From 59176ab4cfeed86d3f892add735b7bbeddad6946 Mon Sep 17 00:00:00 2001
From: rnhmjoj <rnhmjoj@inventati.org>
Date: Thu, 28 May 2020 20:49:08 +0200
Subject: [PATCH] notes: use math mode to write "t-test"

---
 notes/sections/1.md | 6 +++---
 notes/sections/3.md | 8 ++++----
 notes/sections/4.md | 2 +-
 3 files changed, 8 insertions(+), 8 deletions(-)

diff --git a/notes/sections/1.md b/notes/sections/1.md
index 5adb2e9..c69749a 100644
--- a/notes/sections/1.md
+++ b/notes/sections/1.md
@@ -181,7 +181,7 @@ $$
 $$
 
 In order to compare the values $m_e$ and $m_0$, the following compatibility
-t-test was applied:
+$t$-test was applied:
 $$
   p = 1 - \text{erf}\left(\frac{t}{\sqrt{2}}\right)\ \with
   t = \frac{|m_e - m_o|}{\sqrt{\sigma_e^2 + \sigma_o^2}}
@@ -267,7 +267,7 @@ $$
 
 As stated above, the median is less sensitive to extreme values with respect to
 the mode: this lead the result to be much more precise. Applying again the
-aforementioned t-test to this statistic:
+aforementioned $t$-test to this statistic:
 
   - $t=0.761$
   - $p=0.446$
@@ -344,7 +344,7 @@ $$
   \text{observed FWHM: } w_o = \num{4.06 \pm 0.08}
 $$
 
-Applying the t-test to these two values gives
+Applying the $t$-test to these two values gives
 
   - $t=0.495$
   - $p=0.620$
diff --git a/notes/sections/3.md b/notes/sections/3.md
index d32b974..e85f812 100644
--- a/notes/sections/3.md
+++ b/notes/sections/3.md
@@ -369,7 +369,7 @@ See @sec:res_comp for results compatibility.
 
 In order to compare the values $x_L$ and $x_{\chi}$ obtained from both methods
 with the correct ones ({$\alpha_0$, $\beta_0$, $\gamma_0$}), the following
-compatibility t-test was applied:
+compatibility $t$-test was applied:
 
 $$
   p = 1 - \text{erf}\left(\frac{t}{\sqrt{2}}\right)\ \with
@@ -412,7 +412,7 @@ $\chi^2$ results:
 Table: $\chi^2$ results compatibility.
 
 It can be concluded that, with both methods, the parameters $\alpha$ and $\beta$
-were recovered succefully, while $\gamma$ is incompatible. However, the
+were recovered successfully, while $\gamma$ is incompatible. However, the
 covariance was estimated using the Cramér-Rao bound, so the errors may be
 underestimated, which must be the case for $\gamma$.
 
@@ -426,9 +426,9 @@ The issue remains unsolved as no explanation was found.
 ## Isotropic hypothesis testing
 
 What if the probability distribution function were isotropic?
-Is this hypothesys compatible with the observation?
+Is this hypothesis compatible with the observation?
 
 If $F$ is isotropic, $\alpha_I$, $\beta_I$ and $\gamma_I$ would be $1/3$ , 0,
-and 0 respectively, since this gives $F_I = 1/{4 \pi}$. The t-test gives a
+and 0 respectively, since this gives $F_I = 1/{4 \pi}$. The $t$-test gives a
 $p$-value approximately zero for all the three parameters, meaning that there
 is no compatibility at all with this hypothesis.
diff --git a/notes/sections/4.md b/notes/sections/4.md
index 0ac0f63..80775df 100644
--- a/notes/sections/4.md
+++ b/notes/sections/4.md
@@ -212,7 +212,7 @@ $$
 where $\chi_r^2$ is the $\chi^2$ per degree of freedom, proving a good
 convergence.  
 In order to compare $P^{\text{oss}}_{\text{max}}$ with the expected value
-$P_{\text{max}} = 10$, the following compatibility t-test was applied:
+$P_{\text{max}} = 10$, the following compatibility $t$-test was applied:
 
 $$
   p = 1 - \text{erf}\left(\frac{t}{\sqrt{2}}\right)\ \with