null hypothesis if the test statistic is too large or too small.