One of the truly impressive applications of statistics occurred in connection with the design of the 1954 Salk polio-vaccine experiment and analysis of the resulting data. Part of the experiment focused on the efficacy of the vaccine in combating paralytic polio. Because it was thought that without a control group of children, there would be no sound basis for assessment of the vaccine, it was decided to administer the vaccine to one group and a placebo injection (visually indistinguishable from the vaccine but known to have no effect) to a control group. For ethical reasons and also because it was thought that the knowledge of vaccine administration might have an effect on treatment and diagnosis, the experiment was conducted in a double-blind manner. That is, neither the individuals receiving injections nor those administering them actually knew who was receiving vaccine and who was receiving the placebo (samples were numerically coded). (Remember: at that point it was not at all clear whether the vaccine was beneficial.)         Let p1 and p2 be the probabilities of a child getting paralytic polio for the control and treatment conditions, respectively. The objective was to test H0: p1 − p2       0 versus Ha: p1 − p2       0 (the alternative states that a vaccinated child is less likely to contract polio than an unvaccinated child). Supposing the true value of p1 is 0.0003 (an incidence rate of 30 per 100,000), the vaccine would be a significant improvement if the incidence rate was halved—that is, p2 =  . Using a level ? = 0.05 test, it would then be reasonable to ask for sample sizes for which ? = 0.1 when p1 = 0.0003 and p2 = 0.00015. Assuming equal sample sizes, the required n is obtained as n =   1.645   (0.5)(0.00045)(1.99955) + 1.28   (0.00015)(0.99985) + (0.0003)(0.9997)   2   (0.0003 − 0.00015)2   =   (0.0349 + 0.0271)/     2   ≈ 171,000         The actual data for this experiment follows. Sample sizes of approximately 200,000 were used. The reader can easily verify that z = 6.43—a highly significant value. The vaccine was judged a resounding success! Placebo: m = 201,229,     x = number of cases of paralytic polio = 110 Vaccine: n = 200,745,     y = 33

Indicate the levels for which measures are being obtained in each type of study of the observational studies: cross-sectional, case-control, and cohort studies using the book of Robert H. Friis; Thomas Sellers.

Acne is a common skin disease that affects most adolescents and can continue into adulthood. A study compared the effectiveness of three acne treatments and a placebo, all in gel form, applied twice daily for 12 weeks. The study's 517 teenage volunteers were randomly assigned to one of the four treatments. Success was assessed as clear or almost clear skin at the end of the 12 week period. The results of the study can be seen in the table below. Using the appropriate statistical test, determine if there is significant evidence that the four treatments perform differently. If so, how do they compare.

Here is the Statistics problem. Read this passage. What is the explanatory variable in this passage?

Consider the following research questions/study scenarios. For each study, discuss the most appropriate methods for describing the data (graphically and numerically).  What statistical method would be most appropriate for addressing the research questions?  Be sure to provide a justification of the statistical method.  What statistical test is needed, provide appropriate null and research hypotheses. An investigation of the association between drink preferences and the color of teeth is proposed. Subjects will be surveyed as to the type of drink most often consumed (coffee/tea. Juice, caramel-colored soda, water, or milk).  A clinical exam will be performed after dental cleaning to determine the color of the teeth (reddish brown, reddish yellow, gray, reddish gray).

7. Effect size - Cohen's d and r squared An industrial/organizational psychologist has been consulting with a company that runs weekend job-seeking workshops for the unemployed. She collected data on several issues related to these workshops and, after conducting statistical tests, obtained statistically significant findings. She needs to find a way to evaluate effect size so that she can make recommendations to the company. One of the psychologist’s findings is that 18 months after the workshop, a sample of 36 job seekers who received training on resume writing scored an average of 7.3 as measured on a 9-point job-search motivation scale, with a standard deviation of 1.5. The typical job seeker scores 6.1 points. The psychologist finds that the estimated Cohen’s d is    , the t statistic is 4.80, and r² is    .   Using Cohen’s d and Cohen’s guidelines for interpreting the effect size with the estimated Cohen’s d, there is a    treatment effect. Using r² and the extension…

The average income of a large sample of households is $63,000 and the s.d. is $7,000. Assume that the data is approximately bell-shaped. What percent of these households have incomes between $42,000 and $77,000? Don’t forget to properly justify your answer using the empirical rule.

Consider the following research questions/study scenarios. For each study, discuss the most appropriate methods for describing the data (graphically and numerically).  What statistical method would be most appropriate for addressing the research questions?  Be sure to provide justification of the statistical method.  When a statistical test is needed, provide appropriate null and research hypotheses. A study investigating the effects of second-hand smoke in working environments asked the following question: “How often do you experience second-hand smoke in a work environment/function? Never, Occasionally, Fairly Often, Very Often, Almost Always.”  The question was asked of managers and employees to determine whether there was an association between position and the amount of second-hand smoke exposure.  The responses to the questions were grouped into Little/Non and Often, where Little/None was defined as responses of Never or Occasionally and Often was defined as responses of Fairly…

A team of epidemiologists at the Mayo Clinic wanted to find whether there is an association between obesity and cardiovascular disease (CVD). They conducted a prospective cohort study following obese and non-obese individuals who were free of CVD at the beginning of study for five years. The investigators were also interested in assessing age as a potential confounder, effect modifier, or both. Use the data below to answer the accompanying questions.     CVD No CVD Total Obese 10 90 100 Not Obese 35 465 500 Total 45 555 600       CVD No CVD Total Obese 36 164 200 Not Obese 25 175 200 Total 61 339 400   1. Compute the appropriate measure of association for those who were less than age 50.  2. Compute the appropriate measure of association for those who were older or equal to age 50.  3. Compute the crude measure of association?  4. List three attributes that age must satisfy before it could…

How would you explain question a in detail?