A mini-study is made of three police precincts to determine the time (in seconds) required for a police car to be dispatched after a crime is reported. These police precincts are: (1) Burbank, (2) Los Angeles, (3) Glendale.

Hypothesis testing:

I. Formulating the statistical hypotheses (null H₀and alternative H₁)

The null hypothesis H₀reflects the "all is same view of the world". That is, "There is no difference among the police precincts in their response time." In other words, the means of all three conditions are predicted to be equal to one another.

The alternative hypothesis H₁reflects our purpose in examining the three precinct groups, "There is a difference among the police precincts in their response time." In other words, the means of all three conditions are predicted to not be equal to one another.

II. Setting criteria for making a decisionSelecting a significance levelalpha

Usually, we select alpha = .05. But we could be more conservative and use alpha = .01. For this lab, we are going to use alpha = .05.

Choosing a statistical test

Individual observations between the groups are not related. Therefore, we can model the data as independent. However, because we have to compare three groups as opposed to only two, we cannot use the t-test. We have to use theOne Factor Between Subjects ANOVA. (One factor - because we have only one independent variable that serves to group the data - precinct. Between - because the observations in different groups are independent.).

Locating rejection region and formulating the decision rules

In the case of ANOVA, there is only a "one tailed test" alternative. The p-value associated with the observed statistic is expressed as the area from the F-observed to the right.

The decision rule is then:

We reject H₀if the p-value associated with the observed statistic is less than or equal to alpha.

We fail to reject H₀if the p-value associated with the observed statistic is greater than alpha.

III. Calculating the statistic

• Go to the data window.
• Click on "Analyze", select "Compare Means", and click on "One Way ANOVA".
• Select variable "response" and move it into the "Dependent List" field.
• Select variable "precinct" and move it into the "Factor" field.
• Click on thePOST HOC
• Select "Tukey" option, then clickCONTINUE.