# Statistics

| June 22, 2015

Experimental Design Problem Set

1. (20 points) An evaluation was done to find effective ways to reduce bullying at the middle school level in a small state. This program randomly assigned middle schools to four groups and provided to the schools in the treatment groups the resources and technical support to implement an anti-bullying peer support program. Below is a description of the experiment.

Researchable question: Does peer support, coupled with education, reduce bullying in middle school?

Subjects: Public middle schools.

Independent variable (treatment): Anti-bullying education coupled with a peer support and mentoring program between seventh and eighth grade students..

Dependent variable: Self-reported bullying experiences (among both bully and victim)

Design diagram:

R Â Â Â Â Â Â Â  O Â Â Â Â Â Â Â  X Â Â Â Â Â Â Â  O

R Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  X Â Â Â Â Â Â Â  O

R Â Â Â Â Â Â Â  OÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  O

R Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  O

1. (10 points) What type of design is being employed in this experiment? Discuss how this would be administered and the justification for the four groups from a standpoint of validity.
1. (10 points) What are the practical disadvantages of including the no-pretest groups in this experiment?
1. (50 points) Concerned about rising rates of obesity and Type 2 diabetes among young adolescents, Whitcomb County implemented a public health program to improve adolescent healthy eating and increase exercise. Physicians in the Countyâ€™s wellness center referred at risk teenagers (based on Body Mass Index) to the program.Â Â  Of 600 youth referred, 450 entered the program. Of these, 150 were referred to a nutritionist to develop a healthy eating program; 150 were involved in an after-school exercise program, and 150 were enrolled in both the nutrition and exercise program. The 150 youth who did not choose to enter the program agreed to be monitored as a control group. A variety of health measures were gathered prior to beginning the program and for several intervals during the program.
1. (10 points) Use the R X O notation to summarize the design.
1. (20 points) Shortly after the study started, the area high schools banned vending machines and implemented healthier school lunches.
• Would this affect the internal validity of the study? Why or why not?
• Would this affect the external validity of the study? Why or why not?
1. (10 points) A number of the students involved in the exercise program ran into conflicts with after school sports programs. The study administrator permitted them to move to the nutrition-only group. Discuss the effect on internal validity. What should the administrator have done?
1. (10 points) Discuss the selection of the no-treatment group. What issues does it raise for internal validity?
1. (25 points) In the late 1980s the Tennessee state legislature funded a four-year experiment to evaluate the effect of small class sizes on learning. The experiment compared different class arrangements for children in kindergarten through third grade:

– a regular-size class (size 22-25 pupils) with a single teacher â€“ the control group

– a small class (size 13-17 pupils) with a single teacher â€“ the treatment group

Each participating school had at least one class of each type. Within schools both pupils and teachers were randomly assigned to one of the two types of classes. Each year the children were given standardized tests (the SAT).

1. (15 points) In the excel file you will find the reading and math scores of the 2nd grade boys and girls. Please fill out the table below and use the standard significance levels of (*t<.05; **t<.01; ***t<.001) to determine the effects.
1. (15 points) In 1-3 paragraphs (250 words max), please summarize the results. Does being in a small class positively affect student test scores?

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Category: Statistics

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