The table below shows the results from a drug trial for a new ADHD medication. Find the frequencies that we would expect if improvement of symptoms was independent of whether a participant received the placebo.

• A. E_1,1 = 25.0; E_2,1 = 25.0; E_1,2 = 25.0; E_2,2 = 25.0
• B. E_1,1 = 28.6; E_2,1 = 26.4; E_1,2 = 23.4; E_2,2 = 21.6
• C. E_1,1 = 26.4; E_2,1 = 21.6; E_1,2 = 28.6; E_2,2 = 23.4
• D. E_1,1 = 18; E_2,1 = 30; E_1,2 = 37; E_2,2 = 15

Answer: (C)

Verified step by step guidance

1. Step 1: Understand the problem. We are tasked with finding the expected frequencies under the assumption that improvement of symptoms is independent of whether a participant received the placebo. This involves using the formula for expected frequency in a contingency table: E = (row total × column total) / grand total.
2. Step 2: Identify the totals from the table. The row totals are: Improved = 55, Not Improved = 45. The column totals are: Placebo = 48, Non-Placebo = 52. The grand total is 100.
3. Step 3: Calculate the expected frequency for each cell using the formula E = (row total × column total) / grand total. For example, for the 'Improved and Placebo' cell: E1,1 = (55 × 48) / 100.
4. Step 4: Repeat the calculation for the other cells: 'Improved and Non-Placebo' (E1,2), 'Not Improved and Placebo' (E2,1), and 'Not Improved and Non-Placebo' (E2,2). Use the same formula for each cell.
5. Step 5: Verify that the sum of the expected frequencies for each row and column matches the respective row and column totals. This ensures the calculations are consistent with the independence assumption.