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Analysis of Statistical Experiments - Shoe Testing, Market Demand and Clinical Trials

## Question 1 - Shoe Testing Experiment

Question 1 - A shoe manufacturer (Niko) wants to test the effectiveness of its newly designed running shoes. Niko designs an experiment by having six randomly selected Olympic runners run as fast as they can with their old running shoe first in the sports stadium and then run the same event again with the new, expensive running shoe. After analysing the results, Niko claims that the new shoe is a success and the results are statistically significant:

(a)  Determine the response variable in order to show that the new shoe is effective or ineffective?
(b) What is the factor?
(c) What is the meaning of statistically significant in this context?
(d) In analysing the data, should a two sample T test or a Paired T test be used? Explain. Briefly state the testing plan.

(e) Criticise the experiment and point out four problems with generalising the results to the population.

(a) Run Time with new shoe — Run time with old shoe is the response variable. [Note: the reverse is fine too, as long as it is a difference]. The factor is type of shoe (new shoe vs old shoe). It means that there is sufficient evidence to reject the null hypothesis that the population average running time of both types of shoes are the same.

Question 2 - A bank wants to test the market demand for a new loan product "FlexLoan". There are two factors that the bank think is important in affecting demand: (I) the annual fee charged and (2) the baseline interest rate charged. The bank selected some people at random from a mailing list. It sent out (i) 50.000 offers with \$10 annual fee and 5 % interest rate, and (ii) 50,000 offers with \$70 annual fee and 10 % interest rate:

(a)  Is this a single factor or two factor factorial experiment? Explain.
(b) Explain how to isolate and compute the effect of interest rate only.
The bank management wants to know the effect of raising interest rate by I percentage point. Propose to implement an experimental design and analysis plan. State your outcome variable and factors.

(a) Neither. This is a 2 factor experiment with only  two combinations of factor levels. (L, L) and (H. H).  We need at least 4 different combinations of the 2 factor levels. Then we could either use ANOVA to establish statistical significance and use the average outcome value as the effect, or use linear regression of outcome on the two factors.

## Question 2 - Market Demand Experiment

Question 3 -Suppose you've become involved in a clinical trial in which you are testing a new antidepressant drug called Joyzepam. In order to construct a fair test of the drug's effectiveness, the study involves three different drugs to be administered. One is a placebo. and the other is an existing antidepressant / anti-anxiety drug called Anxifrec. A collection of I8 participants with moderate to severe depression are recruited for your initial testing. Because the drugs are sometimes administered in conjunction with psychological therapy, your study includes nine people undergoing cognitive behavioural therapy (CBT) and nine who are not.

-Participants are randomly assigned (doubly blinded, of course) a treatment, such that there are three CBT people and no-therapy people assigned to each of the three drugs. A psychologist assesses the mood of each person after a three month run with each drug: and the overall improvement in each person's mood (Mood Gain) is assessed on a scale ranging from —5 to +5. Positive score is an improvement, Negative score is a deterioration:

(a) Explain the meaning of double blind in context and how this could be implemented in this study.
(b) Explain the purpose of including persons not undergoing CBT in this study. (4 marks)

• Double blind means that both the participants and staff providing the treatment to the participants are unaware of the type of treatment given. • All the three types of drugs look the same to the participants and staff. • Participants are randomized within each block (CBT or not) to receive one of 3 types of drugs.

• Serves as part of the intended market for the drug. • To show that the non-CBT will benefit too or at least no adverse reactions.  Null Hypotheses: The population means of mood gain of each drug are the same. Alt Hypotheses: At least one population mean of mood gain of one drug differs from the other population means.

• Reject the null hypothesis in favour of the alt hypothesis and conclude there is strong evidence to conclude that at least one population mean of mood gain of one drug differs from the other population means because • the P-value 8.65e-05 is very small, much smaller than 5%. • To compute the Power, we need information about the specific alternative hypothesis.

• Assuming the null hypothesis is true.

• the probability of observing the sample test statistic (or more extreme) is 8.65e-05.
• Disagree. Linear Reg can be used.

• The X variable can be categorical variable Drug Type with dummy coding.
• No. ANOVA results only state at least one drug effect is different.