Matched pairs--Treatment effects of a drug on cognitive functioning in children with mental retardation and ADHD

This activity offers students direct experience with the 4 steps involved in hypothesis testing for matched pairs designs:

1. State the appropriate null and alternative hypotheses, Ho and Ha.
2. Obtain a random sample, collect relevant data, and check whether the data meet the conditions under which the test can be used. If the conditions are met, summarize the data by a test statistic.
3. Find the p-value of the test.
4. Based on the p-value, decide whether or not the results are significant and draw your conclusions in context.

Inference for the difference in means in a matched pairs design

Use this activity for in-class collaborative group work.

Estimate for completion time: 45 minutes

Materials needed:

• 4-step hypothesis testing template (shown below) for each group (handout, in .odt file format--OpenOffice.org Writer)
• Analysis software (SPSS, PPSP, SAS, R, Minitab, Excel, Calc)
• Dataset: [1] (excel file format)

(: reminder to add handout, in .odt file format )

Activity

Comparing cognitive functioning in children with mental retardation and ADHD under two treatment conditions A 2003 study investigated the cognitive effects of stimulant medication in children with mental retardation and Attention-Deficit/Hyperactivity Disorder (ADHD). This activity utilizes the data for the Delay of Gratification (DOG) task, only. 24 children were given 4 dosages of a drug, methylphenidate (MPH), and then completed the DOG task as part of a larger battery of tests. The order of doses was counterbalanced so that each dose appeared equally often in each position. For example, six children received the lowest dose first, six received it second, etc. The children were on each dose one week before testing. The DOG task, adapted from the preschool delay task of the Gordon Diagnostic System, measures the ability to suppress or delay impulsive behavioral responses. Children were told that a star would appear on the computer screen if they waited “long enough” to press a response key. If a child responded sooner in less than four seconds after their previous response, they did not earn a star, and the 4-second counter restarted. The DOG differentiates children with and without ADHD of normal intelligence (e.g., Mayes et al., 2001), and is sensitive to MPH treatment in these children (Hall & Kataria, 1992). In this activity we will be concerned only with testing the difference between the mean in the placebo (D0) condition and mean in the highest dosage condition (D60). Note that the children in this experiment are not organized in independent groups. The scores in the D0 condition are from the same subjects as the scores in the D60 condition. There is only one group of subjects, with each subject being tested in both the D0 and D60 conditions. The dataset includes 5 variables: ID: subject identification number D0: Number of correct responses after taking a placebo D15: Number of correct responses after taking .15 mg/kg of the drug D30: Number of correct responses after taking .30 mg/kg of the drug D60: Number of correct responses after taking .60 mg/kg of the drug Design and implement hypothesis test Form students into groups of 2-4 students. Each group will need access to a laptop with statistical software loaded and a copy of the handout. Have the students complete the handout as a group, which includes the following information. State the appropriate null and alternative hypotheses and set the significance level. Ho: Ha: Significance level: Identify and define the random variable for this test. State what test statistic will be used to summarize the data. Indicate whether a one-tailed or two-tailed test will be used. Open the dataset into the statistical software. Check whether the data meet the conditions under which the test can be used. If the conditions are met, summarize the data by a test statistic. Because this is a matched pairs design, calculate the difference score (which is the variable of interest). For the difference score, calculate summary statistics and create a histogram (or stemplot). If desired, create a normal quantile plot for the difference score to further assess the normality of the distributions. Confirm that the conditions for use of the chosen test statistic have been met. (Continue even if the conditions are not met, and be ready to discuss noted violations in follow-up.) Calculate the test statistic. Find the p-value of the test. p-value: Explain what the p-value means. On a sketch of the normal distribution, label the x axis and shade the region(s) corresponding to the p-value Based on the p-value, decide whether or not the results are significant and draw your conclusions in context. Indicate whether or not Ho is rejected. Provide a reason for this decision. Draw conclusions based on the results, given the context of the scenario. If Ho is rejected, create a confidence interval appropriate to the given significance level and interpret this interval in the context of the research question. Thought question If in error you had run this t-test as an independent groups t-test. What do you think would be the result? Why? If you have time, try to reformat the data and run the independent groups t-test. Follow-up discussion Review the results. Were the conditions met? Were the test results significant? What can we conclude about our research question based on the results. Are there limitations to our study? Sample -- is the sample an SRS? Sample size? Would alternative methods to matched pairs t-test be more appropriate? other limitations?

Resources

This activity is based on the case study "ADHD Treatment" included in Online Statistics: An Interactive Multimedia Course of Study.