In a study of depression medications, researchers randomly sampled patients from medical clinics in major metropolitan areas across the country and invited them to participate in the study. Researchers randomly assigned patients to one of the 3 treatment groups: Imipramine, Lithium or a Placebo. The study was double-blinded with additional background data collected for each patient. Researchers followed patients for 4 years to see whether or not they had a recurrence of depression. Patients that did not have a recurrence within this time frame were labeled a Success. If they did have a recurrence, it was considered a Failure and the weeks to relapse were recorded. Here are the variables: Hospt: Which hospital the patient was from: Labeled 1, 2, 3, 5 or 6 Treat: ( 0= ) Lithium; 1 =Imipramine; ( 2= ) Placebo Outcome: ( 0= ) Success 1 =Failure (recurrence of depression) Time: Number of weeks until a recurrence (if outcome=1) or until study ended (if outcome=0) AcuteT: How long the patient was depressed before the start of the current study, measured in days Age: Age in years Gender: 1 =Female 2=Male Researchers tested the following hypotheses: Null hypothesis: There is no relationship between treatment and time to relapse. (Equivalently, the mean time to relapse is the same for those taking Lithium, Imipramine and a Placebo.) Alternative hypothesis: There is a relationship between treatment and time to relapse. (Equivalently, the mean time to relapse differs for those taking Lithium, Imipramine and a Placebo.) Analysis of Variance results: Responses: Time Factors: Treat Response statistics by factor egin{tabular}{|l|c|c|c|c|} hline multicolumn{1}{|c|}{ Treat } & ( underline{mathrm{n}} ) & ( underline{ ext { Mean }} ) & ( underline{underline{S t d} . ext { Dev. }} ) & ( underline{underline{S t d} ext {. Error }} ) \ hline Imipramine & 38 & 63.063868 & 49.485291 & 8.0275743 \ hline Lithium & 37 & 37.725919 & 40.822979 & 6.7112564 \ hline Placebo & 34 & 37.584059 & 40.265052 & 6.9053994 \ hline end{tabular} ANOVA table egin{tabular}{|l|r|r|c|c|c|} hline Source & DF & multicolumn{1}{c|}{ SS } & MS & F-Stat & P-value \ hline Treat & 2 & 15976.944 & 7988.472 & 4.1487983 & 0.0184 \ hline Error & 106 & 204102 & 1925.4905 & & \ hline Total & 108 & 220078.94 & & & \ hline end{tabular} Question 1 5 pts Which of the following conclusions is appropriate at a ( 5 % ) level of significance? Check all that apply. Imipramine is more effective because the mean time to recurrence of depression symptoms is longer for those taking Imipramine. The differences observed in sample means do not provide strong evidence of a difference in mean recurrence time for the three treatment types in the population. There are statistically significant differences in mean time to recurrence of depression symptoms for patients in the three treatment groups. This suggests that there is a treatment effect. For the population of depressed people who take Lithium or Imipramine or who do not receive treatment, the mean time it takes for depression to reoccur differs. No conclusion is possible because conditions for use of the ANOVA F-test are not met.
Added by Elizbeth H.
Close
Step 1
The p-value for the Treat factor is 0.0184, which is less than the significance level of 0.05. This means that we have evidence to reject the null hypothesis and conclude that there are statistically significant differences in mean time to recurrence of depression Show more…
Show all steps
Your feedback will help us improve your experience
Kirsty Gledhill and 58 other Elementary Statistics a Step by Step Approach educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Each person who came to the clinic was screened for depression. Those who were diagnosed as "moderately depressed" were invited to participate in a treatment comparison study we were conducting. One of the IVs is the therapy condition, whether patients received cognitive-behavioral therapy (CBT), art therapy, or a support group control. Because of ethical concerns, patients were not randomly assigned to treatment conditions. Rather, each was permitted to choose which treatment they would receive. In addition, each patient was permitted to decide when they would begin treatment, in the Summer or Winter. As well as collecting the DV score (rating of depression, bigger scores indicating more depression), after 18 weeks of therapy, the researchers also recorded the initial depression score for each patient. The psychologist generated the following output from their analysis: ## Anova Table (Type III tests) ## ## Response: DepressionRating ## Sum Sq Df F value Pr(>F) ## (Intercept) 2097759 1 44.9959 1.575e-09 *** ## InitialDepression 19183 1 0.4115 0.5228 ## Therapy 92192 2 0.9887 0.3760 ## StartTherapy 26829 1 0.5755 0.4500 ## Therapy:StartTherapy 71879 2 0.7709 0.4656 ## Residuals 4289140 92 ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Dominador T.
Clinical depression is the most common mental illness in the United States, affecting 19 million adults each year (Source: NIMH, 1999). Nearly 50% of individuals who experience a major episode will have a recurrence within 2-3 years. Researchers are interested in comparing therapeutic solutions that could delay or reduce the incidence of recurrence. In a study conducted by the National Institutes of Health, 109 clinically depressed patients were separated into three groups, and each group was given one of two active drugs (imipramine or lithium) or no drug at all. For each patient, the dataset contains the treatment used, the outcome of the treatment, and several other interesting characteristics. Below is a summary of the variables in our dataset. Use this to answer the questions below. Hospt: The patient's hospital, represented by a code for each of the 5 hospitals 1, 2, 3, 4, 5, or 6 Treat: The treatment received by the patient (Lithium, Imipramine, or Placebo) Outcome: Whether or not a recurrence occurred during the patient's treatment (Recurrence or No Recurrence) Time: Either the time in days till the first recurrence, or if a recurrence did not occur, the length in days of the patient's participation in the study. AcuteT: The time in days that the patient was depressed prior to the study. Age: The age of the patient in years, when the patient entered the study. Gender: The patient's gender (1 = Female, 2 = Male)
Adi S.
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD
Elementary Statistics a Step by Step Approach educators are ready to help you.