From 7a7730b86eef45c9ecd1591486aab1658dbdc81c Mon Sep 17 00:00:00 2001 From: yh202109 Date: Sun, 21 Jul 2024 14:49:55 -0400 Subject: [PATCH] v0.2.20 --- docs/statlab_kappa2.rst | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/docs/statlab_kappa2.rst b/docs/statlab_kappa2.rst index 80f5cfc1..821acd9c 100644 --- a/docs/statlab_kappa2.rst +++ b/docs/statlab_kappa2.rst @@ -250,7 +250,7 @@ More Details probability of having agreement for a sample from two randomly selected raters estimated from :numref:`Tabel %s `. :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)`