Question

Please note that for all problems in this course, the standard cut-off (alpha) for a test of significance will be .05, and you always report the exact power unless SPSS output states p=.000 (you’d report p<.001). Also, remember that we divide the p value in half when reporting one-tailed tests with 1 – 2 groups.

Problem Set 3: (8 pts) This study investigated the cognitive effects of stimulant medication in children with Attention-Deficit/Hyperactivity Disorder (ADHD). Shown below are data for the Connors’ Continuous Performance Test (CPT) for 15 children diagnosed with ADHD. This is a visual vigilance task that requires the child to respond to the computer screen any time they see any letter other than “X”. An overall index is calculated that can be used to indicate attention problems based on reaction time, omission errors, and variability of responses. A higher number indicates more problems with attention. Children were given various daily dosages of a drug methylphenidate (MPH) – given 0, 5mg, 10mg, and 25mg). The order of doses was counterbalanced so that all children received all doses at one point in the experiment. The children were on each dose one week before taking the CPT test (so each child took the test four times). 0 mg 5 mg 10 mg 25 mg 11 9 11 10 10 7 9 10 11 10 10 9 10 9 10 11 9 7 9 8 7 7 8 8 10 11 10 10 11 10 10 11 10 9 9 11 9 8 8 9 10 9 9 9 8 8 9 10 10 9 10 8 12 11 11 9 9 10 10 8

9. Conduct the appropriate statistical analysis to determine if there is an effect of drug dose on CPT performance in ADHD patients. Paste SPSS output. (2 pts)

10. Create an appropriate graph for the data set. (2 pts)

11.   Write an APA-style Results section based on your analysis. All homework “Results sections” should follow the examples provided in the presentations and textbooks. They should include the statistical statement within a complete sentence that mentions the type of test conducted, whether the test was significant, and if relevant, effect size and/or post hoc analyses. Don’t forget to include a decision about the null hypothesis. (4 pts)

Answer 1

1)

We will set up the null hypothesis that

  At least two means are different.

Under the null hypothesis the test can be carried using ANOVA. The ANOVA table obtained using SPSS is given below.

One-way ANOVA: 0 mg, 5 mg, 10 mg, 25 mg

Source	DF	SS	MS	F	P.Value
Factor	3	5.92	1.97	1.44	0.241
Error	56	76.67	1.37
Total	59	82.58

Since P.Value = 0.241 which is greater then 0.05 hence we will accept our null hypothesis that all means are equal.

2)

The residual plot along with the histogram of residual is given below

3)

Since the drugs are not significant to each other then we can go for post-hoc test using turkey test

Where q is obtained from studentized range table for k = no of treatment and n = total no of observation.

here   

The means for four different groups are given below

Mean 1	Mean 2	Mean 3	Mean 4
9.8	8.93	9.53	9.4

|Mean 1 - Mean 2|	0.87	<1.145	not significant
|Mean 1 - Mean 3|	0.27	<1.145	not significant
|Mean 1 - Mean 4|	0.4	<1.145	not significant
|Mean 2 - Mean 3|	0.6	<1.145	not significant
|Mean 2 - Mean 4|	0.47	<1.145	not significant
|Mean 3 - Mean 4|	0.4	<1.145	not significant

none of the treatment is significant