- Calculate the total vaccinated participants: \(2,321 - 1,085 = 1,236\).
- Determine vaccinated-negative: \(1,236 - 465 = 771\).
- Calculate not vaccinated-negative and positive: \(1,371 - 771 = 600\) and \(1,085 - 600 = 485\).
- Fill the table: \(\boxed{\text{See final table below}}\).
\[ @@TABLE_TOKEN_0@@ \]
Explanation
- Identify knowns and calculate total vaccinated participants
We are given a study with a total of \(2,321\) participants. We know the following:
- \(1,085\) people were not vaccinated.
- \(465\) people were vaccinated and tested positive.
- \(1,371\) people tested negative overall.
To construct the table, we need to calculate the missing values. First, we find the total number of vaccinated people:
\(Total\ Vaccinated = Total\ Participants - Not\ Vaccinated = 2,321 - 1,085 = 1,236\).
- Calculate the specific subgroups for vaccinated and not vaccinated participants
Next, we determine the status of the vaccinated group:
- We know \(465\) vaccinated people tested positive.
- The number of vaccinated people who tested negative is \(Total\ Vaccinated - Vaccinated\ Positive = 1,236 - 465 = 771\).
Now for the not vaccinated group:
- The total number of people who tested negative is \(1,371\). We know \(771\) of these were vaccinated.
- Therefore, the number of not vaccinated people who tested negative is \(1,371 - 771 = 600\).
- Since there are \(1,085\) not vaccinated people in total, the number of not vaccinated people who tested positive is \(1,085 - 600 = 485\).
- Calculate total positive tests and verify values against the provided list
Finally, we calculate the total number of positive tests:
- \(Total\ Positive = Total\ Participants - Total\ Negative = 2,321 - 1,371 = 950\).
Checking against the provided values (\(465, 771, 1,236, 485, 600, 1,085, 950, 1,371, 2,321\)), all calculated values are present. We can now complete the table.
- Construct the final two-way table
The final two-way table is as follows:
\[ @@TABLE_TOKEN_1@@ \]
Examples
In clinical trials or public health research, constructing a two-way table is a standard method for organizing categorical data. For instance, if you were analyzing the effectiveness of a new safety protocol, you might use such a table to quickly compare the frequency of "safe" versus "unsafe" outcomes across different groups, such as those who followed the protocol versus those who did not. This visual structure makes it much easier to perform further statistical tests, such as chi-square tests, to determine if there is a significant relationship between variables.