I calculate the difference in conditional proportions

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(i) Calculate the difference in conditional proportions and compare it to the original study. (ii) Without calculating, do you suspect the p-value for comparing this new response variable between the two groups will be larger or smaller or about the same as the p-value you determined above? Explain your reasoning. (b) The above study was operationally identical to that of another study and the results of the two studies were combined. Of the 399 combined patients randomly assigned to standard CPR, 44 survived to discharge from the hospital. Of the 351 combined patients randomly assigned to chest compression alone, 47 survived to discharge. (i) Calculate the difference in conditional proportions and compare it to the original study. (ii) Without calculating, do you suspect the p-value for this comparison will be larger, smaller, or the same as the p-value you determined? Explain your reasoning.
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Chance/Rossman, 2015 ISCAM III Investigation 3.9 226 SECTION 4: OTHER STATISTICS Investigation 3.9: Flu Vaccine A recent study (Jain et al, 2013) tested a vaccine for influenza in children ages 3 to 8. Children from 8 countries were randomly assigned to receive either the vaccine for influenza or a control (hepatitis A vaccine). An influenza-like illness was defined as a temperature of 37.8°C or higher, with at least one of the following: cough, sore throat, runny nose, or nasal congestion. Suspected cases were confirmed clinically. The results are shown in the table below: Hepatitis A vaccine (“control”) Quadrivalent influenza vaccine Total Developed Influenza A or B 148 62 210 Did not develop influenza 2436 2522 4958 Total 2584 2584 5168 (a) Calculate the proportion of children developing influenza in each group. Does this appear to be a large difference to you? (b ) Use Fisher’s Exact Test to investigate whether these data provide convincing evidence that the probability of influenza is lower among children who receive the influenza vaccine. [ Hint : State the hypotheses in symbols and in words. Define the random variable and outcomes of interest in computing your p-value.] Do you consider this strong evidence that the vaccine is effective? (c) Would you feel any differently about the magnitude of the difference in proportions if the conditional proportions with influenza had been 0.500 and 0.533? Explain. Discussion : When the baseline rate (probability) of success is small, an alternative statistic to consider rather than the difference in the conditional proportions (which will also have to be small by the nature of the data) is the ratio of the conditional proportions. First used with medical studies where “success” is often defined to be an unpleasant event (e.g., death), this ratio was termed the relative risk . Definition: The relative risk is the ratio of the conditional proportions, often intentionally set up so that the value is larger than one: Relative risk = Proportion of successes in group 1 (the larger proportion) Proportion of successes in group 2 (the smaller proportion)
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Chance/Rossman, 2015 ISCAM III Investigation 3.9 227
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