Question

8. Visualizing variability A researcher designs an intervention to combat anti-Arab oppression. He also designs a questionnaire to measure anti-Arab oppression so he can test the participants' level of anti-Arab oppression before and after the intervention. He tests one version of his questionnaire with 45 statements and a shorter version with 12 statements. In both questionnaires, the participants respond to each statement with a rating on a 5-point Likert scale with 0 equaling "strongly disagree" and 4 equaling "strongly agree." The overall score for each participant is the mean of his or her ratings for the different statements on the questionnaire. Look at the following graphs. Graph I graphs the results from the long version, and Graph II graphs the results from the short version. Graph I Graph II PARTICIPANTS PARTICIPANTS

Answer 1

We can see that the graph 1 is more spread than graph 2

The range of Graph 1 is larger than the range for Graph 2.

We can see the curve is symmetrical on 2 for both graphs which means both graphs have mean equal to 2 approximately.

The mean of Graph 1 is equal to the mean for Graph 2.

The variance of Graph 1 is greater than the variance for Graph 2.

So, there is much more variation in case of longer questionnaire as compared to shorter questionnaire.

This implies that the shorter questionnaire will be better and more accurate than the longer questionnaire at detecting differences before and after the intervention.