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yh202109 · Jul 22, 2024 · 03b04be · 03b04be
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diff --git a/_downloads/214d05cd65dcc9387b037da1ce5a5c33/report.html b/_downloads/214d05cd65dcc9387b037da1ce5a5c33/report.html
diff --git a/_downloads/9911a4d807ac9f1a695f0aa2cf687076/coverage.xml b/_downloads/9911a4d807ac9f1a695f0aa2cf687076/coverage.xml
@@ -1,5 +1,5 @@
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+<coverage version="7.6.0" timestamp="1721615960831" lines-valid="1494" lines-covered="642" line-rate="0.4297" branches-covered="0" branches-valid="0" branch-rate="0" complexity="0">
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diff --git a/_images/4cd44a2a004d681aab3cbb72afe7536c2407426ef57d7ab86175e399660b4e56.png b/_images/4cd44a2a004d681aab3cbb72afe7536c2407426ef57d7ab86175e399660b4e56.png
diff --git a/_images/82f878b8d8450009ea9f3b8434afd4a147fa4501db9f66766beaffc03493b60c.png b/_images/82f878b8d8450009ea9f3b8434afd4a147fa4501db9f66766beaffc03493b60c.png
diff --git a/_images/b48368b32682c4cc9ab6249c62eef7d29bd38d3e5a903ca07b6c911f1f2a03f5.png b/_images/b48368b32682c4cc9ab6249c62eef7d29bd38d3e5a903ca07b6c911f1f2a03f5.png
diff --git a/_images/cfddb32ab3f2294e749768f3ba9bf366367e88e301af8cde289f5acf8720780c.png b/_images/cfddb32ab3f2294e749768f3ba9bf366367e88e301af8cde289f5acf8720780c.png
diff --git a/_sources/statlab_kappa2.rst.txt b/_sources/statlab_kappa2.rst.txt
@@ -251,13 +251,14 @@ probability of having agreement for a sample from two randomly selected raters e
 :eq:`eq_exp1` corresponds to the expected 
 probability of having agreement for a sample from two randomly selected raters under the assumption of no agreement, 
 which corresponds to the assumption of :math:`(N_{i1},\ldots, N_{iJ}) \sim multi(R, (p_1,\ldots, p_J))` where :math:`R>4`.
-Note that the notations in this page did not use conventional 'hat' to represent estimated :math:`p_j`.
 
+
+Let :math:`S_{p2} = \sum_j p_j^2`, :math:`S_{p3} = \sum_j p_j^3`, and :math:`S_{p4} = \sum_j p_j^4`. 
 The equation :eq:`eq_kappa1` can be expressed as [2]_ :sup:`(Eq. 9)`,
 
 .. math::
 
-  \kappa = \frac{\sum_{i=1}^{n}\sum_{j=1}^J N_{ij}^2 - nR\left(1+(R-1)\sum_{j=1}^J p_j^2\right)}{nR(R-1)(1-\sum_{j=1}^J p_j^2)}
+  \kappa = \frac{\sum_{i=1}^{n}\sum_{j=1}^J N_{ij}^2 - nR\left(1+(R-1) S_{p2} \right)}{nR(R-1)(1- S_{p2} )}
 
 
 Note that Fleiss (1971) assumed large :math:`n` and fixed :math:`p_j` while deriving variance of kappa.
@@ -272,7 +273,7 @@ where
 
 .. math::
 
-  c(n,R,\{p_j\}) = n^{-1}\left(R(R-1)\left(1-\sum_{j=1}^J p_j^2\right)\right)^{-2},
+  c(n,R,\{p_j\}) = n^{-1}\left(R(R-1)\left(1-S_{p2}\right)\right)^{-2},
 
 and 
 
@@ -294,16 +295,16 @@ The first element of :eq:`eq_kappa2_vn2` can be calculated as [2]_ :sup:`(Eq. 12
   :label: eq_kappa2_vn3
 
   E\left(\sum_{j} N_{ij}^4\right)
-  = R + 7R(R-1)\sum_j p_j^2 + 6R(R-1)(R-2)\sum_j p_j^3 + R(R-1)(R-2)(R-3)\sum_j p_j^4
+  = R + 7R(R-1)S_{p2} + 6R(R-1)(R-2)S_{p3} + R(R-1)(R-2)(R-3)S_{p4}
 
 The third element of :eq:`eq_kappa2_vn2` can be calculated as [2]_ :sup:`(Eq. 14)`
 
 .. math::
   :label: eq_kappa2_vn4
 
   \left(E\left(\sum_{j} N_{ij}^2\right)\right)^2 
-  =& R^2\left(1 + (R-1)\sum_{j} p_j^2 \right)^2  \\
-  =& R^2 + R^2(R-1)\left(2\sum_{j} p_j^2 + (R-1)(\sum_j p_j^2)^2\right) 
+  =& R^2\left(1 + (R-1)S_{p2} \right)^2  \\
+  =& R^2 + R^2(R-1)\left(2 S_{p2} + (R-1)S_{p2}^2\right) 
 
 The second element of :eq:`eq_kappa2_vn2` can be calculated, using 
 :math:`E\left( N_{ij}^2 N_{ik}^2 \right) = R(R-1)p_j(p_k+(R-2)p_k^2) + R(R-1)(R-2)p_j^2(p_k+(R-3)p_k^2)`, as
@@ -312,17 +313,17 @@ The second element of :eq:`eq_kappa2_vn2` can be calculated, using
   :label: eq_kappa2_vn5
 
   E\left( \sum_j\sum_{k \neq j} N_{ij}^2 N_{ik}^2 \right) 
-  =& R(R-1) + R(R-1)(2R-5)\left(\sum_j p_j^2\right) 
-  - 2R(R-1)(R-2)\left(\sum_j p_j^3\right) \\
-  &- R(R-1)(R-2)(R-3)\left(\sum_j p_j^4 \right) + R(R-1)(R-2)(R-3) \left(\sum_{j} p_j^2\right)^2
+  =& R(R-1) + R(R-1)(2R-5)S_{p2} 
+  - 2R(R-1)(R-2)S_{p3} \\
+  &- R(R-1)(R-2)(R-3)S_{p4} + R(R-1)(R-2)(R-3) S_{p2}^2
 
 Combining :eq:`eq_kappa2_vn3`, :eq:`eq_kappa2_vn4`, and :eq:`eq_kappa2_vn5`, 
 :eq:`eq_kappa2_vn2` can be calculated as [2]_ :sup:`(Eq. 15)`
 
 .. math::
 
   var\left(\sum_{j} N_{ij}^2 \right) 
-  = 2R(R-1)\left(\sum_j p_j^2 - (2R-3)\left(\sum_j p_j^2\right)^2 + 2(R-2)\sum_j p_j^3\right).
+  = 2R(R-1)\left(S_{p2} - (2R-3)S_{p2}^2 + 2(R-2)S_{p3}\right).
 
 *************
 Lab Exercise

diff --git a/_static/reports/coverage/coverage.xml b/_static/reports/coverage/coverage.xml
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diff --git a/_static/reports/junit/junit.xml b/_static/reports/junit/junit.xml
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diff --git a/_static/reports/junit/report.html b/_static/reports/junit/report.html
diff --git a/example_cdtg.html b/example_cdtg.html
@@ -133,15 +133,11 @@ <h1>U/Graph/Categorical Plots Using catPlotter<a class="headerlink" href="#u-gra
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/home/runner/.cache/pypoetry/virtualenvs/mtbp3-STzYEG9e-py3.10/lib/python3.10/site-packages/seaborn/categorical.py:3399: UserWarning: 11.1% of the points cannot be placed; you may want to decrease the size of the markers or use stripplot.
-  warnings.warn(msg, UserWarning)
-/home/runner/.cache/pypoetry/virtualenvs/mtbp3-STzYEG9e-py3.10/lib/python3.10/site-packages/seaborn/categorical.py:3399: UserWarning: 25.0% of the points cannot be placed; you may want to decrease the size of the markers or use stripplot.
-  warnings.warn(msg, UserWarning)
-/home/runner/.cache/pypoetry/virtualenvs/mtbp3-STzYEG9e-py3.10/lib/python3.10/site-packages/seaborn/categorical.py:3399: UserWarning: 30.0% of the points cannot be placed; you may want to decrease the size of the markers or use stripplot.
+<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/home/runner/.cache/pypoetry/virtualenvs/mtbp3-STzYEG9e-py3.10/lib/python3.10/site-packages/seaborn/categorical.py:3399: UserWarning: 35.0% of the points cannot be placed; you may want to decrease the size of the markers or use stripplot.
   warnings.warn(msg, UserWarning)
 </pre></div>
 </div>
-<img alt="_images/b48368b32682c4cc9ab6249c62eef7d29bd38d3e5a903ca07b6c911f1f2a03f5.png" src="_images/b48368b32682c4cc9ab6249c62eef7d29bd38d3e5a903ca07b6c911f1f2a03f5.png" />
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 </div>
 </div>
 <p>To create a line plot:</p>
@@ -153,7 +149,7 @@ <h1>U/Graph/Categorical Plots Using catPlotter<a class="headerlink" href="#u-gra
 </div>
 </div>
 <div class="cell_output docutils container">
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 </div>
 </div>
 </section>