The table below displays the diagnoses of multiple sclerosis for two neurologists. The categories are (1) Certain multiple sclerosis, (2) probable multiple sclerosis, (3) possible multiple sclerosis, and (4) doubtful, unlikely or definitely not multiple sclérosis. (Note that the last category was created by collapsing 3 categories). The first number in each cell is the observed cell count while the second number is the number that would be expected (to three decimal places) under independence. (The expected count for the first cell is missing.) Neurologist B Neurologist A 1 2 3 4 1 38 ### 33 26.497 10 19.732 3 12.966 2 5 10.926 11 11.671 14 8.6913 7 5.7114 Calculate the expected value in the first cell, to three decimal places. 3 0 3.2482 33 3.4698 5 2.5839 3 1.698 4 1 8.0201 6 3.3087 0 3.3087 10 2.6242

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Out of the four diagnose cells, how many demonstrate an observed cell count greater than what would be expected under independence between the neurologist ratings?
The table below displays the diagnoses of multiple sclerosis for two neurologists. The categories are (1) Certain multiple sclerosis, (2) probable multiple sclerosis, (3) possible multiple sclerosis, and (4) doubtful, unlikely or definitely not multiple sclerosis. (Note that the last category was created by collapsing 3 categories). The first number in each cell is the observed cell count while the second number is the number that would be expected (to three decimal places) under independence. (The expected count for the first cell is missing.)

\[
\begin{array}{|c|c|c|c|c|}
\hline
\text{Neurologist A} & \text{Neurologist B 1} & \text{2} & \text{3} & \text{4} \\
\hline
1 & 38 \, \#\#\# & 5\, 10.926 & 0 \, 3.2482 & 1 \, 8.0201 \\
\hline
2 & 33 \, 26.497 & 11 \, 11.671 & 3 \, 3.4698 & 6 \, 3.3087 \\
\hline
3 & 10 \, 19.732 & 14 \, 8.6913 & 5 \, 2.5839 & 0 \, 3.3087 \\
\hline
4 & 3 \, 12.966 & 7 \, 5.7114 & 3 \, 1.698 & 10 \, 2.6242 \\
\hline
\end{array}
\]

Calculate the expected value in the first cell, to three decimal places.

[Text Box]

For an educational context, this table illustrates how agreement between two neurologists in diagnosing multiple sclerosis can be analyzed. Each cell contains two numbers: the actual observed count of diagnoses and the expected count if diagnoses were independent. This comparison helps in assessing the agreement and independence between the decisions made by the two neurologists.
Transcribed Image Text:The table below displays the diagnoses of multiple sclerosis for two neurologists. The categories are (1) Certain multiple sclerosis, (2) probable multiple sclerosis, (3) possible multiple sclerosis, and (4) doubtful, unlikely or definitely not multiple sclerosis. (Note that the last category was created by collapsing 3 categories). The first number in each cell is the observed cell count while the second number is the number that would be expected (to three decimal places) under independence. (The expected count for the first cell is missing.) \[ \begin{array}{|c|c|c|c|c|} \hline \text{Neurologist A} & \text{Neurologist B 1} & \text{2} & \text{3} & \text{4} \\ \hline 1 & 38 \, \#\#\# & 5\, 10.926 & 0 \, 3.2482 & 1 \, 8.0201 \\ \hline 2 & 33 \, 26.497 & 11 \, 11.671 & 3 \, 3.4698 & 6 \, 3.3087 \\ \hline 3 & 10 \, 19.732 & 14 \, 8.6913 & 5 \, 2.5839 & 0 \, 3.3087 \\ \hline 4 & 3 \, 12.966 & 7 \, 5.7114 & 3 \, 1.698 & 10 \, 2.6242 \\ \hline \end{array} \] Calculate the expected value in the first cell, to three decimal places. [Text Box] For an educational context, this table illustrates how agreement between two neurologists in diagnosing multiple sclerosis can be analyzed. Each cell contains two numbers: the actual observed count of diagnoses and the expected count if diagnoses were independent. This comparison helps in assessing the agreement and independence between the decisions made by the two neurologists.
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