diff --git a/notebooks/metamorphic_stat_tests.ipynb b/notebooks/metamorphic_stat_tests.ipynb
new file mode 100644
index 0000000..6f8ffa1
--- /dev/null
+++ b/notebooks/metamorphic_stat_tests.ipynb
@@ -0,0 +1,290 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "804a65dc",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from giskard.ml_worker.testing.stat_utils import equivalence_t_test, paired_t_test\n",
+    "from giskard.ml_worker.testing.stat_utils import equivalence_wilcoxon, paired_wilcoxon \n",
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "# if using a Jupyter notebook, includue:\n",
+    "%matplotlib inline\n",
+    "import scipy.stats as stats"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "68b742b4",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "cases={\"Invariant\":{'loc_pop': 0.5, 'scale_pop': 0.5, 'loc_perturb': 0, 'scale_perturb': 1e-2, 'direction':'Invariant'},\n",
+    "      \"Increasing\":{'loc_pop': 0.5, 'scale_pop': 0.5, 'loc_perturb': 0.1, 'scale_perturb': 1e-1, 'direction':'Increasing'},\n",
+    "      \"Decreasing\":{'loc_pop': 0.5, 'scale_pop': 0.5, 'loc_perturb': -0.1, 'scale_perturb': 1e-1, 'direction':'Decreasing'}}\n",
+    "\n",
+    "n=15\n",
+    "threshold=0.05\n",
+    "\n",
+    "population={}\n",
+    "perturbation={}\n",
+    "\n",
+    "np.random.seed(3)\n",
+    "\n",
+    "for key in cases.keys():\n",
+    "    population[key] = np.random.normal(cases[key]['loc_pop'], cases[key]['scale_pop'], size=n)\n",
+    "    perturbation[key] = np.random.normal(cases[key]['loc_perturb'], cases[key]['scale_perturb'], size=n)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "d7725dd9",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "not enough evidence to reject null hypothesis\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "result_inc, p_value_inc = paired_t_test(population[\"Increasing\"], population[key]+perturbation[\"Increasing\"], alternative=\"less\")\n",
+    "result_dec, p_value_dec = paired_t_test(population[\"Decreasing\"], population[key]+perturbation[\"Decreasing\"], alternative=\"greater\")\n",
+    "result_inv, p_value_inv = equivalence_t_test(population[\"Invariant\"], population[key]+perturbation[\"Invariant\"])\n",
+    "\n",
+    "dict_mapping_t_test = {'Invariant':  (result_inv, p_value_inv),\n",
+    "                'Decreasing': (result_dec, p_value_dec),\n",
+    "                'Increasing': (result_inc, p_value_inc)}\n",
+    "\n",
+    "for key in cases.keys():\n",
+    "    \n",
+    "    plt.hist(population[key], 20,\n",
+    "             density=True,\n",
+    "             histtype='bar',\n",
+    "             facecolor='b',\n",
+    "             alpha=0.5,\n",
+    "            label=\"population\")\n",
+    "\n",
+    "    plt.hist(population[key]+perturbation[key], 20,\n",
+    "             density=True,\n",
+    "             histtype='bar',\n",
+    "             facecolor='r',\n",
+    "             alpha=0.5,\n",
+    "            label=\"perturbation\")\n",
+    "\n",
+    "    status=key+\" \"\n",
+    "    if dict_mapping_t_test[key][1] < 0.05:\n",
+    "        status+=\"Test Passed\"\n",
+    "        comp=\" < \"\n",
+    "    else:\n",
+    "        status+=\"Test did not Pass\"\n",
+    "        comp=\" > \"\n",
+    "\n",
+    "\n",
+    "    plt.legend(title=status+\"\\n p-value (t-test)=\"+str(\"{:.1e}\".format(dict_mapping_t_test[key][1]))+comp+\"threshold=\"+str(threshold))\n",
+    "    plt.show()\n",
+    "    \n",
+    "    \n",
+    "    #if p_value < critical_quantile ==> null cannot be rejected \n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "7210d37d",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "not enough evidence to reject null hypothesis\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "threshold=0.05\n",
+    "\n",
+    "\n",
+    "result_inc, p_value_inc = paired_wilcoxon(population[\"Increasing\"], population[key]+perturbation[\"Increasing\"], alternative=\"less\")\n",
+    "result_dec, p_value_dec = paired_wilcoxon(population[\"Decreasing\"], population[key]+perturbation[\"Decreasing\"], alternative=\"greater\")\n",
+    "result_inv, p_value_inv = equivalence_wilcoxon(population[\"Invariant\"], population[key]+perturbation[\"Invariant\"])\n",
+    "\n",
+    "dict_mapping_wilcoxon = {'Invariant':  (result_inv, p_value_inv),\n",
+    "                'Decreasing': (result_dec, p_value_dec),\n",
+    "                'Increasing': (result_inc, p_value_inc)}\n",
+    "\n",
+    "for key in cases.keys():\n",
+    "    \n",
+    "    plt.hist(population[key], 20,\n",
+    "             density=True,\n",
+    "             histtype='bar',\n",
+    "             facecolor='b',\n",
+    "             alpha=0.5,\n",
+    "            label=\"population\")\n",
+    "\n",
+    "    plt.hist(population[key]+perturbation[key], 20,\n",
+    "             density=True,\n",
+    "             histtype='bar',\n",
+    "             facecolor='r',\n",
+    "             alpha=0.5,\n",
+    "            label=\"perturbation\")\n",
+    "\n",
+    "    status=key+\" \"\n",
+    "    if dict_mapping_wilcoxon[key][1] < 0.05:\n",
+    "        status+=\"Test Passed\"\n",
+    "        comp=\" < \"\n",
+    "    else:\n",
+    "        status+=\"Test did not Pass\"\n",
+    "        comp=\" > \"\n",
+    "\n",
+    "\n",
+    "    plt.legend(title=status+\"\\n p-value (Wilcoxon)=\"+str(\"{:.1e}\".format(dict_mapping_wilcoxon[key][1]))+comp+\"threshold=\"+str(threshold))\n",
+    "    plt.show()\n",
+    "    \n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "67e322c2",
+   "metadata": {},
+   "source": [
+    "# Summary"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "e7dc5aaa",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Sample size= 30 \n",
+      "\n",
+      "t-test\n",
+      "False p-value[ Invariant ]= 0.2826319087341232\n",
+      "True p-value[ Decreasing ]= 4.0602683599443865e-07\n",
+      "False p-value[ Increasing ]= 0.41556736963041396\n",
+      "\n",
+      "Wilcoxon\n",
+      "False p-value[ Invariant ]= 0.3985491515033976\n",
+      "True p-value[ Decreasing ]= 1.8621323639728217e-05\n",
+      "False p-value[ Increasing ]= 0.32916526204406704\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(\"Sample size=\",n,\"\\n\")\n",
+    "\n",
+    "# Prints the nicely formatted dictionary\n",
+    "\n",
+    "print(\"t-test\")\n",
+    "for key in dict_mapping_t_test.keys():\n",
+    "    print(dict_mapping_t_test[key][0], \"p-value[\",key,\"]=\",dict_mapping_t_test[key][1])\n",
+    "print()\n",
+    "print(\"Wilcoxon\")\n",
+    "for key in dict_mapping_wilcoxon.keys():\n",
+    "    print(dict_mapping_wilcoxon[key][0], \"p-value[\",key,\"]=\",dict_mapping_wilcoxon[key][1])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "d0d4becf",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.8.14"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}