Basics of Environmental Sampling and Analysis - Fundamentals of Environmental Sampling and Analysis - page 25

2.2.3 Type I and II Errors: False Positive and False
Negative

The previous discussion refers to a confidence level such as 95%. This is to say that
the probability for correctly accepting a null hypothesis is 95%, and there is 5%
chance of making an error. To illustrate two types of errors, let us first use an easy-to-
understand example by setting:

Null hypothesis H 0 : Defendant is innocent
Alternative hypothesis H a : Defendant is not innocent
A Type I error occurs if we reject a null hypothesis when it is true, and a Type II error
occurs if we accept a null hypothesis when it is false. This is equivalent to saying a
Type I error is to put innocent people in jail whereas a Type II error is to set criminals
free (Table 2.1).

Table 2.1 Type I and Type II errors in a court decision

True state of nature
Defendant is innocent Defendant is guilty

Court decision (H 0 is true) (H a is true)

Defendant is innocent Correct decision Type II error

Defendant is guilty Type I error Correct decision

If we denote the probability of committing a Type I error (reject H 0 when H 0 is
true) and Type II error (accept H 0 when H 0 is false) is a and b, respectively, then we
have:

aþb ¼ 1 ð2:23Þ

The above equation tells us that reducing one error will certainly increase the other
type of error. Let us now look at the following example to demonstrate why this
concept is important in environmental analysis and decision-making (Table 2.2).

Table 2.2 Type I and Type II errors in environmental analysis

True state of nature

Possible decision based on Contaminant not present Contaminant present

analytical results of samples (H 0 is true) (H a is true)

Contaminant not detected Correct decision Type II error

(False negative)

Contaminant detected Type I error Correct decision

(False positive)

Reference: Keith (1991)