A researcher is interested in testing two interventions designed to reduce racist graffiti in an inner city area. He recruited ten neighborhoods that have a problem with racist graffiti and asked assistants from the community to provide measures of the square feet of new racist graffiti each week. After four weeks of baseline recording, a six week sensitivity training workshop was begun in five of the ten neighborhoods and an advertising campaign was conducted in the other five neighborhoods. Community members continued to measure the extent of any new racist graffiti each week, yielding data from the 10 neighborhoods for 10 consecutive weeks, 4 prior to workshops and 6 after workshops began. The researcher wants to know if the interventions reduced the amount of new racist graffiti and if they differed in any effect. What statistical technique would you advise?

#### Chi-square test of independence

Incorrect.

Chi-square is used to assess relationships between categorical variables using frequency data.

In this problem, we have two groups of cases (type of intervention) and a continuous dependent variable that is measured 10 times. While the type of intervention is a categorical variable, the extent of new graffiti is a continuous measure.

#### Regression Analysis

Incorrect.

Regression analysis can be used to derive an equation from which we can predict scores on one variable based on scores on one or more other variables.

In this example we have two groups with 10 measures for each group. We are interested in differences between the groups as well as the pattern of change over time.

#### One-way ANOVA

Incorrect.

One-way ANOVA can be used to test hypotheses regarding the equality of three or more groups. However, One-way ANOVA is appropriate for research situations in which the DV is measured only once. In this problem, the DV is measured 10 times.

#### Repeated Measures ANOVA

Correct!

Repeated measures ANOVA can be used to test hypotheses regarding the equality of group means and changes in a DV over time. In this example, Repeated Measures ANOVA can be used to assess overall differences between the two interventions, changes in the amount of new racist graffiti over time, and differences in the pattern of change for the two interventions (this is an interaction between type of intervention and pattern of change). Contrasts can be used to test specific comparisons, such as the rate of change and a comparison of the pattern before and after the intervention. The interaction between type of intervention and pattern of change can also be tested.

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#### The Expert says…

The null hypotheses are that there is no change in the extent new racist graffiti from before to after the interventions and that the interventions do not differ.

Repeated measures over time require special techniques because observations cannot be assumed to be independent. With a long series of observations (say 30+), time series analysis may be appropriate.

With fewer observations, as we have here, a repeated measures ANOVA would be appropriate. We may wish to use contrasts to test for specific patterns of data before and after the intervention. For example, we may look for a trend across the time of the intervention, and we may test for a difference in trends before vs. during the intervention, or a difference in the mean before and after intervention. Further, we can compare the two interventions in overall means as well as with changes associated with the introduction of the intervention. This is a ‘split-plot’ design, where we have one ore more between cases effects (type of intervention) and one or more within cases effects (changes over time). Because each neighborhood is measured multiple times, a multivariate analysis of variance (MANOVA) could also be applied.

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