![](\"https://raw.githubusercontent.com/tirthajyoti/Stats-Maths-with-Python/master/images/Conf_interval.png\")
\n",
"\n",
"**Source**: https://psu.instructure.com/courses/1844486/pages/chapter-3-confidence-intervals\n",
"\n",
"\n", "
![](\"https://raw.githubusercontent.com/tirthajyoti/Stats-Maths-with-Python/master/images/Hypothesis_test.jpg\")
\n",
"\n",
"### Research Question\n",
"\n",
"*Is there a significant difference between the population proportions of parents of Black children and parents of Hispanic children who report that their child has had some swimming lessons*? (**A real-life study from the Univ. of Michigan**)\n",
"\n",
"### Formulation\n",
"\n",
"***Populations***: All parents of black children age 6-18 and all parents of Hispanic children age 6-18 \n",
"***Parameter of Interest***: p1 - p2, where p1 = black and p2 = hispanic \n",
"\n",
"***Null Hypothesis:*** p1 - p2 = 0 \n",
"***Alternative Hypthosis:*** p1 - p2 $\\neq$ 0\n",
"\n",
"### Data\n",
"\n",
"247 Parents of Black Children\n",
"36.8% of parents report that their child has had some swimming lessons.\n",
"\n",
"308 Parents of Hispanic Children\n",
"38.9% of parents report that their child has had some swimming lessons.\n",
"\n",
"### Function used in the code\n",
"\n",
"[Numpy Binomial distribution](https://docs.scipy.org/doc/numpy-1.14.0/reference/generated/numpy.random.binomial.html) because this is a matter of YES/NO answers (from the parents)\n",
"\n",
"[Scipy independent t-test](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ttest_ind.html) because we are interested in a two-sided test of equal/unequal means"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {},
"colab_type": "code",
"id": "Qw7Gxize9Kmb"
},
"outputs": [],
"source": [
"import scipy.stats"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {},
"colab_type": "code",
"id": "rZpS2CSj8yLz"
},
"outputs": [],
"source": [
"n1 = 247\n",
"p1 = .37\n",
"\n",
"n2 = 308\n",
"p2 = .39\n",
"\n",
"population1 = np.random.binomial(1, p1, n1)\n",
"population2 = np.random.binomial(1, p2, n2)\n"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 138
},
"colab_type": "code",
"executionInfo": {
"elapsed": 348,
"status": "ok",
"timestamp": 1567293099058,
"user": {
"displayName": "Tirthajyoti Sarkar",
"photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mD6d7dlMqdpzL4sermIF1ujmpSRxY2WnE4tuB-UsQ=s64",
"userId": "01914075970409030121"
},
"user_tz": 420
},
"id": "9urVpKfEFzGj",
"outputId": "fbccbae7-68ad-4be6-d198-fe74ddcdbbc5"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Parents of Black children\n",
"-------------------------------------------------------\n",
"86 parents answered YES and 161 parents answered NO\n",
"\n",
"Parents of Hispanic children\n",
"-------------------------------------------------------\n",
"114 parents answered YES and 194 parents answered NO\n"
]
}
],
"source": [
"print(\"Parents of Black children\")\n",
"print(\"-\"*55)\n",
"print(f\"{population1.sum()} parents answered YES and {n1-population1.sum()} parents answered NO\")\n",
"print(\"\\nParents of Hispanic children\")\n",
"print(\"-\"*55)\n",
"print(f\"{population2.sum()} parents answered YES and {n2-population2.sum()} parents answered NO\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {},
"colab_type": "code",
"id": "siZnSAlqFxQO"
},
"outputs": [],
"source": [
"t_stat,pval=scipy.stats.ttest_ind(population1, population2)"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 52
},
"colab_type": "code",
"executionInfo": {
"elapsed": 320,
"status": "ok",
"timestamp": 1567293100903,
"user": {
"displayName": "Tirthajyoti Sarkar",
"photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mD6d7dlMqdpzL4sermIF1ujmpSRxY2WnE4tuB-UsQ=s64",
"userId": "01914075970409030121"
},
"user_tz": 420
},
"id": "wMIQ1tcS89b5",
"outputId": "611c5d9a-d53c-4b0e-b6b1-387aeb8b9c58"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The t-statistic from this data: -0.5344882669395735\n",
"Corresponding p-value from this data: 0.5932185803894023\n"
]
}
],
"source": [
"print(\"The t-statistic from this data:\",t_stat)\n",
"print(\"Corresponding p-value from this data:\",pval)"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 69
},
"colab_type": "code",
"executionInfo": {
"elapsed": 332,
"status": "ok",
"timestamp": 1567292890659,
"user": {
"displayName": "Tirthajyoti Sarkar",
"photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mD6d7dlMqdpzL4sermIF1ujmpSRxY2WnE4tuB-UsQ=s64",
"userId": "01914075970409030121"
},
"user_tz": 420
},
"id": "JNoPujIA9f_O",
"outputId": "081a446c-0606-4de7-c46f-5d0aec69f7a2"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Based on this data, NULL hypothesis cannot be rejected \n",
"i.e. there is no significant difference between the proportion of Black and Hispanic parents,\n",
"who reporpted that their children had a swimming lesson\n"
]
}
],
"source": [
"if pval>0.05:\n",
" print(\"Based on this data, NULL hypothesis cannot be rejected \\ni.e. there is no significant difference between the proportion of Black and Hispanic parents,\\nwho reporpted that their children had a swimming lesson\")\n",
"else:\n",
" print(\"There seems to be a statisticlly significant difference in the proportion of Black and Hispanic parents,\\nwho reporpted that their children had a swimming lesson\")"
]
}
],
"metadata": {
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"name": "Conf_inv_sampling_hypothesis.ipynb",
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