## Hypothesis Testing For Statistical Significance

One of the most important things to understand about statistics is the concept of hypothesis testing. Hypothesis testing is the formal procedure for using statistical concepts and measures in performing decision-making (Ayyub and McCuen 2003, p. 290). This concept forms the basis for likelihood ratios that were mentioned briefly in the previous section and will be described in more detail in Chapter 21.

Six steps are typically involved in making a statistical analysis of a hypothesis (Figure 19.1): (1) formulate two competing hypotheses; (2) select the appropriate statistical model (theorem) that identifies the test statistic; (3) specify the level of significance, which is a measure of risk; (4) collect a sample of data and compute an estimate of the test statistic; (5) define the region of rejection for the test statistic; and (6) select the appropriate hypothesis (Ayyub and McCuen 2003, p. 290).

The first step is to formulate usually two hypotheses for testing. The first hypothesis is called the null hypothesis, and is denoted by H0. The null hypothesis is formulated as an equality and indicates that a difference does not exist. The second hypothesis is usually referred to as the alternative hypothesis and is

Figure 19.1

Flow chart illustrating the steps in hypothesis testing. The null hypothesis (H0) is mutually exclusive of the alternative hypothesis (H1). Adapted from Graham (2003).

### Figure 19.1

Flow chart illustrating the steps in hypothesis testing. The null hypothesis (H0) is mutually exclusive of the alternative hypothesis (H1). Adapted from Graham (2003).

denoted by Hj or HA. The null and alternative hypotheses are set up to represent mutually exclusive conditions so that when a statistical analysis of the sampled data suggests that the null hypothesis should be rejected, the alternative hypothesis must be accepted. Thus, the data collected (evidence gathered) should tip the scales towards either the null hypothesis or the alternative hypothesis.

In the context of a forensic DNA evidence examination, the null hypothesis put forward by the prosecution is that the defendant contributed the crime scene DNA profile while the alternative hypothesis championed by the defense is that someone else other than the defendant contributed the crime scene DNA profile in question. These two hypotheses are then expressed in the form of a likelihood ratio with H0 or Hp (hypothesis of the prosecution) in the numerator and Hj or Hd (hypothesis of the defense) in the denominator.

The available situations and potential decisions/outcomes of a hypothesis test are shown in Figure 19.2. There are two types of errors that can be made with hypothesis testing. A type I error involves rejecting the null hypothesis when in fact it is really true. This might be considered a 'false negative.' A type II error on the other hand involves accepting the null hypothesis when in fact it is really false. A type II error is a 'false positive.'

The level of significance, which is a primary element of the decision-making process in hypothesis testing, represents the probability of making a type I error and is denoted by a (D.N.A. Box 19.1). The value chosen for a is typically based on convention and the historical custom, with values for a of 0.05 and 0.01 being

Figure 19.2 (a) Comparison of decisions based on hypothesis testing and the relationship of type I and type II errors. (b) Example demonstrating how type I and type II errors correlate to false-positive and false-negative results. Adapted from Graham (2003).

(a) Hypothesis Testing Decisions