diff --git a/_downloads/214d05cd65dcc9387b037da1ce5a5c33/report.html b/_downloads/214d05cd65dcc9387b037da1ce5a5c33/report.html
index 8618a6fc..c63f9999 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 18:27:32 by <a href="https://pypi.python.org/pypi/pytest-html">pytest-html</a>
+    <p>Report generated on 21-Jul-2024 at 18:50:56 by <a href="https://pypi.python.org/pypi/pytest-html">pytest-html</a>
         v4.1.1</p>
     <div id="environment-header">
       <h2>Environment</h2>
@@ -429,7 +429,7 @@ <h2>Summary</h2>
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   </body>
   <footer>
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&#34;tests/test_cdt.py::TestCdt::test_diff_2cols_in_2df_with_non_existing_column&#34;: [{&#34;extras&#34;: [], &#34;result&#34;: &#34;Passed&#34;, &#34;testId&#34;: &#34;tests/test_cdt.py::TestCdt::test_diff_2cols_in_2df_with_non_existing_column&#34;, &#34;duration&#34;: &#34;1 ms&#34;, &#34;resultsTableRow&#34;: [&#34;&lt;td class=\&#34;col-result\&#34;&gt;Passed&lt;/td&gt;&#34;, &#34;&lt;td class=\&#34;col-testId\&#34;&gt;tests/test_cdt.py::TestCdt::test_diff_2cols_in_2df_with_non_existing_column&lt;/td&gt;&#34;, &#34;&lt;td class=\&#34;col-duration\&#34;&gt;1 ms&lt;/td&gt;&#34;, &#34;&lt;td class=\&#34;col-links\&#34;&gt;&lt;/td&gt;&#34;], &#34;log&#34;: &#34;No log output captured.&#34;}], &#34;tests/test_cdt.py::TestCdt::test_diff_2cols_in_2df_with_non_existing_group&#34;: [{&#34;extras&#34;: [], &#34;result&#34;: &#34;Passed&#34;, &#34;testId&#34;: &#34;tests/test_cdt.py::TestCdt::test_diff_2cols_in_2df_with_non_existing_group&#34;, &#34;duration&#34;: &#34;1 ms&#34;, 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&#34;tests/test_health_emt.py::TestEmt::test_find_hlgt&#34;: [{&#34;extras&#34;: [], &#34;result&#34;: &#34;Passed&#34;, &#34;testId&#34;: &#34;tests/test_health_emt.py::TestEmt::test_find_hlgt&#34;, &#34;duration&#34;: &#34;4 ms&#34;, &#34;resultsTableRow&#34;: [&#34;&lt;td class=\&#34;col-result\&#34;&gt;Passed&lt;/td&gt;&#34;, &#34;&lt;td class=\&#34;col-testId\&#34;&gt;tests/test_health_emt.py::TestEmt::test_find_hlgt&lt;/td&gt;&#34;, &#34;&lt;td class=\&#34;col-duration\&#34;&gt;4 ms&lt;/td&gt;&#34;, &#34;&lt;td class=\&#34;col-links\&#34;&gt;&lt;/td&gt;&#34;], &#34;log&#34;: &#34;No log output captured.&#34;}], &#34;tests/test_health_emt.py::TestEmt::test_find_hlt&#34;: [{&#34;extras&#34;: [], &#34;result&#34;: &#34;Passed&#34;, &#34;testId&#34;: &#34;tests/test_health_emt.py::TestEmt::test_find_hlt&#34;, &#34;duration&#34;: &#34;4 ms&#34;, &#34;resultsTableRow&#34;: [&#34;&lt;td class=\&#34;col-result\&#34;&gt;Passed&lt;/td&gt;&#34;, &#34;&lt;td 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&#34;tests/test_health_emt.py::TestEmt::test_find_soc&#34;: [{&#34;extras&#34;: [], &#34;result&#34;: &#34;Passed&#34;, &#34;testId&#34;: &#34;tests/test_health_emt.py::TestEmt::test_find_soc&#34;, &#34;duration&#34;: &#34;4 ms&#34;, &#34;resultsTableRow&#34;: [&#34;&lt;td class=\&#34;col-result\&#34;&gt;Passed&lt;/td&gt;&#34;, &#34;&lt;td class=\&#34;col-testId\&#34;&gt;tests/test_health_emt.py::TestEmt::test_find_soc&lt;/td&gt;&#34;, &#34;&lt;td class=\&#34;col-duration\&#34;&gt;4 ms&lt;/td&gt;&#34;, &#34;&lt;td class=\&#34;col-links\&#34;&gt;&lt;/td&gt;&#34;], &#34;log&#34;: &#34;No log output captured.&#34;}], &#34;tests/test_health_emt.py::TestEmt::test_list_files&#34;: [{&#34;extras&#34;: [], &#34;result&#34;: &#34;Passed&#34;, &#34;testId&#34;: &#34;tests/test_health_emt.py::TestEmt::test_list_files&#34;, &#34;duration&#34;: &#34;25 ms&#34;, &#34;resultsTableRow&#34;: [&#34;&lt;td class=\&#34;col-result\&#34;&gt;Passed&lt;/td&gt;&#34;, &#34;&lt;td 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diff --git a/_downloads/9911a4d807ac9f1a695f0aa2cf687076/coverage.xml b/_downloads/9911a4d807ac9f1a695f0aa2cf687076/coverage.xml
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+++ b/_downloads/9911a4d807ac9f1a695f0aa2cf687076/coverage.xml
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diff --git a/_sources/statlab_kappa2.rst.txt b/_sources/statlab_kappa2.rst.txt
index 80f5cfc1..821acd9c 100644
--- a/_sources/statlab_kappa2.rst.txt
+++ b/_sources/statlab_kappa2.rst.txt
@@ -250,7 +250,7 @@ More Details
 probability of having agreement for a sample from two randomly selected raters estimated from :numref:`Tabel %s <tbl_count1>`.
 :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))`.
+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`.
 
 The equation :eq:`eq_kappa1` can be expressed as [2]_ :sup:`(Eq. 9)`,
@@ -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`). 
 
 The first element of :eq:`eq_kappa2_vn2` can be calculated as [2]_ :sup:`(Eq. 12)`
 
@@ -313,7 +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)
-  = 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)
+  = 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)
 
 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)`
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diff --git a/_static/reports/junit/report.html b/_static/reports/junit/report.html
index 8618a6fc..c63f9999 100644
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+++ b/_static/reports/junit/report.html
@@ -328,7 +328,7 @@
   </head>
   <body>
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-    <p>Report generated on 21-Jul-2024 at 18:27:32 by <a href="https://pypi.python.org/pypi/pytest-html">pytest-html</a>
+    <p>Report generated on 21-Jul-2024 at 18:50:56 by <a href="https://pypi.python.org/pypi/pytest-html">pytest-html</a>
         v4.1.1</p>
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&#34;tests/test_stdiso_pdfsummary.py::TestPdfSummary::test_show_outline_tree&#34;: [{&#34;extras&#34;: [], &#34;result&#34;: &#34;Passed&#34;, &#34;testId&#34;: &#34;tests/test_stdiso_pdfsummary.py::TestPdfSummary::test_show_outline_tree&#34;, &#34;duration&#34;: &#34;846 ms&#34;, &#34;resultsTableRow&#34;: [&#34;&lt;td class=\&#34;col-result\&#34;&gt;Passed&lt;/td&gt;&#34;, &#34;&lt;td class=\&#34;col-testId\&#34;&gt;tests/test_stdiso_pdfsummary.py::TestPdfSummary::test_show_outline_tree&lt;/td&gt;&#34;, &#34;&lt;td class=\&#34;col-duration\&#34;&gt;846 ms&lt;/td&gt;&#34;, &#34;&lt;td class=\&#34;col-links\&#34;&gt;&lt;/td&gt;&#34;], &#34;log&#34;: &#34;No log output captured.&#34;}]}, &#34;renderCollapsed&#34;: [&#34;passed&#34;], &#34;initialSort&#34;: &#34;result&#34;, &#34;title&#34;: &#34;report.html&#34;}"></div>
     <script>
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 const { getCollapsedCategory, setCollapsedIds } = require('./storage.js')
diff --git a/example_cdtg.html b/example_cdtg.html
index 6961ea43..9cb6ff87 100644
--- a/example_cdtg.html
+++ b/example_cdtg.html
@@ -133,13 +133,7 @@ <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: 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)
-</pre></div>
-</div>
-<img alt="_images/97a420d71e1361b711e9e67a2ed8dbc5ed1ebc55ff669adabdd6cf2c995300f8.png" src="_images/97a420d71e1361b711e9e67a2ed8dbc5ed1ebc55ff669adabdd6cf2c995300f8.png" />
+<img alt="_images/833bf347c2aca2fa4418132f6024d14cac03816c51d733a6cecd3b37f4f6c949.png" src="_images/833bf347c2aca2fa4418132f6024d14cac03816c51d733a6cecd3b37f4f6c949.png" />
 </div>
 </div>
 <p>To create a line plot:</p>
@@ -151,7 +145,7 @@ <h1>U/Graph/Categorical Plots Using catPlotter<a class="headerlink" href="#u-gra
 </div>
 </div>
 <div class="cell_output docutils container">
-<img alt="_images/533c386576f281089b9bf96459fc1da2b1d74b711328feaa8ad023239134a57e.png" src="_images/533c386576f281089b9bf96459fc1da2b1d74b711328feaa8ad023239134a57e.png" />
+<img alt="_images/542a85bd24c1987e4732c0b26f6649f4390a8c15e1a5ad716744c3c796163b41.png" src="_images/542a85bd24c1987e4732c0b26f6649f4390a8c15e1a5ad716744c3c796163b41.png" />
 </div>
 </div>
 </section>
diff --git a/example_clinical.html b/example_clinical.html
index 6c738c26..ce66cea8 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     1615
-1  STD1      TRT1  SUBJ01  VISIT1     2      632
+0  STD1      TRT1  SUBJ01  VISIT1     1     1903
+1  STD1      TRT1  SUBJ01  VISIT1     2      768
 </pre></div>
 </div>
 </div>
@@ -150,11 +150,11 @@ <h2>Example 1<a class="headerlink" href="#example-1" title="Link to this heading
 <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               3   
-1  STD1      TRT1  SUBJ02  VISIT1            2               0   
+1  STD1      TRT1  SUBJ01  VISIT2            0               4   
 
    N(1000&lt;=V&lt;=2000)  N(all)  
-0                 1       4  
-1                 3       5  
+0                 2       5  
+1                 1       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          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
+0   STD1      TRT1  VISIT1          2         10           8      20
+1   STD1      TRT1  VISIT2          4          6           7      17
+2   STD1      TRT1  VISIT3          4          9           0      13
+3   STD1      TRT1  VISIT4          2          1           2       5
+4   STD1      TRT2  VISIT1          2         12           6      20
+5   STD1      TRT2  VISIT2          5          3           3      11
+6   STD1      TRT2  VISIT3          3          4           0       7
+7   STD1      TRT2  VISIT4          2          0           2       4
+8   STD2      TRT1  VISIT1          6         11           3      20
+9   STD2      TRT1  VISIT2          6          7           3      16
+10  STD2      TRT1  VISIT3          2          9           1      12
+11  STD2      TRT1  VISIT4          1          3           1       5
+12  STD2      TRT2  VISIT1          1         15           4      20
+13  STD2      TRT2  VISIT2          4          7           5      16
+14  STD2      TRT2  VISIT3          3          9           0      12
+15  STD2      TRT2  VISIT4          1          2           0       3
 </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           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
+0   STD1      TRT1  VISIT1            4           36            40        80
+1   STD1      TRT1  VISIT2            8           23            35        66
+2   STD1      TRT1  VISIT3            8           33             0        41
+3   STD1      TRT1  VISIT4            4            3            10        17
+4   STD1      TRT2  VISIT1            4           43            30        77
+5   STD1      TRT2  VISIT2           10           11            15        36
+6   STD1      TRT2  VISIT3            6           13             0        19
+7   STD1      TRT2  VISIT4            4            0            10        14
+8   STD2      TRT1  VISIT1           12           41            15        68
+9   STD2      TRT1  VISIT2           12           23            15        50
+10  STD2      TRT1  VISIT3            4           33             5        42
+11  STD2      TRT1  VISIT4            2           10             5        17
+12  STD2      TRT2  VISIT1            2           56            20        78
+13  STD2      TRT2  VISIT2            8           28            25        61
+14  STD2      TRT2  VISIT3            6           32             0        38
+15  STD2      TRT2  VISIT4            2            8             0        10
 </pre></div>
 </div>
 </div>
diff --git a/example_ectd.html b/example_ectd.html
index 178de194..e81ceb6c 100644
--- a/example_ectd.html
+++ b/example_ectd.html
@@ -561,6 +561,9 @@ <h2>Module 4<a class="headerlink" href="#module-4" title="Link to this heading">
     └── 4.3 Literature references
 </pre></div>
 </div>
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>
+</pre></div>
+</div>
 </div>
 </div>
 </section>
diff --git a/example_emt3.html b/example_emt3.html
index 91d2f278..e642970b 100644
--- a/example_emt3.html
+++ b/example_emt3.html
@@ -295,91 +295,91 @@ <h2>FMQ Tree<a class="headerlink" href="#fmq-tree" title="Link to this heading">
     ├── Abdominal Pain:
     │   ├── [Classification] Broad:
     │   │   ├── [SOC] soc214dfxgAelhGHfEFFkgrAsFYzZBAFs:
-    │   │   │   ├── [PT01] Carnett&#39;s sign positive
-    │   │   │   ├── [PT02] Gastric irritation
-    │   │   │   ├── [PT03] Gastritis erosive
-    │   │   │   ├── [PT04] Gastroenteritis escherichia coli
-    │   │   │   ├── [PT05] Gastroenteritis Escherichia coli
-    │   │   │   ├── [PT06] Gastroenterostomy
-    │   │   │   ├── [PT07] Haemorrhagic erosive gastritis
-    │   │   │   ├── [PT08] Helicobacter duodenal ulcer
-    │   │   │   └── [PT09] Yao syndrome
+    │   │   │   ├── [PT01] Gastritis erosive
+    │   │   │   ├── [PT02] Gastroenterostomy
+    │   │   │   ├── [PT03] Helicobacter duodenal ulcer
+    │   │   │   ├── [PT04] Large intestine infection
+    │   │   │   ├── [PT05] Ulcerative duodenitis
+    │   │   │   ├── [PT06] Visceral pain
+    │   │   │   ├── [PT07] CRIA syndrome
+    │   │   │   └── [PT08] Peritoneoplasty
     │   │   ├── [SOC] soc360phgmkaCxrALPg:
-    │   │   │   ├── [PT10] Large intestine infection
-    │   │   │   ├── [PT11] Ulcerative duodenitis
-    │   │   │   ├── [PT12] CRIA syndrome
-    │   │   │   └── [PT13] Peritoneoplasty
+    │   │   │   ├── [PT09] Complicated appendicitis
+    │   │   │   ├── [PT10] Gastric irritation
+    │   │   │   ├── [PT11] Gastroenteritis Escherichia coli
+    │   │   │   ├── [PT12] Gastro-enterostomy
+    │   │   │   ├── [PT13] Peptic ulcer
+    │   │   │   ├── [PT14] Bauhin&#39;s valve syndrome
+    │   │   │   ├── [PT15] Yao syndrome
+    │   │   │   └── [PT16] Segmental arterial mediolysis
     │   │   └── [SOC] soc972ZiuFsAfKKVWFbSZdYcgUoCiSTyEYKu:
-    │   │       ├── [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
+    │   │       ├── [PT17] Carnett&#39;s sign positive
+    │   │       ├── [PT18] Gastroenteritis escherichia coli
+    │   │       ├── [PT19] Haemorrhagic erosive gastritis
+    │   │       └── [PT20] Infantile colic
     │   └── [Classification] Narrow:
     │       ├── [SOC] soc214dfxgAelhGHfEFFkgrAsFYzZBAFs:
-    │       │   ├── [PT21] Abdominal discomfort
-    │       │   ├── [PT22] Abdominal pain
-    │       │   ├── [PT23] Abdominal rebound tenderness
-    │       │   ├── [PT24] Acute abdomen
-    │       │   └── [PT25] Ilioinguinal neuralgia
+    │       │   ├── [PT21] Abdominal pain
+    │       │   ├── [PT22] Abdominal pain lower
+    │       │   ├── [PT23] Abdominal pain NOS
+    │       │   ├── [PT24] Abdominal pain upper
+    │       │   ├── [PT25] Abdominal rebound tenderness
+    │       │   ├── [PT26] Abdominal rigidity
+    │       │   ├── [PT27] Gastrointestinal pain
+    │       │   ├── [PT28] Spleen pain
+    │       │   ├── [PT29] Stomach discomfort
+    │       │   └── [PT30] Ilioinguinal neuralgia
     │       ├── [SOC] soc360phgmkaCxrALPg:
-    │       │   ├── [PT26] Abdominal pain aggravated
-    │       │   ├── [PT27] Abdominal tenderness
-    │       │   ├── [PT28] Enteric neuropathy
-    │       │   ├── [PT29] Epigastric discomfort
-    │       │   ├── [PT30] Gastrointestinal discomfort
-    │       │   ├── [PT31] Gastrointestinal pain
-    │       │   ├── [PT32] Gastrointestinal pain NOS
-    │       │   ├── [PT33] Intestinal spasm
-    │       │   ├── [PT34] Perihepatic discomfort
-    │       │   ├── [PT35] Spleen pain
-    │       │   └── [PT36] Ulcer type pain
+    │       │   ├── [PT31] Abdominal discomfort
+    │       │   ├── [PT32] Abdominal migraine
+    │       │   ├── [PT33] Abdominal pain aggravated
+    │       │   ├── [PT34] Enteric neuropathy
+    │       │   ├── [PT35] Epigastric discomfort
+    │       │   └── [PT36] Gastrointestinal pain NOS
     │       └── [SOC] soc972ZiuFsAfKKVWFbSZdYcgUoCiSTyEYKu:
-    │           ├── [PT37] Abdominal migraine
-    │           ├── [PT38] Abdominal pain lower
-    │           ├── [PT39] Abdominal pain NOS
-    │           ├── [PT40] Abdominal pain upper
-    │           ├── [PT41] Abdominal rigidity
-    │           ├── [PT42] Gastrointestinal upset
-    │           └── [PT43] Stomach discomfort
+    │           ├── [PT37] Abdominal tenderness
+    │           ├── [PT38] Acute abdomen
+    │           ├── [PT39] Gastrointestinal discomfort
+    │           ├── [PT40] Gastrointestinal upset
+    │           ├── [PT41] Intestinal spasm
+    │           ├── [PT42] Perihepatic discomfort
+    │           └── [PT43] Ulcer type pain
     └── Abnormal Uterine Bleeding:
         ├── [Classification] Broad:
         │   ├── [SOC] soc214dfxgAelhGHfEFFkgrAsFYzZBAFs:
-        │   │   ├── [PT01] Bleeding anovulatory
-        │   │   └── [PT02] Menstrual disorder
+        │   │   └── [PT01] Dysmenorrhea
         │   ├── [SOC] soc360phgmkaCxrALPg:
+        │   │   ├── [PT02] Bleeding anovulatory
         │   │   ├── [PT03] Follicle-stimulating hormone deficiency
-        │   │   ├── [PT04] Uterine dehiscence
-        │   │   └── [PT05] Ovarian dysfunction
+        │   │   ├── [PT04] Follicle stimulating hormone deficiency
+        │   │   ├── [PT05] Menstrual disorder
+        │   │   ├── [PT06] Uterine dehiscence
+        │   │   └── [PT07] Ovarian dysfunction
         │   └── [SOC] soc972ZiuFsAfKKVWFbSZdYcgUoCiSTyEYKu:
-        │       ├── [PT06] Anovulatory cycle
-        │       ├── [PT07] Dysmenorrhea
-        │       ├── [PT08] Dysmenorrhoea
-        │       └── [PT09] Follicle stimulating hormone deficiency
+        │       ├── [PT08] Anovulatory cycle
+        │       └── [PT09] Dysmenorrhoea
         └── [Classification] Narrow:
             ├── [SOC] soc214dfxgAelhGHfEFFkgrAsFYzZBAFs:
-            │   ├── [PT10] Menometrorrhagia
-            │   ├── [PT11] Menorrhagia
-            │   ├── [PT12] Menstruation delayed
-            │   └── [PT13] Postmenopausal haemorrhage
+            │   ├── [PT10] Abnormal withdrawal bleeding
+            │   ├── [PT11] Dysfunctional uterine bleeding
+            │   ├── [PT12] Hypomenorrhoea
+            │   ├── [PT13] Menometrorrhagia
+            │   ├── [PT14] Menstruation delayed
+            │   ├── [PT15] Polymenorrhoea
+            │   └── [PT16] Uterine rupture
             ├── [SOC] soc360phgmkaCxrALPg:
-            │   ├── [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
+            │   ├── [PT17] Abnormal uterine bleeding
+            │   ├── [PT18] Cervix haemorrhage uterine
+            │   ├── [PT19] Heavy menstrual bleeding
+            │   ├── [PT20] Oligomenorrhoea
+            │   ├── [PT21] Polymenorrhagia
+            │   └── [PT22] Uterine haemorrhage
             └── [SOC] soc972ZiuFsAfKKVWFbSZdYcgUoCiSTyEYKu:
-                ├── [PT22] Cervix haemorrhage uterine
-                ├── [PT23] Hypomenorrhoea
-                ├── [PT24] Intermenstrual bleeding
+                ├── [PT23] Intermenstrual bleeding
+                ├── [PT24] Menorrhagia
                 ├── [PT25] Menstruation irregular
                 ├── [PT26] Metrorrhagia
-                ├── [PT27] Uterine rupture
+                ├── [PT27] Postmenopausal haemorrhage
                 └── [PT28] Vaginal haemorrhage
 </pre></div>
 </div>
@@ -404,92 +404,92 @@ <h2>FMQ Tree<a class="headerlink" href="#fmq-tree" title="Link to this heading">
                                             Abdominal Pain ──┤    
                                 Broad [Classification] ──┤   │    
            soc214dfxgAelhGHfEFFkgrAsFYzZBAFs [SOC] ──┤   │   │    
-               Complicated appendicitis [PT01] ──┤   │   │   │    
-                      Gastroenterostomy [PT02] ──┤   │   │   │    
-              Large intestine infection [PT03] ──┤   │   │   │    
-                           Peptic ulcer [PT04] ──┤   │   │   │    
-                           Yao syndrome [PT05] ──┘   │   │   │    
+                Bauhin&#39;s valve syndrome [PT04] ──┤   │   │   │    
+                Carnett&#39;s sign positive [PT01] ──┤   │   │   │    
+            Helicobacter duodenal ulcer [PT02] ──┤   │   │   │    
+                           Peptic ulcer [PT03] ──┤   │   │   │    
+                        Peritoneoplasty [PT05] ──┤   │   │   │    
+          Segmental arterial mediolysis [PT06] ──┘   │   │   │    
                          soc360phgmkaCxrALPg [SOC] ──┤   │   │    
-                Carnett&#39;s sign positive [PT06] ──┤   │   │   │    
+                          CRIA syndrome [PT11] ──┤   │   │   │    
                      Gastric irritation [PT07] ──┤   │   │   │    
-                     Gastro-enterostomy [PT09] ──┤   │   │   │    
-       Gastroenteritis escherichia coli [PT08] ──┤   │   │   │    
-            Helicobacter duodenal ulcer [PT10] ──┤   │   │   │    
-                        Peritoneoplasty [PT12] ──┤   │   │   │    
-                          Visceral pain [PT11] ──┘   │   │   │    
+         Haemorrhagic erosive gastritis [PT08] ──┤   │   │   │    
+              Large intestine infection [PT09] ──┤   │   │   │    
+                  Ulcerative duodenitis [PT10] ──┘   │   │   │    
         soc972ZiuFsAfKKVWFbSZdYcgUoCiSTyEYKu [SOC] ──┘   │   │    
-                Bauhin&#39;s valve syndrome [PT19] ──┤       │   │    
-                          CRIA syndrome [PT18] ──┤       │   │    
+               Complicated appendicitis [PT12] ──┤       │   │    
                       Gastritis erosive [PT13] ──┤       │   │    
-       Gastroenteritis Escherichia coli [PT14] ──┤       │   │    
-         Haemorrhagic erosive gastritis [PT15] ──┤       │   │    
-                        Infantile colic [PT16] ──┤       │   │    
-          Segmental arterial mediolysis [PT20] ──┤       │   │    
-                  Ulcerative duodenitis [PT17] ──┘       │   │    
+                     Gastro-enterostomy [PT17] ──┤       │   │    
+       Gastroenteritis Escherichia coli [PT15] ──┤       │   │    
+       Gastroenteritis escherichia coli [PT14] ──┤       │   │    
+                      Gastroenterostomy [PT16] ──┤       │   │    
+                        Infantile colic [PT18] ──┤       │   │    
+                          Visceral pain [PT19] ──┤       │   │    
+                           Yao syndrome [PT20] ──┘       │   │    
                                Narrow [Classification] ──┘   │    
            soc214dfxgAelhGHfEFFkgrAsFYzZBAFs [SOC] ──┤       │    
-              Abdominal pain aggravated [PT21] ──┤   │       │    
+                     Abdominal migraine [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] ──┘   │       │    
+                   Abdominal pain upper [PT23] ──┤   │       │    
+                     Abdominal rigidity [PT24] ──┤   │       │    
+            Gastrointestinal discomfort [PT25] ──┤   │       │    
+              Gastrointestinal pain NOS [PT26] ──┤   │       │    
+                 Gastrointestinal upset [PT27] ──┘   │       │    
                          soc360phgmkaCxrALPg [SOC] ──┤       │    
-                   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] ──┘   │       │    
+           Abdominal rebound tenderness [PT28] ──┤   │       │    
+                   Abdominal tenderness [PT29] ──┤   │       │    
+                  Epigastric discomfort [PT30] ──┤   │       │    
+                 Ilioinguinal neuralgia [PT33] ──┤   │       │    
+                       Intestinal spasm [PT31] ──┤   │       │    
+                     Stomach discomfort [PT32] ──┘   │       │    
         soc972ZiuFsAfKKVWFbSZdYcgUoCiSTyEYKu [SOC] ──┘       │    
-                     Abdominal migraine [PT38] ──┤           │    
-                     Abdominal pain NOS [PT40] ──┤           │    
-                         Abdominal pain [PT39] ──┤           │    
-                   Abdominal tenderness [PT41] ──┤           │    
-                  Epigastric discomfort [PT42] ──┤           │    
-                  Gastrointestinal pain [PT43] ──┘           │    
+                   Abdominal discomfort [PT34] ──┤           │    
+                     Abdominal pain NOS [PT37] ──┤           │    
+                         Abdominal pain [PT35] ──┤           │    
+              Abdominal pain aggravated [PT36] ──┤           │    
+                          Acute abdomen [PT38] ──┤           │    
+                     Enteric neuropathy [PT39] ──┤           │    
+                  Gastrointestinal pain [PT40] ──┤           │    
+                 Perihepatic discomfort [PT41] ──┤           │    
+                            Spleen pain [PT42] ──┤           │    
+                        Ulcer type pain [PT43] ──┘           │    
                                  Abnormal Uterine Bleeding ──┘    
                                 Broad [Classification] ──┤        
            soc214dfxgAelhGHfEFFkgrAsFYzZBAFs [SOC] ──┤   │        
-                   Bleeding anovulatory [PT01] ──┤   │   │        
-                           Dysmenorrhea [PT02] ──┤   │   │        
-                     Menstrual disorder [PT03] ──┤   │   │        
-                    Ovarian dysfunction [PT04] ──┘   │   │        
+Follicle-stimulating hormone deficiency [PT01] ──┤   │   │        
+                     Uterine dehiscence [PT02] ──┘   │   │        
                          soc360phgmkaCxrALPg [SOC] ──┤   │        
-                      Anovulatory cycle [PT05] ──┤   │   │        
-Follicle-stimulating hormone deficiency [PT06] ──┤   │   │        
-                     Uterine dehiscence [PT07] ──┘   │   │        
+                      Anovulatory cycle [PT03] ──┤   │   │        
+                          Dysmenorrhoea [PT04] ──┤   │   │        
+Follicle stimulating hormone deficiency [PT05] ──┤   │   │        
+                    Ovarian dysfunction [PT06] ──┘   │   │        
         soc972ZiuFsAfKKVWFbSZdYcgUoCiSTyEYKu [SOC] ──┘   │        
-                          Dysmenorrhoea [PT08] ──┤       │        
-Follicle stimulating hormone deficiency [PT09] ──┘       │        
+                   Bleeding anovulatory [PT07] ──┤       │        
+                           Dysmenorrhea [PT08] ──┤       │        
+                     Menstrual disorder [PT09] ──┘       │        
                                Narrow [Classification] ──┘        
            soc214dfxgAelhGHfEFFkgrAsFYzZBAFs [SOC] ──┤            
-           Abnormal withdrawal bleeding [PT10] ──┤   │            
-             Cervix haemorrhage uterine [PT11] ──┤   │            
-                            Menorrhagia [PT12] ──┤   │            
-                           Metrorrhagia [PT13] ──┤   │            
-                    Uterine haemorrhage [PT14] ──┤   │            
-                    Vaginal haemorrhage [PT15] ──┘   │            
+               Heavy menstrual bleeding [PT10] ──┤   │            
+                         Hypomenorrhoea [PT11] ──┤   │            
+                Intermenstrual bleeding [PT12] ──┤   │            
+                   Menstruation delayed [PT13] ──┤   │            
+                        Polymenorrhagia [PT14] ──┤   │            
+                    Uterine haemorrhage [PT15] ──┤   │            
+                    Vaginal haemorrhage [PT16] ──┘   │            
                          soc360phgmkaCxrALPg [SOC] ──┤            
-              Abnormal uterine bleeding [PT16] ──┤   │            
-               Heavy menstrual bleeding [PT17] ──┤   │            
-                       Menometrorrhagia [PT18] ──┤   │            
-                        Oligomenorrhoea [PT19] ──┤   │            
-                        Polymenorrhagia [PT20] ──┤   │            
-             Postmenopausal haemorrhage [PT21] ──┤   │            
-                        Uterine rupture [PT22] ──┘   │            
+           Abnormal withdrawal bleeding [PT17] ──┤   │            
+             Cervix haemorrhage uterine [PT18] ──┤   │            
+         Dysfunctional uterine bleeding [PT19] ──┤   │            
+                            Menorrhagia [PT20] ──┤   │            
+                           Metrorrhagia [PT21] ──┤   │            
+                        Oligomenorrhoea [PT22] ──┤   │            
+                         Polymenorrhoea [PT23] ──┘   │            
         soc972ZiuFsAfKKVWFbSZdYcgUoCiSTyEYKu [SOC] ──┘            
-         Dysfunctional uterine bleeding [PT23] ──┤                
-                         Hypomenorrhoea [PT24] ──┤                
-                Intermenstrual bleeding [PT25] ──┤                
-                   Menstruation delayed [PT26] ──┤                
-                 Menstruation irregular [PT27] ──┤                
-                         Polymenorrhoea [PT28] ──┘                
+              Abnormal uterine bleeding [PT24] ──┤                
+                       Menometrorrhagia [PT25] ──┤                
+                 Menstruation irregular [PT26] ──┤                
+             Postmenopausal haemorrhage [PT27] ──┤                
+                        Uterine rupture [PT28] ──┘                
 </pre></div>
 </div>
 </div>
diff --git a/example_files.html b/example_files.html
index 351d1e1a..3208079d 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_5/
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>testfolder_11/
 ├── 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_5/  &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_11/  &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 18:28:14 2024  Sun Jul 21 18:28:14 2024  testfile3   None   
+1  Sun Jul 21 18:51:38 2024  Sun Jul 21 18:51:38 2024  testfile3   None   
 
   N_column N_row  
 0     None  None  
diff --git a/searchindex.js b/searchindex.js
index 3977be0b..bcc7468f 100644
--- a/searchindex.js
+++ b/searchindex.js
@@ -1 +1 @@
-Search.setIndex({"alltitles": {"API Reference": [[0, null]], "Algorithm - 1": [[31, "algorithm-1"]], "Appendix - View PTs Given Any FMQ": [[26, "appendix-view-pts-given-any-fmq"]], "Assign FMQ File Path": [[26, "assign-fmq-file-path"]], "Assign MedDRA Distribution Folder": [[24, "assign-meddra-distribution-folder"], [25, "assign-meddra-distribution-folder"]], "Attributes": [[2, "attributes"], [5, "attributes"], [10, "attributes"], [12, "attributes"]], "Attribution": [[18, "attribution"]], "Background": [[30, "background"], [31, "background"], [32, "background"], [33, "background"]], "Bootstrap CI": [[32, "bootstrap-ci"]], "Bubble Plot": [[32, "bubble-plot"]], "CDISC Foundational Standards": [[34, "cdisc-foundational-standards"]], "CDISC Library Resource": [[34, "cdisc-library-resource"]], "Changelog": [[17, null]], "Classes": [[1, "classes"], [2, "classes"], [3, "classes"], [4, "classes"], [5, "classes"], [6, "classes"], [7, "classes"], [8, "classes"], [10, "classes"], [12, "classes"], [13, "classes"], [14, "classes"], [15, "classes"], [16, "classes"]], "Code of Conduct": [[18, null], [19, "code-of-conduct"]], "Cohen\u2019s Kappa Interpretation (Cohen, 1960)": [[32, "id21"]], "Cohen\u2019s Kappa Interpretation (McHugh, 2012)": [[32, "id22"]], "Cohen\u2019s \\kappa = -0.7241379310344827": [[32, "id28"]], "Cohen\u2019s \\kappa = -1": [[32, "id27"]], "Cohen\u2019s \\kappa = 0": [[32, "id23"], [32, "id24"]], "Cohen\u2019s \\kappa = 1": [[32, "id25"], [32, "id26"]], "Contributing": [[19, null], [29, "contributing"]], "Count of Ratings": [[33, "tbl-count1"]], "Counts for 2 categories": [[32, "id19"]], "Counts for 3 or more categories": [[32, "id20"]], "Credits": [[29, "credits"]], "EMA Implementation of IDMP": [[35, "ema-implementation-of-idmp"]], "EU Database - xEVMPD": [[35, "eu-database-xevmpd"]], "Enforcement": [[18, "enforcement"]], "Example - Group-1": [[30, "example-group-1"], [31, "example-group-1"], [32, "example-group-1"], [33, "example-group-1"]], "Example 1": [[21, "example-1"]], "Extensions": [[32, "extensions"]], "FMQ Tree": [[26, "fmq-tree"]], "Find MedDRA Terms Across Different Hierarchical Levels": [[24, "find-meddra-terms-across-different-hierarchical-levels"]], "Find MedDRA Terms Given a SMQ": [[25, "find-meddra-terms-given-a-smq"]], "Find MedDRA Terms Within a Given Hierarchical Level": [[24, "find-meddra-terms-within-a-given-hierarchical-level"]], "Find SMQ Terms": [[25, "find-smq-terms"]], "Find Sections Using Keywords": [[22, "find-sections-using-keywords"], [23, "find-sections-using-keywords"]], "Find Terms Given a FMQ": [[26, "find-terms-given-a-fmq"]], "Fix Bugs": [[19, "fix-bugs"]], "Fleiss\u2019s \\kappa = -0.0909090909090909": [[33, "id11"]], "Fleiss\u2019s \\kappa = 1.0": [[33, "id10"]], "Functions": [[5, "functions"], [13, "functions"], [15, "functions"]], "Get CT Packages": [[34, "get-ct-packages"]], "Get Started!": [[19, "get-started"]], "H/Clinical/Grouped Summary": [[21, null]], "H/ICH/MedDRA/(MLGs by CIOMS)": [[27, null]], "H/ICH/MedDRA/Basics": [[24, null]], "H/ICH/MedDRA/FMQs by FDA": [[26, null]], "H/ICH/MedDRA/SMQs by ICH": [[25, null]], "H/ICH/eCTD/US/3.2/Heading": [[22, null]], "H/ICH/eCTD/US/4.0/Heading": [[23, null]], "How to Cite": [[29, "how-to-cite"]], "How-to": [[30, "how-to"], [31, "how-to"], [31, "id5"], [32, "how-to"], [33, "how-to"]], "Implement Features": [[19, "implement-features"]], "Installation": [[29, "installation"]], "Interpretation of Cohen\u2019s Kappa Suggested in Literature": [[32, "interpretation-of-cohen-s-kappa-suggested-in-literature"]], "Kendall\u2019s \\tau = -1.0": [[31, "id3"]], "Kendall\u2019s \\tau = 1.0": [[31, "tbl-ex1"]], "Lab Exercise": [[31, "lab-exercise"], [32, "lab-exercise"], [33, "lab-exercise"], [33, "id7"]], "License": [[29, "license"]], "Module 1": [[22, "module-1"], [23, "module-1"]], "Module 2": [[22, "module-2"], [23, "module-2"]], "Module 3": [[22, "module-3"], [23, "module-3"]], "Module 4": [[22, "module-4"], [23, "module-4"]], "Module 5": [[22, "module-5"], [23, "module-5"]], "Module Contents": [[1, "module-contents"], [2, "module-contents"], [3, "module-contents"], [6, "module-contents"], [8, "module-contents"], [10, "module-contents"], [12, "module-contents"], [13, "module-contents"], [14, "module-contents"], [16, "module-contents"]], "More Details": [[30, "more-details"], [33, "more-details"]], "Notation": [[30, "notation"], [31, "notation"], [32, "notation"], [33, "notation"]], "Observed Value": [[30, "tbl-count1"], [31, "tbl-count1"]], "Other Options": [[24, "other-options"], [28, "other-options"]], "Our Pledge": [[18, "our-pledge"]], "Our Responsibilities": [[18, "our-responsibilities"]], "Our Standards": [[18, "our-standards"]], "Package Contents": [[4, "package-contents"], [5, "package-contents"], [7, "package-contents"], [15, "package-contents"]], "Pull Request Guidelines": [[19, "pull-request-guidelines"]], "Reference": [[22, "reference"], [23, "reference"], [24, "reference"], [25, 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\ No newline at end of file
diff --git a/statlab_kappa2.html b/statlab_kappa2.html
index 8afca011..850bdb86 100644
--- a/statlab_kappa2.html
+++ b/statlab_kappa2.html
@@ -355,7 +355,7 @@ <h2>More Details<a class="headerlink" href="#more-details" title="Link to this h
 probability of having agreement for a sample from two randomly selected raters estimated from <a class="reference internal" href="#tbl-count1"><span class="std std-numref">Tabel 11</span></a>.
 <a class="reference internal" href="#equation-eq-exp1">Eq. (2)</a> 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 <span class="math notranslate nohighlight">\((N_{i1},\ldots, N_{iJ}) \sim multi(R, (p_1,\ldots, p_J))\)</span>.
+which corresponds to the assumption of <span class="math notranslate nohighlight">\((N_{i1},\ldots, N_{iJ}) \sim multi(R, (p_1,\ldots, p_J))\)</span> where <span class="math notranslate nohighlight">\(R&gt;4\)</span>.
 Note that the notations in this page did not use conventional ‘hat’ to represent estimated <span class="math notranslate nohighlight">\(p_j\)</span>.</p>
 <p>The equation <a class="reference internal" href="#equation-eq-kappa1">Eq. (3)</a> can be expressed as <a class="footnote-reference brackets" href="#id9" id="id3" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a> <sup>(Eq. 9)</sup>,</p>
 <div class="math notranslate nohighlight">
@@ -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">\(E\left(N_{ij}^4\right) =\)</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>
+<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>).</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)
@@ -390,7 +390,7 @@ <h2>More Details<a class="headerlink" href="#more-details" title="Link to this h
 <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>\[E\left( N_{ij}^2 N_{ik}^2 \right)
-= R(R-1)p_j(p_k+(R-2)p_k^2) + R(R-1)(R-2)p_j^2(p_k+(R-3)2p_k^2)\]</div>
+= 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)\]</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">
