{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import scipy as sp\n", "import scipy.special\n", "import scipy.stats\n", "import pandas as pd\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Simply speaking, the **Analysis of Variance**(ANOVA) is a technique of comparing means of multiple$(\\geq 3)$ populations, the name derives from the way how calculations are performed. \n", "\n", "For example, a common hypotheses of ANOVA are \n", "$$\n", "H_0:\\quad \\mu_1=\\mu_2=\\mu_3=\\cdots=\\mu_n\\\\\n", "H_1:\\quad \\text{At least two means differ}\n", "$$\n", "\n", "The first doubt pops up in mind: why aren't we using same old $t$-tests such that\n", "$$\n", "H_0: \\mu_1=\\mu_2 \\qquad H_0: \\mu_1=\\mu_3 \\qquad H_0: \\mu_1=\\mu_4 \\qquad H_0:\\quad \\mu_2=\\mu_3\\quad\\cdots\\\\\n", "H_1: \\mu_1\\neq\\mu_2 \\qquad H_1: \\mu_1\\neq\\mu_3\\qquad H_1:\\mu_1\\neq\\mu_4 \\qquad H_1:\\quad \\mu_2\\neq\\mu_3\\quad\\cdots\\\\\n", "$$\n", "and so on so forth, till exhaustion of all pairwise combination.\n", "\n", "Apparently, the number of $t$-tests will be as large as ${n \\choose 2} $ where $n$ is the number of populations. If there are $5$ populations, then we have to test ${5 \\choose 2}=10$ pairs. With $95\\%$ confidence level, $10$ $t$-tests would cut back confidence level dramatically to $95\\%^{10}=59.8\\%$, which also means the probability of _type I_ error would be around $40\\%$.\n", "\n", "A sidenote, econometric ANOVA is a standard practice that all statistical packages automatically print, however the terminologies in statistics are peculiar to econometric practioners, but still semantically sensible that will be clarified in later discussion." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# One-Way Analysis of Variance " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If samples are independently drawn from populations, the technique of ANOVA is called **One-Way ANOVA**. The statistic that measures the proximity of the sample means to each other is called **sum of squares for treatments** (SST). The terminology _treatment_ was introduced in 1920s when conducting ANOVA on different treatments of fertilisers for testing potential yields. For instance, an agronomist can sample three different corn yields applied with three different fertilisers. \n", "\n", "The sum of squares for treatments (SST) represents the **between-treatment variation**, the mathematical form is\n", "$$\n", "SST=\\sum_{i=1}^kn_i(\\bar{x}_i-\\bar{\\bar{x}})^2\n", "$$\n", "where $n_i$ is the sample size of treatments $i$, $\\bar{\\bar{x}}$ is the grand mean, i.e. the _mean of the sample means_, $k$ is the number of treatments.\n", "\n", "There are also **within-treatments variations** which is denoted by **sum of squares for error** (SSE), it measures the deviation of all observations from its sample mean. \n", "$$\n", "SSE=\\sum_{i=1}^k\\sum_{j=1}^{n_i}(x_{ij}-\\bar{x}_i)^2=\\sum_{j=1}^{n_1}(x_{j1}-\\bar{x}_1)^2+\\sum_{j=1}^{n_2}(x_{j2}-\\bar{x}_2)^2+\\cdots+\\sum_{j=1}^{n_k}(x_{jk}-\\bar{x}_k)^2\n", "$$\n", "If we divide $SSE$ by $(n_i-1)$, i.e. the degree of freedom of each sample, $SSE$ can be rewritten more consicely as\n", "$$\n", "SSE =(n_1-1)s_1^2+(n_2-1)s_2^2+\\cdots+(n_k-1)s_k^2\n", "$$\n", "where $s_i^2$ is the sample variance of sample $i$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In order to construct $F$-statistic, we need to introduce two more statistics, the first one is **Mean Square for Treatments** (MST)\n", "$$\n", "MST=\\frac{SST}{k-1}\n", "$$\n", "And the second one is **Mean Square for Error** (MSE)\n", "$$\n", "MSE=\\frac{SSE}{n-k}\n", "$$\n", "Join them together, an $F$-statistic is constructed\n", "$$\n", "F=\\frac{MST}{MSE}\n", "$$\n", "\n", "There are three assumptions for an ANOVA test to be valid.\n", "
    \n", "
  1. Each sample is independent to each other.
    2. \n", "
  2. Each sample is drawn from a normally distributed population.
    3. \n", "
  3. Population standard deviation are homoskedastic, i.e. constant variance.
    4. \n", "
\n", "Though in practice you might frequently encounter violation of the assumptions, you should be fully aware of the potentially misleading interpretation of the test results." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If $SST$ is large, then so is $MST$, more likely to produce a larger $F$-statistic, then a higher probability to reject null hypothesis, the rejection rule is\n", "$$\n", "F>F_{\\alpha, k-1, n-k}\n", "$$\n", "\n", "\n", "Critical value $F_{\\alpha, k-1, n-k}$ can be returned by ```scipy.stats.f.ppf()```. For instance, the number of treatment is $4$, sum of sample sizes is $342$, with $95\\%$ confidence level the crtical value is " ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.6321415117354894" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sp.stats.f.ppf(.95, 3, 328)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The widely-known variance decomposition equation is \n", "$$\n", "SS(Total)=SST+SSE\n", "$$\n", "Mathematically\n", "$$\n", "\\sum_{i=1}^k \\sum_{j=1}^{n_i}(x_{ij}-\\bar{\\bar{x}})^2= \\sum_{i=1}^kn_i(\\bar{x}_i-\\bar{\\bar{x}})^2+(n_1-1)s_1^2+(n_2-1)s_2^2+\\cdots+(n_k-1)s_k^2\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## An Example of Population Height " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here is a simple example, we will use three samples of male heights to perform an ANOVA analysis. The hypotheses are\n", "$$\n", "H_0: \\mu_1=\\mu_2=\\mu_3\\\\\n", "H_1: \\text{At least two means differ}\\\\\n", "$$" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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JapaneseDutchDanish
0161.783130187.726286174.746213
1145.329934179.338741174.133579
2174.569597176.566656178.966745
3160.003162184.570245179.335222
4162.242898184.056181167.497992
\n", "
" ], "text/plain": [ " Japanese Dutch Danish\n", "0 161.783130 187.726286 174.746213\n", "1 145.329934 179.338741 174.133579\n", "2 174.569597 176.566656 178.966745\n", "3 160.003162 184.570245 179.335222\n", "4 162.242898 184.056181 167.497992" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df = pd.read_excel('dataset/height_anova2.xlsx')\n", "df.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here are ANOVA formulae typed in a verbatim manner." ] }, { "cell_type": "code", "execution_count": 168, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "F-statistic: 37.96057544749984\n", "p-value: 2.3363533330211794e-12\n" ] } ], "source": [ "dutch_mean = df['Dutch'].mean()\n", "japanese_mean = df['Japanese'].mean()\n", "danish_mean = df['Danish'].mean()\n", "grand_mean = (dutch_mean+japanese_mean+danish_mean)/3\n", "\n", "SST = len(df['Japanese'])*(japanese_mean-grand_mean)**2\\\n", " +len(df['Dutch'])*(dutch_mean-grand_mean)**2\\\n", " +len(df['Danish'])*(danish_mean-grand_mean)**2\n", "MST = SST/2\n", "\n", "SSE = (len(df['Japanese'])-1)*df['Japanese'].var(ddof=1)\\\n", " +(len(df['Dutch'])-1)*df['Dutch'].var(ddof=1)\\\n", " +(len(df['Danish'])-1)*df['Danish'].var(ddof=1)\n", "n = len(df['Japanese']) + len(df['Dutch']) + len(df['Danish'])\n", "k = 3\n", "MSE = SSE/(n-k)\n", "\n", "F = MST/MSE\n", "print('F-statistic: {}'.format(F))\n", "print('p-value: {}'.format(1 - sp.stats.f.cdf(F, 2, n-k)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The test results favours the alternative hypothesis overwhelmingly. \n", "\n", "Before we close the case, let's exam the sample variance." ] }, { "cell_type": "code", "execution_count": 169, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Japanese sample variance: 145.93369676074872\n", "Danish sample variance: 20.108195066929262\n", "Dutch sample variance: 15.844843124694973\n" ] } ], "source": [ "print('Japanese sample variance: {}'.format(df['Japanese'].var(ddof=1)))\n", "print('Danish sample variance: {}'.format(df['Danish'].var(ddof=1)))\n", "print('Dutch sample variance: {}'.format(df['Dutch'].var(ddof=1)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Apparently they violate on of assumptions of ANOVA, therefore cautious must be taken when interpreting the results, though we firmly know the mean heights in these three countries are different. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A Simulation View of Factors That Affects $F$-Statistic" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Rather than stating that the $F$-tests might be invalid due to violation of critial assumptions, we'll step further to generate simulations to show how various parameters affect $F$-statistics.\n", "\n", "The plotting codes are messy, thus hidden in the ```plot_material.anova_plot()```, there 9 groups of charts, e.g. titled as 'Simulation X', each group has a two axes surrounded by a black frame.\n", "\n", "We will repetitively draw samples from three populations, each with its own parameters $\\mu$, $\\sigma$ and $N$, i.e. population mean, population variance and sample size. Each draw can be computed an $F$-statistic, we perform this simuation in a loop of $1000$ rounds, then we plot the fequency distribution of $F$-statistic on the upper axes, and the $p$-value on the lower axes. \n", "\n", "And the red vertical line is the critical value of $F$-statistic, any test results fall to the right-side of the red line shall conclude a rejection to the null hypothesis." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For instance, the simulation $1$ has $\\mu_1=3, \\mu_2=6, \\mu_3 = 9$, it surely indicate a large $F$-statistic, because larger $MST$, however we could still see yet a smaller amount of $F$'s that fall short than critical value. The distributions of corresponding p-values are also plotted under the $F$-statistic distribution. \n", "\n", "The simulation $2$ has $\\mu_1=3, \\mu_2=3.1, \\mu_3 = 2.9$, unless the standard deviation are dominantly trivial, we won't expect a high chance of rejecting null hypothesis, and that's also what the chart shows.\n", "\n", "The difference between simulation $2$ and $3$ is the $\\sigma$, apparently the latter one violates the assumption of homoskedasticity, and the $\\sigma$'s mainly are larger than Simulation $1$, thus it pushes more distributions of $F$-statistic to the left side of $F_c$, i.e. fail to reject null.\n", "\n", "The simulation $4$ complies with assumption of homoskedasticity, and due to variaous $\\mu$'s, presumably we would expect a higher volume of rejection of null hypothesis. Visually, yet a large amount of tests fail to reject, possibly due to relative larger standard deviations.\n", "\n", "The simulation $5$ and $6$ privide some interesting insight, when the sample size are small such as $n=10$ and relatively large $\\sigma$ would result in a predominant amout of false negative. The straightforward remedy is to increase the sample size as in the simulation $6$.\n", "\n", "You can experiment on parameters of simulation $7$, $8$ and $9$. " ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import plot_material\n", "plot_material.anova_plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## LSD Confidence Intervals" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If you have rejected the null hypothesis, but still need further investigation into which treatments deviate from the rest, you need one technique to identify the source of discrepancy. Here's the example of the technique.\n", "\n", "The same height example, there is one more column of Finnish in the sheet 2. Let's import the sheet 2." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "df2 = pd.read_excel('height_anova2.xlsx', 'Sheet2')" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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JapaneseDutchDanishFinnish
0161.783130187.726286174.746213175.855378
1145.329934179.338741174.133579175.513979
2174.569597176.566656178.966745173.363995
3160.003162184.570245179.335222178.515200
4162.242898184.056181167.497992173.108095
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" ], "text/plain": [ " Japanese Dutch Danish Finnish\n", "0 161.783130 187.726286 174.746213 175.855378\n", "1 145.329934 179.338741 174.133579 175.513979\n", "2 174.569597 176.566656 178.966745 173.363995\n", "3 160.003162 184.570245 179.335222 178.515200\n", "4 162.242898 184.056181 167.497992 173.108095" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df2.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The method we are going to introduce is called **Fisher's Least Significant Difference** (LSD), mathematically as \n", "$$\n", "LSD= t_{\\alpha/2}\\sqrt{MSE\\bigg(\\frac{1}{n_i}+\\frac{1}{n_j}\\bigg)}\n", "$$\n", "where degree of freedom is $n_1+n_2-2$, and the confidence interval estimator of mean difference is\n", "$$\n", "(\\bar{x}_i-\\bar{x}_j)\\pm t_{\\alpha/2}\\sqrt{MSE\\bigg(\\frac{1}{n_i}+\\frac{1}{n_j}\\bigg)}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, calculate the $MSE$." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "dutch_mean = df2['Dutch'].mean()\n", "japanese_mean = df2['Japanese'].mean()\n", "danish_mean = df2['Danish'].mean()\n", "finnish_mean = df2['Finnish'].mean()\n", "grand_mean = (dutch_mean+japanese_mean+danish_mean+finnish_mean)/4\n", "\n", "SSE = (len(df2['Japanese'])-1)*df2['Japanese'].var(ddof=1)\\\n", " +(len(df2['Dutch'])-1)*df2['Dutch'].var(ddof=1)\\\n", " +(len(df2['Danish'])-1)*df2['Danish'].var(ddof=1)\\\n", " +(len(df2['Finnish'])-1)*df2['Finnish'].var(ddof=1)\n", "\n", "n = len(df2['Japanese']) + len(df2['Dutch']) + len(df2['Danish']) + len(df2['Finnish'])\n", "k = 4\n", "MSE = SSE/(n-k)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The $LSD$ statistic are intended for each pair of treatments.\n", "\n", "$4$ groups means there are $\\binom{4}{2}=6$ pairs to test. Let's write a simple function of $LSD$." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "def lsd(sig_level, MSE, n1, n2):\n", " t = sp.stats.t.ppf(1-sig_level/2, n1+n2-2)\n", " return t*np.sqrt(MSE*(1/n1+1/n2))" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Comparison, Point Estimate, Lower Bound, Upper Bound\n", "Japanese - Dutch : -17.7116, -21.3998, -14.0233\n", "Japanese - Danish : -12.2196, -15.9078, -8.5313\n", "Japanese - Finnish : -12.8530, -16.5413, -9.1648\n", "Dutch - Danish : 5.4920, 1.8038, 9.1803\n", "Dutch - Finnish : 4.8585, 1.1703, 8.5468\n", "Danish - Finnish : -0.6335, -4.3217, 3.0548\n" ] } ], "source": [ "jadu = japanese_mean-dutch_mean\n", "jada = japanese_mean-danish_mean\n", "jafi = japanese_mean-finnish_mean\n", "duda = dutch_mean-danish_mean\n", "dufi = dutch_mean-finnish_mean\n", "dafi = danish_mean-finnish_mean\n", "\n", "jadu_lsd_low = jadu - lsd(.05, MSE, len(df2['Japanese']), len(df2['Dutch']))\n", "jadu_lsd_high = jadu + lsd(.05, MSE, len(df2['Japanese']), len(df2['Dutch']))\n", "\n", "jada_lsd_low = jada - lsd(.05, MSE, len(df2['Japanese']), len(df2['Danish']))\n", "jada_lsd_high = jada + lsd(.05, MSE, len(df2['Japanese']), len(df2['Danish']))\n", "\n", "jafi_lsd_low = jafi - lsd(.05, MSE, len(df2['Japanese']), len(df2['Finnish']))\n", "jafi_lsd_high = jafi + lsd(.05, MSE, len(df2['Japanese']), len(df2['Finnish']))\n", "\n", "duda_lsd_low = duda - lsd(.05, MSE, len(df2['Dutch']), len(df2['Danish']))\n", "duda_lsd_high = duda + lsd(.05, MSE, len(df2['Dutch']), len(df2['Danish']))\n", "\n", "dufi_lsd_low = dufi - lsd(.05, MSE, len(df2['Dutch']), len(df2['Finnish']))\n", "dufi_lsd_high = dufi + lsd(.05, MSE, len(df2['Dutch']), len(df2['Finnish']))\n", "\n", "dafi_lsd_low = dafi - lsd(.05, MSE, len(df2['Danish']), len(df2['Finnish']))\n", "dafi_lsd_high = dafi + lsd(.05, MSE, len(df2['Danish']), len(df2['Finnish']))\n", "\n", "\n", "print('Comparison, Point Estimate, Lower Bound, Upper Bound')\n", "print('Japanese - Dutch : {:.4f}, {:.4f}, {:.4f}'.format(jadu, jadu_lsd_low, jadu_lsd_high))\n", "print('Japanese - Danish : {:.4f}, {:.4f}, {:.4f}'.format(jada, jada_lsd_low , jada_lsd_high))\n", "print('Japanese - Finnish : {:.4f}, {:.4f}, {:.4f}'.format(jafi, jafi_lsd_low , jafi_lsd_high))\n", "print('Dutch - Danish : {:.4f}, {:.4f}, {:.4f}'.format(duda, duda_lsd_low , duda_lsd_high))\n", "print('Dutch - Finnish : {:.4f}, {:.4f}, {:.4f}'.format(dufi, dufi_lsd_low , dufi_lsd_high))\n", "print('Danish - Finnish : {:.4f}, {:.4f}, {:.4f}'.format(dafi, dafi_lsd_low , dafi_lsd_high))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Point estimate is straightforward to interprete, if the estimate is further away from $0$, we have stronger evidence that two sample means differ. \n", "\n", "But to give a clear statistical inference with $\\alpha$ significance level, we should look at confidence interval. If the interval excludes $0$, we could conclude a rejection of $\\mu_i=\\mu_j$. In our example, the only fail to rejection is between Danish and Finnish, it means their male heights are largely indifferentiable.\n", "\n", "Therefore we conclude that the $MST$ is mostly contributed by Japanese compared to other countries." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Chi-Squared Goodness-of-Fit Test" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is the last topic of the this tutorial session. Let's walk through an example, then you will be able to grasp the essence of **chi-squared goodness-of-fit test**.\n", "\n", "There are three marksman, who are competing shooting beer bottles hanging on a tree $300m$ away, according to their historical records. Here is their hitting rates.\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
MarksmanHitting Rate
A$24\\%$
B$40\\%$
C$36\\%$
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Apparently $24\\%+40\\%+36\\%=1$, which is a feature of **multinomial experiment**. \n", "\n", "In order to improve performance, Marksman A attended a hunter training camp, then they agree to compete again. They take turn to shoot and will stop until the 500th bottle is shot. Here is the result. \n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
MarksmanBottles
A$142$
B$187$
C$172$
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We would like to know if Marksman A has improved which also causes the hitting rate changes. The null hypothesis is specified as\n", "$$\n", "H_0: p_1=24\\%, p_2 = 40\\%, p_3=36\\%\\\\\n", "H_1: \\text{At least one $p_i$ is not equal to its specified value}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Without seeing the lastest competition result, we are looking forward to the **expected frequency** to be\n", "$$\n", "e_1 = 500\\times 24\\% = 120\\\\\n", "e_2 = 500\\times 40\\% = 200\\\\\n", "e_3 = 500\\times 36\\% = 180\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And here's the comparison bar chart." ] }, { "cell_type": "code", "execution_count": 71, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "labels = ['Marksman 1', 'Marksman 2', 'Marksman 3']\n", "post_training = np.array([142, 187, 172])\n", "exp_frequency = np.array([120, 200, 180])\n", "\n", "x = np.arange(len(labels)) # the label locations\n", "width = .2 # the width of the bars\n", "\n", "fig, ax = plt.subplots(figsize = (10, 4))\n", "rects1 = ax.bar(x - width/2, post_training, width, label='Post-Training')\n", "rects2 = ax.bar(x + width/2, exp_frequency, width, label='Exp. Freq.')\n", "\n", "ax.set_ylabel('Scores')\n", "ax.set_title('Scores of Exp. Freq. And Post-Training')\n", "ax.set_xticks(x)\n", "ax.set_xticklabels(labels)\n", "ax.legend()\n", "\n", "fig.tight_layout()\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If the expected and observed frequencies differ significantly, we would conclude a rejection to the null hypothesis. The test statistic is \n", "$$\n", "\\chi^2=\\sum_{i=1}^k\\frac{(f_i-e_i)^2}{e_i}\n", "$$\n", "where $f_i$ and $e_i$ are observed and expected frequencies. In this example, $\\chi^2$ is\n", "$$\n", "\\chi^2 = \\frac{(f_1-e_1)^2}{e_1}+\\frac{(f_2-e_2)^2}{e_2}+\\frac{(f_3-e_3)^2}{e_3}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compute the $\\chi^2$" ] }, { "cell_type": "code", "execution_count": 74, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "5.233888888888888" ] }, "execution_count": 74, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sum((post_training - exp_frequency)**2/exp_frequency)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Degree of freedom is $\\nu=k-1=2$, therefore the rejection region is \n", "$$\n", "\\chi^2>\\chi^2_{.05, 2}\n", "$$\n", "which can be found by ```sp.stats.chi2.ppf```." ] }, { "cell_type": "code", "execution_count": 78, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "5.991464547107979" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sp.stats.chi2.ppf(.95, 2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Because $\\chi^2$-statistic did not surpass the critical value, we conclude a fail to rejection of null hypothesis. That means even though the post-traning result is better than expectation, it's likely to be a statistical fluke rather than evidence of skill improvement." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.8.8" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }