There is wide consensus among scientists and methodologists that replications ar
ID: 3225545 • Letter: T
Question
There is wide consensus among scientists and methodologists that replications are crucial for establishing the validity of research results. Let us examine quantitatively some of the contingencies involving two independent replications of a given experiment. Two investigators conduct the same kind of experiment on two independent random samples from the same populations. Both test the same null hypothesis H_0 and, assuming H_0 is true, each of the tests is conducted at a level of significance of 0.05. Compute the following: (a) The probability that both tests will turn out statistically significant. (b) The probability that at least one experimenter will obtain a statistically significant result. (c) The probability that only one of the tests will come out statistically significant. (d) The probability that neither test will turn out significant. (e) The conditional probability that the second investigator will obtain a statistically significant result, given that the first one did so.[l, 3.1.13]Explanation / Answer
a) We assume that both null hypothesis are true
The given level of significance = 5% that is alpha = 0.05
When we reject null hypothesis then we say that there are significance evidence
So probability of both the test will turn out statistically significance when null hypothesis is true = 0.05 *0,05 = 0.0025
b) The probability of atleast one test is significance = 1 - both the test are not statistically significanct = 1 - (0.95 * 0.95) = 1 - 0.9025 = 0.0975
c) The probability of onlyone of the test is significance = 0.05 * 0.95 + 0.95 *0.05 = 0.0475
d) The probability of neither test will tern out significant = 0.95 * 0.95 = 0.9025
e) Since they do test independentally so that the conditional probability is same as nonconditional probability = probability of the investigator will ontain statistically significant result = 0.05
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