102 Compare two doses of a drug. A drug manufacturer is studying how a new drug
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102 Compare two doses of a drug. A drug manufacturer is studying how a new drug behaves in patients. Investigators compare two doses: 5 milligrams (mg) and 10 mg. The drug can be administered by injection, by a skin patch, or by intravenous drip. Concentration in the blood after 30 minutes (the response variable) may depend both on the dose and on the method of administration. (a) Make a sketch that describes the treatments formed by combining dose and method. Then use a diagram to outline a completely randomized design for this two- factor experiment. (b) "How many subjects?" is a tough issue. What can yo say now about the advantage of using larger groups of subjects? 103 Would the results be different for men and women? The drug that is the subject of the experiment in Exercise 102 may behave differently in men and women. How would you modify your experimental design to take this into accountExplanation / Answer
102. (a) Here, only the different doses of the drug do not form the treatment. Rather, a combination of the dise and the method of drug administration together form a treatment. Let:
A: dose, which has 2 levels: low level =5mg; high level =10mg.
B: method of administration, which has 3 levels: injection, skin patch, intravenous drip.
Combining the dose and method, ie, the several levels of the 2 factors, 6 treatments are formed, as follows:
Experimental units are assigned to each of the above mentioned treatments and the response variable (Concentration in the blood after 30 mins) is noted. Here, treatment degrees of freedom or df is 5. A completely randomized design (CRD) is performed on this 2-factor experiment. Thus apart from treatments, there is another source of variation and that is error. Suppose there is a total of "n" observations, obtained from all of the treatments. So total df will be (6n-1) and error df will be [(6n-1) -5]= [6(n-1)]. After computing the sum of squares due to treatment, sum of squares due to error and their respective means of squares (MS) obtained by dividing the sum of squares by the appropriate df, the F-statistic obtained is = MSTreatmeant/MSError.
Compare this value with the table value of F distribution witj degrees of freedom (5, 6(n-1)), at tje given level of significance. If the computed ratio value is greater than the table value, then you may say that the treatments have significantly varying effects. Otherwise, the treatments maybe assumedto have no significantly different effect.
(b) The number of treatment combinations is a constant here, ie, 6. So treatment degrees of freedom or df is (6-1)=5. If number of subjects increases, then total degrees of freedom or df also increases. But treatment df being constant and this being a CRD there is no source of variation other than treatment and error, this increase in total df implies an increase in error df. As error df increases, Mean Square Error or MSE decreases, meaning that error variance reduces. This means lesser amount of error. As a result, the results obtained by analysing the experiment are more accurate. Thus, using larger groups of subjects is more advantageous.
103. To check whether the drug actually affects men and women differently, one should perform RBD or Randomized Block Design instead of CRD or Completely Randomized Design. Here, the blocks are based on gender. Hence, there are 2 blocks - males and females. After administering the treatment according to the blocks, the response variable is first checked whether it is affected by blocking, ie, whether it is affected by gender. Then the effect of the treatment is checked, by taking into consideration the block effect.
54. (a) Multiway (2 stage) sampling. There are 7 sections of the course out of which 3 are chosen randomly. This is the first stage of the sampling procedure. In the next or 2nd stage, from each of these 3 randomly chosen courses, 8 students are again chosen randomly. Note that the (8×3) students are selected from those 3 courses that were selected in the first stage and not from all the 7 courses available. So this is a multiway sampling.
(b) SRS or Simple Random Sampling. There are 55 students in total, out of which 5 are chosen randomly, using a random number table. Here, each student has an equal chance or probability of being selected into the sample and no one gets any preference. Thus it is an SRS.
(c) Voluntary Response Sample. Several people can be assumed to visit the given site and everyone who is visiting, is asked the same question - to choose their favourite television show. While some people may choose to answer the question, others may choose to ignore it. It completely depends upon the person's choice whether or not he will answer. While asking the same question to everyone means no preference is given to who should answer, the decision to answer or not depends upon the individuals. So it is a voluntary response sample.
(d) Stratified Random Sample. The entire population of interest, ie, first year college students in the introductory psychology course, are in the beginning itself, divided into 2 categories or strata, namely male and female. Samples are then selected from each stratum, the sample size typically depending upon the proportion of individuals in each stratum of the population. This stratification is done mainly to ensure that each section or stratum (male and female) of the population is appropriately represented in the sample, so that no section of the population is underrepresented, or no section of the population goes unrepresented in the sample. Hence stratified random sampling is used here.
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