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259 changes: 245 additions & 14 deletions lab-hypothesis-testing.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -51,7 +51,7 @@
},
{
"cell_type": "code",
"execution_count": 3,
"execution_count": 2,
"metadata": {},
"outputs": [
{
Expand Down Expand Up @@ -278,7 +278,7 @@
"[800 rows x 11 columns]"
]
},
"execution_count": 3,
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
Expand All @@ -297,11 +297,83 @@
},
{
"cell_type": "code",
"execution_count": 1,
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"#code here"
"dragon_hp = df[df[\"Type 1\"] == \"Dragon\"][\"HP\"]\n",
"grass_hp = df[df[\"Type 1\"] == \"Grass\"][\"HP\"]"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"T-statistic: 3.3349632905124063\n",
"P-value: 0.0015987219490841197\n"
]
}
],
"source": [
"# T-test\n",
"\n",
"t_stat, p_value = st.ttest_ind(dragon_hp, grass_hp, equal_var=False)\n",
"\n",
"print(\"T-statistic:\", t_stat)\n",
"print(\"P-value:\", p_value)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"One-sided p-value: 0.0007993609745420598\n"
]
}
],
"source": [
"p_value_one_sided = p_value / 2\n",
"\n",
"print(\"One-sided p-value:\", p_value_one_sided)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Reject the null hypothesis\n"
]
}
],
"source": [
"alpha = 0.05\n",
"\n",
"if p_value_one_sided < alpha:\n",
" print(\"Reject the null hypothesis\")\n",
"else:\n",
" print(\"Fail to reject the null hypothesis\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We performed an independent two-sample t-test to compare the HP stats of Dragon and Grass Pokémon. Using a significance level of 0.05, the resulting p-value was below 0.05. Therefore, we reject the null hypothesis and conclude that Dragon-type Pokémon have significantly higher average HP than Grass-type Pokémon."
]
},
{
Expand All @@ -313,11 +385,68 @@
},
{
"cell_type": "code",
"execution_count": 18,
"execution_count": 7,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"HP\n",
"t-stat: 8.981370483625046\n",
"p-value: 1.0026911708035284e-13\n",
"Reject H0 → Significant difference\n",
"\n",
"Attack\n",
"t-stat: 10.438133539322203\n",
"p-value: 2.520372449236646e-16\n",
"Reject H0 → Significant difference\n",
"\n",
"Defense\n",
"t-stat: 7.637078164784618\n",
"p-value: 4.826998494919331e-11\n",
"Reject H0 → Significant difference\n",
"\n",
"Sp. Atk\n",
"t-stat: 13.417449984138461\n",
"p-value: 1.5514614112239816e-21\n",
"Reject H0 → Significant difference\n",
"\n",
"Sp. Def\n",
"t-stat: 10.015696613114878\n",
"p-value: 2.2949327864052826e-15\n",
"Reject H0 → Significant difference\n",
"\n",
"Speed\n",
"t-stat: 11.47504444631443\n",
"p-value: 1.0490163118824507e-18\n",
"Reject H0 → Significant difference\n",
"\n"
]
}
],
"source": [
"#code here"
"legendary = df[df[\"Legendary\"] == True]\n",
"non_legendary = df[df[\"Legendary\"] == False]\n",
"\n",
"stats = [\"HP\",\"Attack\",\"Defense\",\"Sp. Atk\",\"Sp. Def\",\"Speed\"]\n",
"\n",
"for stat in stats:\n",
" \n",
" t_stat, p_value = st.ttest_ind(\n",
" legendary[stat],\n",
" non_legendary[stat],\n",
" equal_var=False\n",
" )\n",
" \n",
" print(f\"{stat}\")\n",
" print(\"t-stat:\", t_stat)\n",
" print(\"p-value:\", p_value)\n",
" \n",
" if p_value < 0.05:\n",
" print(\"Reject H0 → Significant difference\\n\")\n",
" else:\n",
" print(\"Fail to reject H0 → No significant difference\\n\")"
]
},
{
Expand All @@ -337,7 +466,7 @@
},
{
"cell_type": "code",
"execution_count": 5,
"execution_count": 8,
"metadata": {},
"outputs": [
{
Expand Down Expand Up @@ -453,7 +582,7 @@
"4 624.0 262.0 1.9250 65500.0 "
]
},
"execution_count": 5,
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
Expand Down Expand Up @@ -483,17 +612,119 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": []
"source": [
"# Defining School and Hospital coordinates\n",
"\n",
"school = (-118, 34)\n",
"hospital = (-122, 37)"
]
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": []
"source": [
"def euclidean_distance(x1, y1, x2, y2):\n",
" return np.sqrt((x1-x2)**2 + (y1-y2)**2)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"# Calculating distances\n",
"\n",
"df[\"dist_school\"] = euclidean_distance(\n",
" df[\"longitude\"], df[\"latitude\"],\n",
" school[0], school[1]\n",
")\n",
"\n",
"df[\"dist_hospital\"] = euclidean_distance(\n",
" df[\"longitude\"], df[\"latitude\"],\n",
" hospital[0], hospital[1]\n",
")"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"# Defining houses close to either location\n",
"\n",
"df[\"close\"] = (df[\"dist_school\"] < 0.5) | (df[\"dist_hospital\"] < 0.5)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"close_houses = df[df[\"close\"] == True][\"median_house_value\"]\n",
"far_houses = df[df[\"close\"] == False][\"median_house_value\"]"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"T-statistic: 37.992330214201516\n",
"P-value: 3.0064957768592614e-301\n"
]
}
],
"source": [
"# T-test\n",
"\n",
"t_stat, p_value = st.ttest_ind(close_houses, far_houses, equal_var=False)\n",
"\n",
"print(\"T-statistic:\", t_stat)\n",
"print(\"P-value:\", p_value)"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Reject H0\n"
]
}
],
"source": [
"# Decision\n",
"\n",
"alpha = 0.05\n",
"\n",
"if p_value < alpha:\n",
" print(\"Reject H0\")\n",
"else:\n",
" print(\"Fail to reject H0\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We performed an independent two-sample t-test to compare the median house values of neighborhoods located close to a school or hospital and those located farther away. Using a significance level of 0.05, the p-value obtained from the test indicates whether the difference in means is statistically significant. Since the p-value is below 0.05, we reject the null hypothesis and conclude that houses close to schools or hospitals tend to be more expensive."
]
}
],
"metadata": {
Expand All @@ -512,7 +743,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.10.9"
"version": "3.13.11"
}
},
"nbformat": 4,
Expand Down