Type I Error

Hypothesis Testing

Type I errors occur in statistics when hypothesis tests are used to make statistical decisions based on experimental data. In this decision process, a simple statement or null hypothesis is formulated on the true status of an unobserved phenomenon. At the same time, an alternative hypothesis is defined to reflect the opposite situation. For instance, a new drug is tested for its capacity to reduce high blood pressure. The null hypothesis states that the new drug does not change blood pressure. Any differences that are observed are explained by random variation in the measurement process. The alternative hypothesis can be formulated as “the drug reduces high blood pressure.”

Once the appropriate hypotheses have been formulated, one would like to test whether the null can be rejected in favor of the alternative. At this point, an experiment can be designed, a relevant test statistic and its distribution under the null can be derived, and data can be collected. These elements are required in the process to arrive at one of the two following conclusions:

• The null hypothesis can be rejected in favor of the alternative because the observed pattern in the sample cannot be explained merely by random variation, or
• There is not enough evidence to reject the null in favor of the alternative because the observed pattern in the sample is most likely a result of chance.

When the statistical test favors a decision that is in agreement with reality, a correct decision has been made. However, this decision procedure can also result in several errors (see Table 1).

The null hypothesis can be wrongly rejected in favor of the alternative, even if the statement in the null is true. In this case, a Type I error has occurred. One can also fail to reject the null hypothesis when the alternative is true, which results in a Type II error. For instance, in the blood pressure example, a Type I error occurs if a statistically significant [Page 1575]effect of the drug is found when in reality the drug does not influence blood pressure.

Why Type I Errors Occur

Hypothesis testing can be viewed as making an educated guess. Like with any other guess, it is possible to draw the wrong conclusion. The data that are used to validate the null hypothesis are drawn as a random sample from the study population. Just by chance, it is possible that this sample reflects a relationship that is not present in the population. Consider for instance four throws with a six-sided die. If the four throws result in four 1s, this could be interpreted as evidence that the die is loaded in favor of the outcome “1.” However, even with an honest die, a combination of four 1s can occur once in every 1,296 (64) sequences of throws. If in this case the die would be marked as loaded, a Type I error has occurred. Unfortunately, one can never be certain whether a rejected hypothesis is a reflection of the true nature of the studied phenomenon or whether it is the result of an accidental relationship present in the sample.

...