Reduce level of indentation for all examples/ nbs

minireference · Feb 2, 2024 · 85c28da · 85c28da
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diff --git a/examples/ANOVA.ipynb b/examples/ANOVA.ipynb
@@ -5,7 +5,7 @@
    "id": "5b41ceb6-d385-4837-b5e0-5e21e643d6e6",
    "metadata": {},
    "source": [
-    "### Analysis of variance (ANOVA)"
+    "# Analysis of variance (ANOVA)"
    ]
   },
   {
@@ -53,15 +53,15 @@
    "id": "e41da4dc-40bc-4074-b3ca-5f2a2534fdcf",
    "metadata": {},
    "source": [
-    "#### Definitions"
+    "## Definitions"
    ]
   },
   {
    "cell_type": "markdown",
    "id": "442020c3-458a-469b-a82e-c7f3beafb812",
    "metadata": {},
    "source": [
-    "#### Formulas"
+    "## Formulas"
    ]
   },
   {
@@ -79,31 +79,31 @@
    "id": "60311b0a-7c91-4df0-be4a-accc69028d8c",
    "metadata": {},
    "source": [
-    "#### Example"
+    "## Example"
    ]
   },
   {
    "cell_type": "markdown",
    "id": "2edd0ff1-e544-41a3-845a-c0471e345d41",
    "metadata": {},
    "source": [
-    "#### Explanations"
+    "## Explanations"
    ]
   },
   {
    "cell_type": "markdown",
    "id": "bf5f1bcf-d993-47e8-9f1b-52902c63c9e3",
    "metadata": {},
    "source": [
-    "#### Discussion"
+    "## Discussion"
    ]
   },
   {
    "cell_type": "markdown",
    "id": "c6bfa142-4e3f-46a0-bbd9-212692dd1b3d",
    "metadata": {},
    "source": [
-    "#### Equivalence between ANOVA and OLS\n",
+    "## Equivalence between ANOVA and OLS\n",
     "\n",
     "via https://stats.stackexchange.com/questions/175246/why-is-anova-equivalent-to-linear-regression"
    ]

diff --git a/examples/Mann-Whitney_U-test.ipynb b/examples/Mann-Whitney_U-test.ipynb
@@ -5,7 +5,7 @@
    "id": "229b9ce5-9ba8-406a-bb1a-5979d1e2a64f",
    "metadata": {},
    "source": [
-    "### Mann-Whitney U-test\n",
+    "# Mann-Whitney U-test\n",
     "\n",
     "The goal of the Mann-Whitney $U$-test to compare the medians two unknown population.\n",
     "\n",
@@ -61,7 +61,7 @@
    "id": "09804789-d86e-4df9-a3d9-4106bfbf76d1",
    "metadata": {},
    "source": [
-    "#### Data\n",
+    "## Data\n",
     "Two samples of numerical or ordinal observations $\\mathbf{x}=[x_1, x_2, \\ldots, x_n]$\n",
     "and $\\mathbf{y}=[y_1, y_2,\\ldots, y_m]$ from independent populations."
    ]
@@ -71,7 +71,7 @@
    "id": "d69a9922-b2a7-44f3-83f1-ed3713d71e8f",
    "metadata": {},
    "source": [
-    "#### Modeling assumptions\n",
+    "## Modeling assumptions\n",
     "\n",
     "We don't need to make any assumptions about the unknown populations."
    ]
@@ -81,7 +81,7 @@
    "id": "b69c7ac0-31bd-479e-afb4-f9505bfca4ef",
    "metadata": {},
    "source": [
-    "#### Hypotheses\n",
+    "## Hypotheses\n",
     "\n",
     "We're testing $H_0: \\med_X = \\med_Y$ against $H_A: \\med_X \\neq \\med_Y$."
    ]
@@ -91,7 +91,7 @@
    "id": "146b20c4-d535-46fe-86cc-8c2c52bfa39f",
    "metadata": {},
    "source": [
-    "#### Statistical design\n",
+    "## Statistical design\n",
     "\n",
     "???"
    ]
@@ -109,7 +109,7 @@
    "id": "7674af35-fd9d-4608-970a-b74c27ca3475",
    "metadata": {},
    "source": [
-    "#### Test statistic\n",
+    "## Test statistic\n",
     "\n",
     "Compute expressions $U_1 = \\sum_{i=1}^n \\Rank(x_i) - \\frac{n(n+1)}{2}$\n",
     "and  $U_2 = \\sum_{i=1}^m \\Rank(y_i) - \\frac{m(m+1)}{2}$,\n",
@@ -122,7 +122,7 @@
    "id": "46a6143a-ca4b-4568-bf5a-862a577c8c21",
    "metadata": {},
    "source": [
-    "#### Sampling distribution\n",
+    "## Sampling distribution\n",
     "\n",
     "For small sample sizes,\n",
     "the exact sampling distribution is obtained through a computational procedure.\n",
@@ -135,7 +135,7 @@
    "id": "15cf13c7-78bf-495a-baf8-2312c6210c2a",
    "metadata": {},
    "source": [
-    "#### P-value calculation"
+    "## P-value calculation"
    ]
   },
   {
@@ -164,15 +164,15 @@
    "id": "1d4c8b3d-5028-47ae-935e-7fda0667b710",
    "metadata": {},
    "source": [
-    "#### Examples"
+    "## Examples"
    ]
   },
   {
    "cell_type": "markdown",
    "id": "3b991eb0-8635-4e6f-9340-6c5ae3e1cb9c",
    "metadata": {},
    "source": [
-    "##### Example 1\n",
+    "### Example 1\n",
     "\n",
     "The dataset `outliers2.csv` consists of measurements of soil score variable\n",
     "using a specialized equipment for calculating soil quality.\n",
@@ -344,7 +344,7 @@
    "id": "3c8c7fbb-a5d2-449c-b49d-69d470b51024",
    "metadata": {},
    "source": [
-    "###### Using a regular two-sample t-test"
+    "#### Using a regular two-sample t-test"
    ]
   },
   {
@@ -391,7 +391,7 @@
    "id": "5c7b1504-f4a7-4aa1-a19e-c3b92055d06a",
    "metadata": {},
    "source": [
-    "###### Using the Mann-Whitney U-test"
+    "#### Using the Mann-Whitney U-test"
    ]
   },
   {
@@ -449,7 +449,7 @@
    "id": "9ae28def-30d0-4b39-8365-e06ed7cf9081",
    "metadata": {},
    "source": [
-    "#### Confidence interval for the effect size"
+    "## Confidence interval for the effect size"
    ]
   },
   {
@@ -465,7 +465,7 @@
    "id": "6be145e5-8cee-4d19-b215-807f690af3aa",
    "metadata": {},
    "source": [
-    "#### Related\n",
+    "## Related\n",
     "\n"
    ]
   },
@@ -482,7 +482,7 @@
    "id": "aff7ca4d-e061-40ad-9a6f-0c48913a001f",
    "metadata": {},
    "source": [
-    "#### Discussion"
+    "## Discussion"
    ]
   },
   {
@@ -498,7 +498,7 @@
    "id": "fa1f1c61-0742-4945-9618-8ec17f6263d7",
    "metadata": {},
    "source": [
-    "#### Links"
+    "## Links"
    ]
   },
   {

diff --git a/examples/one_sample_t-test.ipynb b/examples/one_sample_t-test.ipynb
@@ -5,7 +5,7 @@
    "id": "229b9ce5-9ba8-406a-bb1a-5979d1e2a64f",
    "metadata": {},
    "source": [
-    "### One-sample t-test for the mean\n",
+    "# One-sample t-test for the mean\n",
     "\n",
     "The goal of the one-sample $t$-test to check if the mean $\\mu$ of an unknown population $X \\sim \\mathcal{N}(\\mu, \\sigma_0)$,\n",
     "equals the mean $\\mu_0$ of a theoretical distribution $X_0 \\sim \\mathcal{N}(\\mu_0, \\sigma_0)$.\n",
@@ -58,7 +58,7 @@
    "id": "09804789-d86e-4df9-a3d9-4106bfbf76d1",
    "metadata": {},
    "source": [
-    "#### Data\n",
+    "## Data\n",
     "One sample of numerical observations $\\mathbf{x}=[x_1, x_2, \\ldots, x_n]$."
    ]
   },
@@ -67,7 +67,7 @@
    "id": "d69a9922-b2a7-44f3-83f1-ed3713d71e8f",
    "metadata": {},
    "source": [
-    "#### Modeling assumptions\n",
+    "## Modeling assumptions\n",
     "\n",
     "We model the unknown population as...\n",
     "\n",
@@ -88,7 +88,7 @@
    "id": "b69c7ac0-31bd-479e-afb4-f9505bfca4ef",
    "metadata": {},
    "source": [
-    "#### Hypotheses\n",
+    "## Hypotheses\n",
     "\n",
     "$H_0: \\mu = \\mu_0$ and $H_A: \\mu \\neq \\mu_0$,\n",
     "where $\\mu$ is the unknown population mean,\n",
@@ -100,7 +100,7 @@
    "id": "146b20c4-d535-46fe-86cc-8c2c52bfa39f",
    "metadata": {},
    "source": [
-    "#### Statistical design\n",
+    "## Statistical design\n",
     "\n",
     "for $n=5$ ...\n",
     "\n",
@@ -121,7 +121,7 @@
    "id": "7674af35-fd9d-4608-970a-b74c27ca3475",
    "metadata": {},
    "source": [
-    "#### Estimates\n",
+    "## Estimates\n",
     "\n",
     "Calculate the sample mean $\\overline{\\mathbf{x}} = \\Mean(\\mathbf{x})$\n",
     "and the sample standard deviation $s_{\\mathbf{x}} = \\Std(\\mathbf{x})$.\n",
@@ -134,7 +134,7 @@
    "id": "ab880b56-b783-4c32-b2cd-8cb66b59f766",
    "metadata": {},
    "source": [
-    "#### Test statistic\n",
+    "## Test statistic\n",
     "\n",
     "Compute $t = \\frac{\\overline{\\mathbf{x}} - \\mu_0}{ \\stderrhat{\\overline{\\mathbf{x}}} }$ from\n",
     "the sample mean $\\overline{\\mathbf{x}}$,\n",
@@ -147,7 +147,7 @@
    "id": "46a6143a-ca4b-4568-bf5a-862a577c8c21",
    "metadata": {},
    "source": [
-    "#### Sampling distribution\n",
+    "## Sampling distribution\n",
     "\n",
     "Student's $t$-distribution with $\\nu=n-1$ degrees of freedom."
    ]
@@ -157,7 +157,7 @@
    "id": "15cf13c7-78bf-495a-baf8-2312c6210c2a",
    "metadata": {},
    "source": [
-    "#### P-value calculation"
+    "## P-value calculation"
    ]
   },
   {
@@ -217,7 +217,7 @@
    "id": "c46e51cc-143b-4e0c-8872-c17a54e7810d",
    "metadata": {},
    "source": [
-    "#### Examples\n",
+    "## Examples\n",
     "\n",
     "For all the examples we present below,\n",
     "we assume the theoretical distribution we expect under the null hypothesis,\n",
@@ -256,7 +256,7 @@
    "id": "f65e1b6e-01a6-44fd-b112-455ec9cb0226",
    "metadata": {},
    "source": [
-    "##### Example A: population different from $H_0$"
+    "### Example A: population different from $H_0$"
    ]
   },
   {
@@ -445,7 +445,7 @@
    "id": "aa3a24ed-d585-4b3c-b5c0-f6ab6446819c",
    "metadata": {},
    "source": [
-    "##### Example B: sample from a population as expected under $H_0$"
+    "### Example B: sample from a population as expected under $H_0$"
    ]
   },
   {
@@ -588,7 +588,7 @@
    "id": "9ae28def-30d0-4b39-8365-e06ed7cf9081",
    "metadata": {},
    "source": [
-    "#### Confidence interval for the unknown mean"
+    "## Confidence interval for the unknown mean"
    ]
   },
   {
@@ -656,15 +656,15 @@
    "id": "9b660562-54a5-4c6c-b54e-fc128e541a56",
    "metadata": {},
    "source": [
-    "#### Effect size estimates"
+    "## Effect size estimates"
    ]
   },
   {
    "cell_type": "markdown",
    "id": "6be145e5-8cee-4d19-b215-807f690af3aa",
    "metadata": {},
    "source": [
-    "#### Related\n",
+    "## Related\n",
     "\n",
     "- Use the one-sample $z$-test if the population standard deviation is known"
    ]
@@ -682,7 +682,7 @@
    "id": "aff7ca4d-e061-40ad-9a6f-0c48913a001f",
    "metadata": {},
    "source": [
-    "#### Discussion"
+    "## Discussion"
    ]
   },
   {
@@ -698,7 +698,7 @@
    "id": "fa1f1c61-0742-4945-9618-8ec17f6263d7",
    "metadata": {},
    "source": [
-    "#### Links"
+    "## Links"
    ]
   },
   {