From 6a68ff77f8c71c98a231914033f92aef8e713276 Mon Sep 17 00:00:00 2001
From: yh202109 <92902613+yh202109@users.noreply.github.com>
Date: Sun, 21 Jul 2024 18:28:25 +0000
Subject: [PATCH] =?UTF-8?q?Deploying=20to=20gh-pages=20from=20@=20yh202109?=
 =?UTF-8?q?/mtbp3@5315b5d621f235e32adc98c4d4f1ac07277f5fa8=20=F0=9F=9A=80?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 .../report.html                               |   4 +-
 .../coverage.xml                              |   2 +-
 ...c27a7cfee6077a57d62ef18dc8985b47ea226f.png | Bin 106864 -> 0 bytes
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 ...e4f4d3909203b45c4ed23f891b91dd1c0d5182.png | Bin 43142 -> 0 bytes
 _sources/statlab_kappa2.rst.txt               |  11 +-
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 _static/reports/junit/junit.xml               |   2 +-
 _static/reports/junit/report.html             |   4 +-
 example_cdtg.html                             |   8 +-
 example_clinical.html                         |  76 ++---
 example_emt3.html                             | 269 +++++++++---------
 example_files.html                            |   6 +-
 searchindex.js                                |   2 +-
 statlab_kappa2.html                           |  13 +-
 16 files changed, 192 insertions(+), 207 deletions(-)
 delete mode 100644 _images/52a37971a191bc5931ba183837c27a7cfee6077a57d62ef18dc8985b47ea226f.png
 create mode 100644 _images/533c386576f281089b9bf96459fc1da2b1d74b711328feaa8ad023239134a57e.png
 create mode 100644 _images/97a420d71e1361b711e9e67a2ed8dbc5ed1ebc55ff669adabdd6cf2c995300f8.png
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diff --git a/_downloads/214d05cd65dcc9387b037da1ce5a5c33/report.html b/_downloads/214d05cd65dcc9387b037da1ce5a5c33/report.html
index 2518d4ac..8618a6fc 100644
--- a/_downloads/214d05cd65dcc9387b037da1ce5a5c33/report.html
+++ b/_downloads/214d05cd65dcc9387b037da1ce5a5c33/report.html
@@ -328,7 +328,7 @@
   </head>
   <body>
     <h1 id="title">report.html</h1>
-    <p>Report generated on 21-Jul-2024 at 14:37:25 by <a href="https://pypi.python.org/pypi/pytest-html">pytest-html</a>
+    <p>Report generated on 21-Jul-2024 at 18:27:32 by <a href="https://pypi.python.org/pypi/pytest-html">pytest-html</a>
         v4.1.1</p>
     <div id="environment-header">
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@@ -429,7 +429,7 @@ <h2>Summary</h2>
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diff --git a/_sources/statlab_kappa2.rst.txt b/_sources/statlab_kappa2.rst.txt
index fe3112ea..80f5cfc1 100644
--- a/_sources/statlab_kappa2.rst.txt
+++ b/_sources/statlab_kappa2.rst.txt
@@ -36,7 +36,7 @@ with categorical rating outcomes [1]_ [2]_.
 Notation 
 *************
 
-Assume there are the same :math:`R+N_0` (:math:`geq 2+N_0`) raters and each of :math:`n` samples were rated by :math:`R` randomly selected raters and were not rated by the rest of :math:`N_0` raters.
+Assume there are the same :math:`R+N_0` (:math:`\geq 2+N_0`) raters and each of :math:`n` samples were rated by :math:`R` randomly selected raters and were not rated by the rest of :math:`N_0` raters.
 For :math:`J` categories rating, let :math:`Y_{r,i} \in \{v_0, v_1,v_2,\ldots, v_J \}` represent rating 
 from rater :math:`r=1,2,\ldots,R+N_0` for sample :math:`i = 1, \ldots, n`.
 Let :math:`N_{ij}` represent the total number of raters gave rating :math:`(v_j)` to sample :math:`i`, where :math:`j \in \{0, 1,\ldots,J\}`.
@@ -287,7 +287,7 @@ To calculate :eq:`eq_kappa2_vn2`,
 we can use the MGF, :math:`\left(\sum_{j}p_je^{t_j}\right)^R`, to derive
 :math:`E\left(N_{ij}^2\right) = Rp_j + R(R-1)p_j^2`, 
 :math:`E\left(N_{ij}^3\right) = Rp_j + 3R(R-1)p_j^2 + R(R-1)(R-2)p_j^3`, and 
-:math:`E\left(N_{ij}^4\right) = ` (Lab Exercise; to be used in :eq:`eq_kappa2_vn3` and :eq:`eq_kappa2_vn5`). 
+:math:`E\left(N_{ij}^4\right) =` (Lab Exercise; to be used in :eq:`eq_kappa2_vn3` and :eq:`eq_kappa2_vn5`). 
 
 The first element of :eq:`eq_kappa2_vn2` can be calculated as [2]_ :sup:`(Eq. 12)`
 
@@ -313,12 +313,7 @@ The second element of :eq:`eq_kappa2_vn2` can be calculated using
   :label: eq_kappa2_vn5
 
   E\left( N_{ij}^2 N_{ik}^2 \right)
-  =& E\left(N_{ik}^2E\left(N_{ij}^2|N_{ik}\right)\right) \\
-  =& \frac{p_j}{1-p_k}E\left(RN_{ik}^2-N_{ik}^3\right) 
-  + \frac{p_j^2}{(1-p_k)^2}E\left((R^2-R)N_{ik}^2 - (2R+1)N_{ik}^3-N_{ik}^4\right)
-  =& \left(\frac{p_j}{1-p_k} + \frac{p_j^2}{(1-p_k)^2}(R^2-R)\right)E(N_{ik}^2) 
-  -\left(\frac{p_j}{1-p_k}E(N_{ik}^3) + \frac{p_j^2}{(1-p_k)^2}(2R+1)\right)E(N_{ik}^3)
-  -\frac{p_j^2}{(1-p_k)^2}E(N_{ik}^4)
+  = R(R-1)p_j(p_k+(R-2)p_k^2) + R(R-1)(R-2)p_j^2(p_k+(R-3)2p_k^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)`
diff --git a/_static/reports/coverage/coverage.xml b/_static/reports/coverage/coverage.xml
index 76e17709..7b0d93b6 100644
--- a/_static/reports/coverage/coverage.xml
+++ b/_static/reports/coverage/coverage.xml
@@ -1,5 +1,5 @@
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 	<sources>
diff --git a/_static/reports/junit/junit.xml b/_static/reports/junit/junit.xml
index 4c914da5..5f4acf3e 100644
--- a/_static/reports/junit/junit.xml
+++ b/_static/reports/junit/junit.xml
@@ -1 +1 @@
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\ No newline at end of file
+<?xml version="1.0" encoding="utf-8"?><testsuites><testsuite name="pytest" errors="0" failures="0" skipped="0" tests="38" time="10.859" timestamp="2024-07-21T18:27:21.666185+00:00" hostname="fv-az885-740"><testcase classname="tests.test_cdt.TestCdt" name="test_diff_2cols_in_1df_invalid_input" time="0.002" /><testcase classname="tests.test_cdt.TestCdt" name="test_diff_2cols_in_1df_missing_column" time="0.001" /><testcase classname="tests.test_cdt.TestCdt" name="test_diff_2cols_in_1df_with_difference" time="0.005" /><testcase classname="tests.test_cdt.TestCdt" name="test_diff_2cols_in_1df_without_difference" time="0.002" /><testcase classname="tests.test_cdt.TestCdt" name="test_diff_2cols_in_2df_with_existing_column" time="0.010" /><testcase classname="tests.test_cdt.TestCdt" name="test_diff_2cols_in_2df_with_non_existing_column" time="0.001" /><testcase classname="tests.test_cdt.TestCdt" name="test_diff_2cols_in_2df_with_non_existing_group" time="0.001" /><testcase classname="tests.test_cdt.TestCdt" name="test_diff_2cols_in_2df_with_same_group_and_column" time="0.001" /><testcase classname="tests.test_health_ectd.TestCtocByFDA" name="test_find_section_given_words" time="0.001" /><testcase classname="tests.test_health_ectd.TestCtocByFDA" name="test_find_section_given_words_invalid_include" time="0.001" /><testcase classname="tests.test_health_ectd.TestCtocByFDA" name="test_find_section_given_words_invalid_outfmt" time="0.001" /><testcase classname="tests.test_health_ectd.TestCtocByFDA" name="test_load_list" time="0.001" /><testcase classname="tests.test_health_ectd.TestCtocByFDA" name="test_show_ctoc_tree" time="0.200" /><testcase classname="tests.test_health_emt.TestEmt" name="test_expected_file_lists" time="0.004" /><testcase classname="tests.test_health_emt.TestEmt" name="test_find_files" time="0.005" /><testcase classname="tests.test_health_emt.TestEmt" name="test_find_hlgt" time="0.004" /><testcase classname="tests.test_health_emt.TestEmt" name="test_find_hlt" time="0.004" /><testcase classname="tests.test_health_emt.TestEmt" name="test_find_llt" time="0.007" /><testcase classname="tests.test_health_emt.TestEmt" name="test_find_pt" time="0.004" /><testcase classname="tests.test_health_emt.TestEmt" name="test_find_pt_given_soc" time="0.006" /><testcase classname="tests.test_health_emt.TestEmt" name="test_find_pt_given_soc_primary_only" time="0.006" /><testcase classname="tests.test_health_emt.TestEmt" name="test_find_soc" time="0.004" /><testcase classname="tests.test_health_emt.TestEmt" name="test_list_files" time="0.025" /><testcase classname="tests.test_lsr.TestLsrTree" name="test_list_files_dataframe" time="0.001" /><testcase classname="tests.test_lsr.TestLsrTree" name="test_list_files_json" time="0.001" /><testcase classname="tests.test_lsr.TestLsrTree" name="test_list_files_list" time="0.001" /><testcase classname="tests.test_lsr.TestLsrTree" name="test_list_files_string" time="0.001" /><testcase classname="tests.test_lsr.TestLsrTree" name="test_list_files_tree" time="0.013" /><testcase classname="tests.test_lsr.TestLsrTree" name="test_list_files_tree2" time="0.008" /><testcase classname="tests.test_statlab_corr.TestCorrCalculator" name="test_calculate_kendall_tau_with_dataframe" time="0.002" /><testcase classname="tests.test_statlab_corr.TestCorrCalculator" name="test_calculate_kendall_tau_with_list" time="0.002" /><testcase classname="tests.test_statlab_corr.TestCorrCalculator" name="test_plot_y_list" time="0.017" /><testcase classname="tests.test_statlab_kappa.TestKappaCalculator" name="test_bootstrap_cohen_ci" time="0.238" /><testcase classname="tests.test_statlab_kappa.TestKappaCalculator" name="test_cohen" time="0.070" /><testcase classname="tests.test_statlab_kappa.TestKappaCalculator" name="test_fleiss_kappa" time="0.067" /><testcase classname="tests.test_stdiso_pdfsummary.TestPdfSummary" name="test_compare_file_size" time="0.767" /><testcase classname="tests.test_stdiso_pdfsummary.TestPdfSummary" name="test_get_outline_list" time="0.875" /><testcase classname="tests.test_stdiso_pdfsummary.TestPdfSummary" name="test_show_outline_tree" time="0.842" /></testsuite></testsuites>
\ No newline at end of file
diff --git a/_static/reports/junit/report.html b/_static/reports/junit/report.html
index 2518d4ac..8618a6fc 100644
--- a/_static/reports/junit/report.html
+++ b/_static/reports/junit/report.html
@@ -328,7 +328,7 @@
   </head>
   <body>
     <h1 id="title">report.html</h1>
-    <p>Report generated on 21-Jul-2024 at 14:37:25 by <a href="https://pypi.python.org/pypi/pytest-html">pytest-html</a>
+    <p>Report generated on 21-Jul-2024 at 18:27:32 by <a href="https://pypi.python.org/pypi/pytest-html">pytest-html</a>
         v4.1.1</p>
     <div id="environment-header">
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@@ -429,7 +429,7 @@ <h2>Summary</h2>
     </table>
   </body>
   <footer>
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     <script>
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 const { getCollapsedCategory, setCollapsedIds } = require('./storage.js')
diff --git a/example_cdtg.html b/example_cdtg.html
index 48882c55..6961ea43 100644
--- a/example_cdtg.html
+++ b/example_cdtg.html
@@ -133,15 +133,13 @@ <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: 16.7% 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: 38.9% 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: 40.0% 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: 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)
 </pre></div>
 </div>
-<img alt="_images/d4bf13e7296f9358479bd81daae4f4d3909203b45c4ed23f891b91dd1c0d5182.png" src="_images/d4bf13e7296f9358479bd81daae4f4d3909203b45c4ed23f891b91dd1c0d5182.png" />
+<img alt="_images/97a420d71e1361b711e9e67a2ed8dbc5ed1ebc55ff669adabdd6cf2c995300f8.png" src="_images/97a420d71e1361b711e9e67a2ed8dbc5ed1ebc55ff669adabdd6cf2c995300f8.png" />
 </div>
 </div>
 <p>To create a line plot:</p>
@@ -153,7 +151,7 @@ <h1>U/Graph/Categorical Plots Using catPlotter<a class="headerlink" href="#u-gra
 </div>
 </div>
 <div class="cell_output docutils container">
-<img alt="_images/52a37971a191bc5931ba183837c27a7cfee6077a57d62ef18dc8985b47ea226f.png" src="_images/52a37971a191bc5931ba183837c27a7cfee6077a57d62ef18dc8985b47ea226f.png" />
+<img alt="_images/533c386576f281089b9bf96459fc1da2b1d74b711328feaa8ad023239134a57e.png" src="_images/533c386576f281089b9bf96459fc1da2b1d74b711328feaa8ad023239134a57e.png" />
 </div>
 </div>
 </section>
diff --git a/example_clinical.html b/example_clinical.html
index a74b3a55..6c738c26 100644
--- a/example_clinical.html
+++ b/example_clinical.html
@@ -131,8 +131,8 @@ <h2>Example 1<a class="headerlink" href="#example-1" title="Link to this heading
 </div>
 <div class="cell_output docutils container">
 <div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>  study treatment subject   visit  meal  calorie
-0  STD1      TRT1  SUBJ01  VISIT1     1     1440
-1  STD1      TRT1  SUBJ01  VISIT1     2      822
+0  STD1      TRT1  SUBJ01  VISIT1     1     1615
+1  STD1      TRT1  SUBJ01  VISIT1     2      632
 </pre></div>
 </div>
 </div>
@@ -149,12 +149,12 @@ <h2>Example 1<a class="headerlink" href="#example-1" title="Link to this heading
 </div>
 <div class="cell_output docutils container">
 <div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>  study treatment subject   visit  N(0&lt;=X&lt;500)  N(500&lt;=X&lt;1000)  \
-0  STD1      TRT1  SUBJ01  VISIT1            0               1   
-1  STD1      TRT1  SUBJ01  VISIT2            0               2   
+0  STD1      TRT1  SUBJ01  VISIT1            0               3   
+1  STD1      TRT1  SUBJ02  VISIT1            2               0   
 
    N(1000&lt;=V&lt;=2000)  N(all)  
-0                 1       2  
-1                 2       4  
+0                 1       4  
+1                 3       5  
 </pre></div>
 </div>
 </div>
@@ -169,22 +169,22 @@ <h2>Example 1<a class="headerlink" href="#example-1" title="Link to this heading
 </div>
 <div class="cell_output docutils container">
 <div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>   study treatment   visit  N(0&lt;=X&lt;3)  N(3&lt;=X&lt;5)  N(5&lt;=V&lt;=7)  N(all)
-0   STD1      TRT1  VISIT1          5         10           5      20
-1   STD1      TRT1  VISIT2          4          7           5      16
-2   STD1      TRT1  VISIT3          1          8           3      12
-3   STD1      TRT1  VISIT4          1          3           3       7
-4   STD1      TRT2  VISIT1          6         11           3      20
-5   STD1      TRT2  VISIT2          1          4          10      15
-6   STD1      TRT2  VISIT3          4          3           2       9
-7   STD1      TRT2  VISIT4          0          0           1       1
-8   STD2      TRT1  VISIT1          3         13           4      20
-9   STD2      TRT1  VISIT2          5         10           1      16
-10  STD2      TRT1  VISIT3          7          1           2      10
-11  STD2      TRT1  VISIT4          0          3           0       3
-12  STD2      TRT2  VISIT1          6         10           4      20
-13  STD2      TRT2  VISIT2          4         11           1      16
-14  STD2      TRT2  VISIT3          1          6           3      10
-15  STD2      TRT2  VISIT4          1          3           2       6
+0   STD1      TRT1  VISIT1          7          7           6      20
+1   STD1      TRT1  VISIT2          2          8           7      17
+2   STD1      TRT1  VISIT3          1          9           3      13
+3   STD1      TRT1  VISIT4          1          7           2      10
+4   STD1      TRT2  VISIT1          4         11           5      20
+5   STD1      TRT2  VISIT2          2          7           5      14
+6   STD1      TRT2  VISIT3          2          4           3       9
+7   STD1      TRT2  VISIT4          1          2           0       3
+8   STD2      TRT1  VISIT1          1         12           7      20
+9   STD2      TRT1  VISIT2          4          8           3      15
+10  STD2      TRT1  VISIT3          3          5           0       8
+11  STD2      TRT1  VISIT4          2          3           0       5
+12  STD2      TRT2  VISIT1          6         11           3      20
+13  STD2      TRT2  VISIT2          4         10           4      18
+14  STD2      TRT2  VISIT3          4          5           4      13
+15  STD2      TRT2  VISIT4          2          5           2       9
 </pre></div>
 </div>
 </div>
@@ -198,22 +198,22 @@ <h2>Example 1<a class="headerlink" href="#example-1" title="Link to this heading
 </div>
 <div class="cell_output docutils container">
 <div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>   study treatment   visit  Sum(0&lt;=X&lt;3)  Sum(3&lt;=X&lt;5)  Sum(5&lt;=V&lt;=7)  Sum(all)
-0   STD1      TRT1  VISIT1           10           36            25        71
-1   STD1      TRT1  VISIT2            8           25            25        58
-2   STD1      TRT1  VISIT3            2           28            15        45
-3   STD1      TRT1  VISIT4            2           11            15        28
-4   STD1      TRT2  VISIT1           12           38            15        65
-5   STD1      TRT2  VISIT2            2           15            50        67
-6   STD1      TRT2  VISIT3            8           11            10        29
-7   STD1      TRT2  VISIT4            0            0             5         5
-8   STD2      TRT1  VISIT1            6           45            20        71
-9   STD2      TRT1  VISIT2           10           36             5        51
-10  STD2      TRT1  VISIT3           14            4            10        28
-11  STD2      TRT1  VISIT4            0           11             0        11
-12  STD2      TRT2  VISIT1           12           36            20        68
-13  STD2      TRT2  VISIT2            8           41             5        54
-14  STD2      TRT2  VISIT3            2           21            15        38
-15  STD2      TRT2  VISIT4            2           12            10        24
+0   STD1      TRT1  VISIT1           14           25            30        69
+1   STD1      TRT1  VISIT2            4           29            35        68
+2   STD1      TRT1  VISIT3            2           30            15        47
+3   STD1      TRT1  VISIT4            2           24            10        36
+4   STD1      TRT2  VISIT1            8           37            25        70
+5   STD1      TRT2  VISIT2            4           22            25        51
+6   STD1      TRT2  VISIT3            4           13            15        32
+7   STD1      TRT2  VISIT4            2            8             0        10
+8   STD2      TRT1  VISIT1            2           41            35        78
+9   STD2      TRT1  VISIT2            8           29            15        52
+10  STD2      TRT1  VISIT3            6           18             0        24
+11  STD2      TRT1  VISIT4            4           10             0        14
+12  STD2      TRT2  VISIT1           12           38            15        65
+13  STD2      TRT2  VISIT2            8           38            20        66
+14  STD2      TRT2  VISIT3            8           16            20        44
+15  STD2      TRT2  VISIT4            4           17            10        31
 </pre></div>
 </div>
 </div>
diff --git a/example_emt3.html b/example_emt3.html
index b5097a09..91d2f278 100644
--- a/example_emt3.html
+++ b/example_emt3.html
@@ -295,92 +295,92 @@ <h2>FMQ Tree<a class="headerlink" href="#fmq-tree" title="Link to this heading">
     ├── Abdominal Pain:
     │   ├── [Classification] Broad:
     │   │   ├── [SOC] soc214dfxgAelhGHfEFFkgrAsFYzZBAFs:
-    │   │   │   ├── [PT01] Complicated appendicitis
+    │   │   │   ├── [PT01] Carnett&#39;s sign positive
     │   │   │   ├── [PT02] Gastric irritation
-    │   │   │   ├── [PT03] Gastroenteritis Escherichia coli
-    │   │   │   ├── [PT04] Helicobacter duodenal ulcer
-    │   │   │   ├── [PT05] Infantile colic
-    │   │   │   ├── [PT06] Visceral pain
-    │   │   │   └── [PT07] CRIA syndrome
+    │   │   │   ├── [PT03] Gastritis erosive
+    │   │   │   ├── [PT04] Gastroenteritis escherichia coli
+    │   │   │   ├── [PT05] Gastroenteritis Escherichia coli
+    │   │   │   ├── [PT06] Gastroenterostomy
+    │   │   │   ├── [PT07] Haemorrhagic erosive gastritis
+    │   │   │   ├── [PT08] Helicobacter duodenal ulcer
+    │   │   │   └── [PT09] Yao syndrome
     │   │   ├── [SOC] soc360phgmkaCxrALPg:
-    │   │   │   ├── [PT08] Carnett&#39;s sign positive
-    │   │   │   ├── [PT09] Gastritis erosive
-    │   │   │   ├── [PT10] Gastroenterostomy
-    │   │   │   ├── [PT11] Large intestine infection
-    │   │   │   └── [PT12] Peritoneoplasty
+    │   │   │   ├── [PT10] Large intestine infection
+    │   │   │   ├── [PT11] Ulcerative duodenitis
+    │   │   │   ├── [PT12] CRIA syndrome
+    │   │   │   └── [PT13] Peritoneoplasty
     │   │   └── [SOC] soc972ZiuFsAfKKVWFbSZdYcgUoCiSTyEYKu:
-    │   │       ├── [PT13] Gastroenteritis escherichia coli
-    │   │       ├── [PT14] Gastro-enterostomy
-    │   │       ├── [PT15] Haemorrhagic erosive gastritis
-    │   │       ├── [PT16] Peptic ulcer
-    │   │       ├── [PT17] Ulcerative duodenitis
-    │   │       ├── [PT18] Bauhin&#39;s valve syndrome
-    │   │       ├── [PT19] Yao syndrome
+    │   │       ├── [PT14] Complicated appendicitis
+    │   │       ├── [PT15] Gastro-enterostomy
+    │   │       ├── [PT16] Infantile colic
+    │   │       ├── [PT17] Peptic ulcer
+    │   │       ├── [PT18] Visceral pain
+    │   │       ├── [PT19] Bauhin&#39;s valve syndrome
     │   │       └── [PT20] Segmental arterial mediolysis
     │   └── [Classification] Narrow:
     │       ├── [SOC] soc214dfxgAelhGHfEFFkgrAsFYzZBAFs:
-    │       │   ├── [PT21] Abdominal migraine
+    │       │   ├── [PT21] Abdominal discomfort
     │       │   ├── [PT22] Abdominal pain
     │       │   ├── [PT23] Abdominal rebound tenderness
-    │       │   ├── [PT24] Gastrointestinal discomfort
+    │       │   ├── [PT24] Acute abdomen
     │       │   └── [PT25] Ilioinguinal neuralgia
     │       ├── [SOC] soc360phgmkaCxrALPg:
-    │       │   ├── [PT26] Abdominal discomfort
-    │       │   ├── [PT27] Abdominal pain lower
-    │       │   ├── [PT28] Abdominal pain upper
-    │       │   ├── [PT29] Abdominal rigidity
-    │       │   ├── [PT30] Enteric neuropathy
+    │       │   ├── [PT26] Abdominal pain aggravated
+    │       │   ├── [PT27] Abdominal tenderness
+    │       │   ├── [PT28] Enteric neuropathy
+    │       │   ├── [PT29] Epigastric discomfort
+    │       │   ├── [PT30] Gastrointestinal discomfort
     │       │   ├── [PT31] Gastrointestinal pain
     │       │   ├── [PT32] Gastrointestinal pain NOS
-    │       │   └── [PT33] Spleen pain
+    │       │   ├── [PT33] Intestinal spasm
+    │       │   ├── [PT34] Perihepatic discomfort
+    │       │   ├── [PT35] Spleen pain
+    │       │   └── [PT36] Ulcer type pain
     │       └── [SOC] soc972ZiuFsAfKKVWFbSZdYcgUoCiSTyEYKu:
-    │           ├── [PT34] Abdominal pain aggravated
-    │           ├── [PT35] Abdominal pain NOS
-    │           ├── [PT36] Abdominal tenderness
-    │           ├── [PT37] Acute abdomen
-    │           ├── [PT38] Epigastric discomfort
-    │           ├── [PT39] Gastrointestinal upset
-    │           ├── [PT40] Intestinal spasm
-    │           ├── [PT41] Perihepatic discomfort
-    │           ├── [PT42] Stomach discomfort
-    │           └── [PT43] Ulcer type pain
+    │           ├── [PT37] Abdominal migraine
+    │           ├── [PT38] Abdominal pain lower
+    │           ├── [PT39] Abdominal pain NOS
+    │           ├── [PT40] Abdominal pain upper
+    │           ├── [PT41] Abdominal rigidity
+    │           ├── [PT42] Gastrointestinal upset
+    │           └── [PT43] Stomach discomfort
     └── Abnormal Uterine Bleeding:
         ├── [Classification] Broad:
         │   ├── [SOC] soc214dfxgAelhGHfEFFkgrAsFYzZBAFs:
-        │   │   ├── [PT01] Anovulatory cycle
-        │   │   ├── [PT02] Bleeding anovulatory
-        │   │   ├── [PT03] Follicle-stimulating hormone deficiency
-        │   │   └── [PT04] Menstrual disorder
+        │   │   ├── [PT01] Bleeding anovulatory
+        │   │   └── [PT02] Menstrual disorder
         │   ├── [SOC] soc360phgmkaCxrALPg:
-        │   │   ├── [PT05] Follicle stimulating hormone deficiency
-        │   │   ├── [PT06] Uterine dehiscence
-        │   │   └── [PT07] Ovarian dysfunction
+        │   │   ├── [PT03] Follicle-stimulating hormone deficiency
+        │   │   ├── [PT04] Uterine dehiscence
+        │   │   └── [PT05] Ovarian dysfunction
         │   └── [SOC] soc972ZiuFsAfKKVWFbSZdYcgUoCiSTyEYKu:
-        │       ├── [PT08] Dysmenorrhea
-        │       └── [PT09] Dysmenorrhoea
+        │       ├── [PT06] Anovulatory cycle
+        │       ├── [PT07] Dysmenorrhea
+        │       ├── [PT08] Dysmenorrhoea
+        │       └── [PT09] Follicle stimulating hormone deficiency
         └── [Classification] Narrow:
             ├── [SOC] soc214dfxgAelhGHfEFFkgrAsFYzZBAFs:
-            │   ├── [PT10] Abnormal uterine bleeding
-            │   ├── [PT11] Menometrorrhagia
-            │   ├── [PT12] Menorrhagia
-            │   ├── [PT13] Menstruation delayed
-            │   ├── [PT14] Uterine haemorrhage
-            │   └── [PT15] Uterine rupture
+            │   ├── [PT10] Menometrorrhagia
+            │   ├── [PT11] Menorrhagia
+            │   ├── [PT12] Menstruation delayed
+            │   └── [PT13] Postmenopausal haemorrhage
             ├── [SOC] soc360phgmkaCxrALPg:
-            │   ├── [PT16] Cervix haemorrhage uterine
-            │   ├── [PT17] Dysfunctional uterine bleeding
-            │   ├── [PT18] Heavy menstrual bleeding
-            │   ├── [PT19] Menstruation irregular
-            │   ├── [PT20] Metrorrhagia
-            │   ├── [PT21] Oligomenorrhoea
-            │   ├── [PT22] Polymenorrhagia
-            │   └── [PT23] Vaginal haemorrhage
+            │   ├── [PT14] Abnormal uterine bleeding
+            │   ├── [PT15] Abnormal withdrawal bleeding
+            │   ├── [PT16] Dysfunctional uterine bleeding
+            │   ├── [PT17] Heavy menstrual bleeding
+            │   ├── [PT18] Oligomenorrhoea
+            │   ├── [PT19] Polymenorrhagia
+            │   ├── [PT20] Polymenorrhoea
+            │   └── [PT21] Uterine haemorrhage
             └── [SOC] soc972ZiuFsAfKKVWFbSZdYcgUoCiSTyEYKu:
-                ├── [PT24] Abnormal withdrawal bleeding
-                ├── [PT25] Hypomenorrhoea
-                ├── [PT26] Intermenstrual bleeding
-                ├── [PT27] Polymenorrhoea
-                └── [PT28] Postmenopausal haemorrhage
+                ├── [PT22] Cervix haemorrhage uterine
+                ├── [PT23] Hypomenorrhoea
+                ├── [PT24] Intermenstrual bleeding
+                ├── [PT25] Menstruation irregular
+                ├── [PT26] Metrorrhagia
+                ├── [PT27] Uterine rupture
+                └── [PT28] Vaginal haemorrhage
 </pre></div>
 </div>
 <div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>
@@ -404,95 +404,92 @@ <h2>FMQ Tree<a class="headerlink" href="#fmq-tree" title="Link to this heading">
                                             Abdominal Pain ──┤    
                                 Broad [Classification] ──┤   │    
            soc214dfxgAelhGHfEFFkgrAsFYzZBAFs [SOC] ──┤   │   │    
-                     Gastric irritation [PT01] ──┤   │   │   │    
-                      Gastritis erosive [PT02] ──┤   │   │   │    
-                     Gastro-enterostomy [PT04] ──┤   │   │   │    
-       Gastroenteritis Escherichia coli [PT03] ──┤   │   │   │    
-         Haemorrhagic erosive gastritis [PT05] ──┤   │   │   │    
-              Large intestine infection [PT06] ──┤   │   │   │    
-                          Visceral pain [PT07] ──┘   │   │   │    
+               Complicated appendicitis [PT01] ──┤   │   │   │    
+                      Gastroenterostomy [PT02] ──┤   │   │   │    
+              Large intestine infection [PT03] ──┤   │   │   │    
+                           Peptic ulcer [PT04] ──┤   │   │   │    
+                           Yao syndrome [PT05] ──┘   │   │   │    
                          soc360phgmkaCxrALPg [SOC] ──┤   │   │    
-                Bauhin&#39;s valve syndrome [PT10] ──┤   │   │   │    
-                          CRIA syndrome [PT09] ──┤   │   │   │    
-               Complicated appendicitis [PT08] ──┘   │   │   │    
+                Carnett&#39;s sign positive [PT06] ──┤   │   │   │    
+                     Gastric irritation [PT07] ──┤   │   │   │    
+                     Gastro-enterostomy [PT09] ──┤   │   │   │    
+       Gastroenteritis escherichia coli [PT08] ──┤   │   │   │    
+            Helicobacter duodenal ulcer [PT10] ──┤   │   │   │    
+                        Peritoneoplasty [PT12] ──┤   │   │   │    
+                          Visceral pain [PT11] ──┘   │   │   │    
         soc972ZiuFsAfKKVWFbSZdYcgUoCiSTyEYKu [SOC] ──┘   │   │    
-                Carnett&#39;s sign positive [PT11] ──┤       │   │    
-       Gastroenteritis escherichia coli [PT12] ──┤       │   │    
-                      Gastroenterostomy [PT13] ──┤       │   │    
-            Helicobacter duodenal ulcer [PT14] ──┤       │   │    
-                        Infantile colic [PT15] ──┤       │   │    
-                           Peptic ulcer [PT16] ──┤       │   │    
-                        Peritoneoplasty [PT19] ──┤       │   │    
+                Bauhin&#39;s valve syndrome [PT19] ──┤       │   │    
+                          CRIA syndrome [PT18] ──┤       │   │    
+                      Gastritis erosive [PT13] ──┤       │   │    
+       Gastroenteritis Escherichia coli [PT14] ──┤       │   │    
+         Haemorrhagic erosive gastritis [PT15] ──┤       │   │    
+                        Infantile colic [PT16] ──┤       │   │    
           Segmental arterial mediolysis [PT20] ──┤       │   │    
-                  Ulcerative duodenitis [PT17] ──┤       │   │    
-                           Yao syndrome [PT18] ──┘       │   │    
+                  Ulcerative duodenitis [PT17] ──┘       │   │    
                                Narrow [Classification] ──┘   │    
            soc214dfxgAelhGHfEFFkgrAsFYzZBAFs [SOC] ──┤       │    
-                         Abdominal pain [PT21] ──┤   │       │    
-              Abdominal pain aggravated [PT22] ──┤   │       │    
-                   Abdominal pain lower [PT23] ──┤   │       │    
-           Abdominal rebound tenderness [PT24] ──┤   │       │    
-            Gastrointestinal discomfort [PT25] ──┤   │       │    
-                  Gastrointestinal pain [PT26] ──┤   │       │    
-                 Ilioinguinal neuralgia [PT30] ──┤   │       │    
-                 Perihepatic discomfort [PT27] ──┤   │       │    
-                     Stomach discomfort [PT28] ──┤   │       │    
+              Abdominal pain aggravated [PT21] ──┤   │       │    
+                   Abdominal pain lower [PT22] ──┤   │       │    
+           Abdominal rebound tenderness [PT23] ──┤   │       │    
+                          Acute abdomen [PT24] ──┤   │       │    
+                     Enteric neuropathy [PT25] ──┤   │       │    
+            Gastrointestinal discomfort [PT26] ──┤   │       │    
+              Gastrointestinal pain NOS [PT27] ──┤   │       │    
+                       Intestinal spasm [PT28] ──┤   │       │    
                         Ulcer type pain [PT29] ──┘   │       │    
                          soc360phgmkaCxrALPg [SOC] ──┤       │    
-                   Abdominal discomfort [PT31] ──┤   │       │    
-                     Abdominal migraine [PT32] ──┤   │       │    
-                     Abdominal pain NOS [PT33] ──┤   │       │    
-                   Abdominal pain upper [PT34] ──┤   │       │    
-                   Abdominal tenderness [PT35] ──┤   │       │    
-                          Acute abdomen [PT36] ──┤   │       │    
-                  Epigastric discomfort [PT37] ──┤   │       │    
-              Gastrointestinal pain NOS [PT38] ──┘   │       │    
+                   Abdominal discomfort [PT30] ──┤   │       │    
+                   Abdominal pain upper [PT31] ──┤   │       │    
+                     Abdominal rigidity [PT32] ──┤   │       │    
+                 Gastrointestinal upset [PT33] ──┤   │       │    
+                 Ilioinguinal neuralgia [PT37] ──┤   │       │    
+                 Perihepatic discomfort [PT34] ──┤   │       │    
+                            Spleen pain [PT35] ──┤   │       │    
+                     Stomach discomfort [PT36] ──┘   │       │    
         soc972ZiuFsAfKKVWFbSZdYcgUoCiSTyEYKu [SOC] ──┘       │    
-                     Abdominal rigidity [PT39] ──┤           │    
-                     Enteric neuropathy [PT40] ──┤           │    
-                 Gastrointestinal upset [PT41] ──┤           │    
-                       Intestinal spasm [PT42] ──┤           │    
-                            Spleen pain [PT43] ──┘           │    
+                     Abdominal migraine [PT38] ──┤           │    
+                     Abdominal pain NOS [PT40] ──┤           │    
+                         Abdominal pain [PT39] ──┤           │    
+                   Abdominal tenderness [PT41] ──┤           │    
+                  Epigastric discomfort [PT42] ──┤           │    
+                  Gastrointestinal pain [PT43] ──┘           │    
                                  Abnormal Uterine Bleeding ──┘    
                                 Broad [Classification] ──┤        
            soc214dfxgAelhGHfEFFkgrAsFYzZBAFs [SOC] ──┤   │        
-                     Menstrual disorder [PT01] ──┤   │   │        
-                    Ovarian dysfunction [PT02] ──┘   │   │        
+                   Bleeding anovulatory [PT01] ──┤   │   │        
+                           Dysmenorrhea [PT02] ──┤   │   │        
+                     Menstrual disorder [PT03] ──┤   │   │        
+                    Ovarian dysfunction [PT04] ──┘   │   │        
                          soc360phgmkaCxrALPg [SOC] ──┤   │        
-                      Anovulatory cycle [PT03] ──┤   │   │        
-                           Dysmenorrhea [PT04] ──┤   │   │        
-                     Uterine dehiscence [PT05] ──┘   │   │        
+                      Anovulatory cycle [PT05] ──┤   │   │        
+Follicle-stimulating hormone deficiency [PT06] ──┤   │   │        
+                     Uterine dehiscence [PT07] ──┘   │   │        
         soc972ZiuFsAfKKVWFbSZdYcgUoCiSTyEYKu [SOC] ──┘   │        
-                   Bleeding anovulatory [PT06] ──┤       │        
-                          Dysmenorrhoea [PT07] ──┤       │        
-Follicle stimulating hormone deficiency [PT09] ──┤       │        
-Follicle-stimulating hormone deficiency [PT08] ──┘       │        
+                          Dysmenorrhoea [PT08] ──┤       │        
+Follicle stimulating hormone deficiency [PT09] ──┘       │        
                                Narrow [Classification] ──┘        
            soc214dfxgAelhGHfEFFkgrAsFYzZBAFs [SOC] ──┤            
-              Abnormal uterine bleeding [PT10] ──┤   │            
-           Abnormal withdrawal bleeding [PT11] ──┤   │            
-         Dysfunctional uterine bleeding [PT12] ──┤   │            
-                       Menometrorrhagia [PT13] ──┤   │            
-                            Menorrhagia [PT14] ──┤   │            
-                   Menstruation delayed [PT15] ──┤   │            
-                           Metrorrhagia [PT16] ──┤   │            
-                        Oligomenorrhoea [PT17] ──┘   │            
+           Abnormal withdrawal bleeding [PT10] ──┤   │            
+             Cervix haemorrhage uterine [PT11] ──┤   │            
+                            Menorrhagia [PT12] ──┤   │            
+                           Metrorrhagia [PT13] ──┤   │            
+                    Uterine haemorrhage [PT14] ──┤   │            
+                    Vaginal haemorrhage [PT15] ──┘   │            
                          soc360phgmkaCxrALPg [SOC] ──┤            
-               Heavy menstrual bleeding [PT18] ──┤   │            
-                         Hypomenorrhoea [PT19] ──┤   │            
-                Intermenstrual bleeding [PT20] ──┤   │            
-                 Menstruation irregular [PT21] ──┤   │            
-                        Uterine rupture [PT22] ──┤   │            
-                    Vaginal haemorrhage [PT23] ──┘   │            
+              Abnormal uterine bleeding [PT16] ──┤   │            
+               Heavy menstrual bleeding [PT17] ──┤   │            
+                       Menometrorrhagia [PT18] ──┤   │            
+                        Oligomenorrhoea [PT19] ──┤   │            
+                        Polymenorrhagia [PT20] ──┤   │            
+             Postmenopausal haemorrhage [PT21] ──┤   │            
+                        Uterine rupture [PT22] ──┘   │            
         soc972ZiuFsAfKKVWFbSZdYcgUoCiSTyEYKu [SOC] ──┘            
-             Cervix haemorrhage uterine [PT24] ──┤                
-                        Polymenorrhagia [PT25] ──┤                
-                         Polymenorrhoea [PT26] ──┤                
-             Postmenopausal haemorrhage [PT27] ──┤                
-                    Uterine haemorrhage [PT28] ──┘                
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>
+         Dysfunctional uterine bleeding [PT23] ──┤                
+                         Hypomenorrhoea [PT24] ──┤                
+                Intermenstrual bleeding [PT25] ──┤                
+                   Menstruation delayed [PT26] ──┤                
+                 Menstruation irregular [PT27] ──┤                
+                         Polymenorrhoea [PT28] ──┘                
 </pre></div>
 </div>
 </div>
diff --git a/example_files.html b/example_files.html
index a5608b75..351d1e1a 100644
--- a/example_files.html
+++ b/example_files.html
@@ -153,7 +153,7 @@ <h1>U/System/List Folder Contents<a class="headerlink" href="#u-system-list-fold
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>testfolder_72/
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>testfolder_5/
 ├── subfolder1/
 └── subfolder2/
     └── testfile3
@@ -170,7 +170,7 @@ <h1>U/System/List Folder Contents<a class="headerlink" href="#u-system-list-fold
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>testfolder_72/  &lt;&lt;&lt;((( F=0; D=2 )))&gt;&gt;&gt;
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>testfolder_5/  &lt;&lt;&lt;((( F=0; D=2 )))&gt;&gt;&gt;
 ├── subfolder1/  &lt;&lt;&lt;((( Empty Folder )))&gt;&gt;&gt;
 └── subfolder2/  &lt;&lt;&lt;((( F=1; D=0 )))&gt;&gt;&gt;
     └── testfile3
@@ -193,7 +193,7 @@ <h1>U/System/List Folder Contents<a class="headerlink" href="#u-system-list-fold
 
                    modified                   created  file_type N_page  \
 0                      None                      None       None   None   
-1  Sun Jul 21 14:38:05 2024  Sun Jul 21 14:38:05 2024  testfile3   None   
+1  Sun Jul 21 18:28:14 2024  Sun Jul 21 18:28:14 2024  testfile3   None   
 
   N_column N_row  
 0     None  None  
diff --git a/searchindex.js b/searchindex.js
index 717ae2e6..3977be0b 100644
--- a/searchindex.js
+++ b/searchindex.js
@@ -1 +1 @@
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\ No newline at end of file
diff --git a/statlab_kappa2.html b/statlab_kappa2.html
index 7d2f0f2b..8afca011 100644
--- a/statlab_kappa2.html
+++ b/statlab_kappa2.html
@@ -116,7 +116,7 @@ <h2>Background<a class="headerlink" href="#background" title="Link to this headi
 </section>
 <section id="notation">
 <h2>Notation<a class="headerlink" href="#notation" title="Link to this heading"></a></h2>
-<p>Assume there are the same <span class="math notranslate nohighlight">\(R+N_0\)</span> (<span class="math notranslate nohighlight">\(geq 2+N_0\)</span>) raters and each of <span class="math notranslate nohighlight">\(n\)</span> samples were rated by <span class="math notranslate nohighlight">\(R\)</span> randomly selected raters and were not rated by the rest of <span class="math notranslate nohighlight">\(N_0\)</span> raters.
+<p>Assume there are the same <span class="math notranslate nohighlight">\(R+N_0\)</span> (<span class="math notranslate nohighlight">\(\geq 2+N_0\)</span>) raters and each of <span class="math notranslate nohighlight">\(n\)</span> samples were rated by <span class="math notranslate nohighlight">\(R\)</span> randomly selected raters and were not rated by the rest of <span class="math notranslate nohighlight">\(N_0\)</span> raters.
 For <span class="math notranslate nohighlight">\(J\)</span> categories rating, let <span class="math notranslate nohighlight">\(Y_{r,i} \in \{v_0, v_1,v_2,\ldots, v_J \}\)</span> represent rating
 from rater <span class="math notranslate nohighlight">\(r=1,2,\ldots,R+N_0\)</span> for sample <span class="math notranslate nohighlight">\(i = 1, \ldots, n\)</span>.
 Let <span class="math notranslate nohighlight">\(N_{ij}\)</span> represent the total number of raters gave rating <span class="math notranslate nohighlight">\((v_j)\)</span> to sample <span class="math notranslate nohighlight">\(i\)</span>, where <span class="math notranslate nohighlight">\(j \in \{0, 1,\ldots,J\}\)</span>.
@@ -377,7 +377,7 @@ <h2>More Details<a class="headerlink" href="#more-details" title="Link to this h
 we can use the MGF, <span class="math notranslate nohighlight">\(\left(\sum_{j}p_je^{t_j}\right)^R\)</span>, to derive
 <span class="math notranslate nohighlight">\(E\left(N_{ij}^2\right) = Rp_j + R(R-1)p_j^2\)</span>,
 <span class="math notranslate nohighlight">\(E\left(N_{ij}^3\right) = Rp_j + 3R(R-1)p_j^2 + R(R-1)(R-2)p_j^3\)</span>, and
-<span class="math notranslate nohighlight">\(E\left(N_{ij}^4\right) = ` (Lab Exercise; to be used in :eq:`eq_kappa2_vn3\)</span> and <a class="reference internal" href="#equation-eq-kappa2-vn5">Eq. (7)</a>).</p>
+<span class="math notranslate nohighlight">\(E\left(N_{ij}^4\right) =\)</span> (Lab Exercise; to be used in <a class="reference internal" href="#equation-eq-kappa2-vn3">Eq. (5)</a> and <a class="reference internal" href="#equation-eq-kappa2-vn5">Eq. (7)</a>).</p>
 <p>The first element of <a class="reference internal" href="#equation-eq-kappa2-vn2">Eq. (4)</a> can be calculated as <a class="footnote-reference brackets" href="#id9" id="id4" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a> <sup>(Eq. 12)</sup></p>
 <div class="math notranslate nohighlight" id="equation-eq-kappa2-vn3">
 <span class="eqno">(5)<a class="headerlink" href="#equation-eq-kappa2-vn3" title="Link to this equation"></a></span>\[E\left(\sum_{j} N_{ij}^4\right)
@@ -389,13 +389,8 @@ <h2>More Details<a class="headerlink" href="#more-details" title="Link to this h
 =&amp; R^2 + R^2(R-1)\left(2\sum_{j} p_j^2 + (R-1)(\sum_j p_j^2)^2\right)\end{split}\]</div>
 <p>The second element of <a class="reference internal" href="#equation-eq-kappa2-vn2">Eq. (4)</a> can be calculated using</p>
 <div class="math notranslate nohighlight" id="equation-eq-kappa2-vn5">
-<span class="eqno">(7)<a class="headerlink" href="#equation-eq-kappa2-vn5" title="Link to this equation"></a></span>\[\begin{split}E\left( N_{ij}^2 N_{ik}^2 \right)
-=&amp; E\left(N_{ik}^2E\left(N_{ij}^2|N_{ik}\right)\right) \\
-=&amp; \frac{p_j}{1-p_k}E\left(RN_{ik}^2-N_{ik}^3\right)
-+ \frac{p_j^2}{(1-p_k)^2}E\left((R^2-R)N_{ik}^2 - (2R+1)N_{ik}^3-N_{ik}^4\right)
-=&amp; \left(\frac{p_j}{1-p_k} + \frac{p_j^2}{(1-p_k)^2}(R^2-R)\right)E(N_{ik}^2)
--\left(\frac{p_j}{1-p_k}E(N_{ik}^3) + \frac{p_j^2}{(1-p_k)^2}(2R+1)\right)E(N_{ik}^3)
--\frac{p_j^2}{(1-p_k)^2}E(N_{ik}^4)\end{split}\]</div>
+<span class="eqno">(7)<a class="headerlink" href="#equation-eq-kappa2-vn5" title="Link to this equation"></a></span>\[E\left( N_{ij}^2 N_{ik}^2 \right)
+= R(R-1)p_j(p_k+(R-2)p_k^2) + R(R-1)(R-2)p_j^2(p_k+(R-3)2p_k^2)\]</div>
 <p>Combining <a class="reference internal" href="#equation-eq-kappa2-vn3">Eq. (5)</a>, <a class="reference internal" href="#equation-eq-kappa2-vn4">Eq. (6)</a>, and <a class="reference internal" href="#equation-eq-kappa2-vn5">Eq. (7)</a>,
 <a class="reference internal" href="#equation-eq-kappa2-vn2">Eq. (4)</a> can be calculated as <a class="footnote-reference brackets" href="#id9" id="id6" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a> <sup>(Eq. 15)</sup></p>
 <div class="math notranslate nohighlight">
