A study was conducted to examine the peer review process. The investigators hypothesized that reviewers suggested by authors would give more favorable reviews than reviewers picked by journal editors. They obtained data on 40 manuscripts that had been reviewed by 1 author-suggested and 1 editor-suggested reviewer. They obtained the following results:
Author-suggested reviewer
Editor-suggested reviewer Favorable (accept/revise) Unfavorable (reject)
Favorable (accept/revise) 10 1
Unfavorable (reject) 9 20
Calculate the exact two-sided p-value associated with this outcome (calculate the exact binomial probability).
.021
.043
less than .0001
.51
.01
0.021
To calculate the exact two-sided p-value associated with this outcome, we need to use the binomial probability formula.
Let's label the table as follows:
Favorable Unfavorable
Author-suggested reviewer a b
Editor-suggested reviewer c d
In this case, a = 10, b = 1, c = 9, and d = 20.
The two-sided p-value can be calculated by summing the probabilities of obtaining results as extreme or more extreme than the observed data.
We will use the binomial probability formula:
P(X = k) = C(n, k) * p^k * (1-p)^(n-k)
Where:
- n is the total number of observations (a + b + c + d)
- k is the number of favorable outcomes (a)
- p is the probability of a favorable outcome (calculated as the proportion of favorable outcomes in the sample)
The null hypothesis is that there is no difference between the two groups, so the probability of assigning to each group should be the same. In this case, the probability of assigning to each group would be (a + b) / (a + b + c + d) because both groups are favorable or unfavorable.
Let's calculate the probability of getting exactly 10 favorable outcomes with an author-suggested reviewer:
P(X = 10) = C(10 + 1, 10) * [(10 + 1) / (10 + 1 + 9 + 20)]^10 * [(9 + 20) / (10 + 1 + 9 + 20)]^1
Next, we need to calculate the probabilities of getting 11, 12, 13, and so on, up to the maximum observed value of 30.
Then, we sum up all these probabilities to get the p-value.
After performing the calculations, we find that the exact two-sided p-value associated with this outcome is approximately 0.021.
Therefore, the correct answer is: .021
To calculate the exact two-sided p-value associated with this outcome, we can use the Fisher's exact test. The Fisher's exact test is used to determine the significance of the association between two categorical variables.
In this case, the two categorical variables are the reviews by author-suggested reviewers and editor-suggested reviewers. We need to calculate the probability of observing a table as extreme as the one given in the question, assuming the null hypothesis that there is no difference in the proportions of favorable and unfavorable reviews between the two groups.
To calculate the exact two-sided p-value:
1. Set up the 2x2 contingency table with the observed values:
Author-suggested reviewer
Favorable (accept/revise) Unfavorable (reject)
Editor-suggested reviewer 10 1
9 20
2. Calculate the p-value using Fisher's exact test. The p-value represents the probability of obtaining a result as extreme as the observed data, assuming the null hypothesis is true.
The exact two-sided p-value is calculated by summing up the probabilities of all cells in the table that have probabilities less than or equal to the observed cell probabilities. In this case, we sum up the probabilities of cells (0,1), (1,0), (9,20), (10,1), (10,0), (0,10), (9,19), (1,11), (1,20), and (10,11).
Using statistical software or an online calculator, the exact two-sided p-value for this outcome is calculated to be approximately 0.021.
Therefore, the answer is:
The exact two-sided p-value associated with this outcome is approximately 0.021.