Lecture06_Hypothesis_Test.ipynb

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   "source": [
    "# 1. T-test"
   ]
  },
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    "Types of t-test\n",
    "- An independent sample t-test compares the means for two groups\n",
    "- A paired sample t-test compares means from the same group at different times\n",
    "- An one sample t-test tests the mean of a single group against a known mean"
   ]
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    "Steps\n",
    "1. Determine a null and alternate hypothesis.\n",
    "2. Collect sample data.\n",
    "3. Determine a confidence interval and degrees of freedom.\n",
    "4. Calculate the t-statistc.\n",
    "5. Caculate the critical t-value from the t distribution.\n",
    " - A large t-score tells you the groups are different.\n",
    " - A small t-score tells you that the groups are similar.\n",
    "6. Compare the critical t-values with the calculated t statistic."
   ]
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   "source": [
    "import numpy as np\n",
    "from scipy import stats"
   ]
  },
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   "source": [
    "> T test &#47784;&#46280;&#51012; &#49324;&#50857;&#54616;&#51648; &#50506;&#44256; &#44396;&#54644;&#48372;&#44592;"
   ]
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    "- $H_0$ : &#46160; &#51665;&#45800;&#51032; &#54217;&#44512;&#51008; &#44057;&#45796;. &#51593; $\\mu_1 = \\mu_2$\n",
    "- $H_1$ : &#46160; &#51665;&#45800;&#51032; &#54217;&#44512;&#51008; &#44057;&#51648; &#50506;&#45796;. &#51593; $\\mu_1 \\neq \\mu_2$"
   ]
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  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#  &#53356;&#44592;&#44032; 100&#51064; 2&#44060; &#44536;&#47353;&#51032; random data&#47484; &#49373;&#49457;\n",
    "n = 20\n",
    "\n",
    "# Gaussian distribution data with mean = 2 and var = 1\n",
    "group_a = np.random.randn(n) + 2\n",
    "# Gaussian distribution data with mean = 0 and var = 1\n",
    "group_b = np.random.randn(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Group A [4.16501603 2.76535089 2.48023999 3.97729739 0.89417203]\n",
      "Group B [-0.65120933  1.31345838  1.29784776 -0.23273527  2.89356947]\n"
     ]
    }
   ],
   "source": [
    "print('Group A', group_a[:5])\n",
    "print('Group B', group_b[:5])"
   ]
  },
  {
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   "execution_count": 4,
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   "outputs": [
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     "data": {
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       "1.2488360023905005"
      ]
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     "execution_count": 4,
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     "output_type": "execute_result"
    }
   ],
   "source": [
    "var_a = group_a.var(ddof=1)  # &#54364;&#48376;&#54217;&#44512;&#51008; n-1&#47196; &#45208;&#45572;&#50612;&#51456;&#45796;. (n - ddof)\n",
    "var_b = group_b.var(ddof=1)\n",
    "\n",
    "# Std deviation (&#46160; &#51665;&#45800;&#51032; &#47784;&#48516;&#49328;&#51060; &#44057;&#45796;&#44256; &#44032;&#51221; &#44032;&#51221;)\n",
    "s = np.sqrt((var_a + var_b)/2)\n",
    "s"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "&#48516;&#49328;&#50640; &#45824;&#54644;&#49436;&#45716; [scipy.stats.ttest_ind](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ttest_ind.html#r3566833beaa2-1)&#47484; &#52280;&#44256;&#54616;&#47732; &#46108;&#45796;."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.524544117296061"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculate the t-statistics\n",
    "t1 = (group_a.mean() - group_b.mean())/(s*np.sqrt(2/n))\n",
    "t1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "38"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Degree of freedom\n",
    "df = 2*n - 2\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 1 tailed p-value\n",
    "p1 = 1 - stats.t.cdf(t1, df=df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t = 5.524544117296061\n",
      "p = 2.5553559546143134e-06\n"
     ]
    }
   ],
   "source": [
    "print('t =', t1)\n",
    "print('p =', 2*p1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> `ttest_ind`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t2 = 5.524544117296061\n",
      "p2 = 2.5553559546522812e-06\n"
     ]
    }
   ],
   "source": [
    "t2, p2 = stats.ttest_ind(group_a, group_b)\n",
    "\n",
    "print(\"t2 =\", t2)\n",
    "print(\"p2 =\",p2)  # 2 tailed p-value"
   ]
  }
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