{ "cells": [ { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import scipy as sp\n", "from scipy import stats\n", "\n", "plt.style.use(\"fivethirtyeight\")\n", "import pandas as pd" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Descriptive Statistics " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Before making any inferences from a dataset, it is crucial that we understand the features of datasets by 'describing' them. We can either describe them by plotting or calculating numerical summarisations.\n", "\n", "We will refresh most common descriptive statistics in this chapter, if you are working with data on a daily basis, no concepts here should sound strange to you.\n", "\n", "Furthermore, we will not engage in complex programming techniques, such as OOP and sophisticated data structures. All the programmes should be self-explanatory to most of audiences." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Frequency Distribution/Histogram" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Strictly speaking, frequency distribution and histogram are different descriptive tools, though they are delivering the largely identical information. Frequency distribution are usually presented in a table, for instance, rolling a dice $1000$ times might give a us frequency distribution table as following:\n", "\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
Rolling A Dice 1000 Times
SidesFrequency
1172
2158
3170
4158
5187
6155
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Or we can draw a frequency histogram, which simply converts the information of table into a graph." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rollings = np.random.randint(1, 7, 1000)\n", "\n", "fig, ax = plt.subplots(figsize=(9, 9))\n", "n, bins, patches = ax.hist(rollings, bins=6)\n", "ax.set_title(\"Frequency Histogram of 1000 Times of Rolling a Dice\", size=19)\n", "ax.set_xlim(0, 7)\n", "ax.set_ylim(0, 400)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we try generating an array from a standard normal distribution $x\\sim N(0, 1)$, then plot the histogram. And note that we add one parameter ```density=True``` in the ```hist``` method, it turns into a **relative frequency histogram**, because the $y$-axis represents relative frequencies." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.random.randn(1000)\n", "fig, ax = plt.subplots(figsize=(9, 9))\n", "n, bins, patches = ax.hist(x, bins=50, density=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Careful audiences might have noticed that while we are plotting the histogram, we also have 3 variables returned ```n```, ```bins``` and ```patches```. ```n``` is (relative) frequency counts, ```bins``` is the location of each bin, ```patches``` is the list of patches objects in the plot.\n", "\n", "The first charts below shows the same information as histogram, but with line plots rather than bars. But the second one is called *Empirical cumulative distribution**, it is empirical because it is not theoretically plotted, i.e. using a **cumulative distribution function (CDF)**. " ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(nrows=2, ncols=1, figsize=(9, 9))\n", "ax[0].plot(bins[:50], n)\n", "ax[1].plot(np.cumsum(n))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Basic Numeric Descriptives" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Measure Of Location" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The most important **mean** we need is **arithmetic mean**, which is prevalent in all kinds of statistical techniques. \n", "$$\n", "\\mu = \\frac{1}{N}\\sum_{i=1}^Nx_i\\\\\n", "\\bar{x} = \\frac{1}{n}\\sum_{i=1}^nx_i\n", "$$\n", "The former one is _population mean_, the latter is _sample mean_. The formulae appear the same, but with different indication. $N$ is the population size, imagine the number of all human beings on earth, on the other hand, $n$ is sample size, for instance a sample of $1000$ persons from UK. \n", "\n", "And one tricky mean commonly used in finance is **geometric mean**, not so intuitive at first sight.\n", "$$\n", "g = \\bigg(\\prod_{i=1}^nx_i\\bigg)^{1/n}\n", "$$\n", "If you can't make sense out of it, accept a fact that geometric mean is commonly used when calculating _compound growth rates_, such as portfolio return. For instance, a portfolio manager has annual return recorded as below" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
Portfolio Return
YearReturn
201536%
201623%
2017-48%
2018-30%
201915%
202031%
Arithmetic Mean4.5%
Geometric Mean-1.4%
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The arithmetic mean of return is $4.45\\%$." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.045000000000000005" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "portfolio_return = np.array([0.36, 0.23, -0.48, -0.3, 0.15, 0.31])\n", "np.mean(portfolio_return)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However the geometric mean of return is $-1.42\\%$. Geometric mean ```sp.stats.mstats.gmean``` is more accurate measurement when considering the compound effect, i.e. the data are related to each other by a growth rate." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-0.014282599080668423" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sp.stats.mstats.gmean(portfolio_return + 1) - 1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Measures Of Variability" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The first measurement of variability is the **range** measuring distance from lowest to highest. We'll generate an array of standard normal distribution for demonstration." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "x = np.random.randn(50)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "4.725332255653198" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rangeLS = x.max() - x.min()\n", "rangeLS" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Percentile** is also a common statistic concept, which could be best explained by an example. For instance, the GRE test result shows percentile besides your absolute score, say you have a percentile of $96\\%$, it means your score is higher than $96\\%$ of candidates. The special percentile of $75\\%$ and $25\\%$ are sometimes called the _third quartile_ and _first quartile_." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.1190705852500262" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "q75, q25 = np.percentile(x, [75, 25]) # IQR\n", "q75 - q25" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Before moving any further, we must clarify two statistical concepts: **population** and **sample**. For example, we want to know the variance of all human adults height, therefore we ought to measure all adults (population) on earth in order to calculate the variance, however the mission is impossible, instead we measure a smaller group of adults (sample) to make inferential statements about population. \n", "\n", "Population and sample variance differ in degree of freedom, where $N$ is the population size, whereas $n$ is the sample size, $\\mu$ is the population mean and $\\bar{x}$ is the sample mean. The formulae of variances are\n", "\n", "$$\n", "\\sigma^2 = \\frac{\\sum(x_i - \\mu)^2}{N}\\\\\n", "s^2 = \\frac{\\sum(x_i - \\bar{x})^2}{n-1}\n", "$$\n", "\n", "The latter is an unbiased estimator of population variance, which is also the _sample variance_.\n", "\n", "To illustrate the idea, let's pretend there are only $N = 1000$ people on earth, we can generate an array to represent the population height, only for demonstrative purpose. We generate a population by setting ```loc=170``` and ```scale=10``` with ```np.random.normal```, i.e. $X\\sim N(170, 10)$, then calculate the population variance by using ```np.var()```." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "108.33360191813833" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "population_height = np.random.normal(170, 10, 1000)\n", "np.var(population_height)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now suppose we know nothing about the population, but we can get a sample of 100 persons. By setting ```ddof=1``` in function, we actually mean the degree of freedom is $N-1$, used on sample estimators." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "98.1270651211727" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sample_height = np.random.choice(population_height, size=100)\n", "np.var(sample_height, ddof=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Theoretically, we can have tremendous amount of samples, say $10000$ samples. Yes, I mean $10000$ samples, not the sample size, but this is just a thought experiment, will never be achieved in real world. Again, pure demonstrative purpose.\n", "\n", "What we are doing next: generate $10000$ samples, calculate the sample variances, plot histogram. The vertical line is the mean of sampling distribution of variance estimates. We set standard deviation of $\\sigma = 10$, the theoretical variance $\\sigma^2=100$, therefore we see the point estimator is doing a fair well job. " ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sample_height_array = []\n", "for i in range(10000):\n", " sample_height = np.random.choice(population_height, size=100)\n", " sample_height_array.append(np.var(sample_height, ddof=1))\n", "fig, ax = plt.subplots(figsize=(9, 9))\n", "n, bins, patches = ax.hist(sample_height_array, bins=50)\n", "ax.axvline(x=np.mean(sample_height_array), color=\"tomato\")\n", "ax.text(\n", " np.mean(sample_height_array) + 1,\n", " np.max(n),\n", " r\"$\\mu_\\sigma = {:.2f}$\".format(np.mean(sample_height_array)),\n", " size=16,\n", ")\n", "ax.set_title(\"Sampling Distribution of Variance Estimates\", size=19)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I guess you have noticed the power of estimators now, if you have many samples, by using an unbiased sample estimator, you will get an accurate estimate of population parameters. Even if you have only one sample, you can still can estimate how possible you would be correct based on sampling distribution." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "But we shall keep in mind that **standard deviation** is the most popular measurement of variability. The population/sample standard deviation is simply the square root of variances respectively." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\sigma = \\sqrt{\\sigma^2}\\\\\n", "s = \\sqrt{s^2}\n", "$$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Similar to variance function in NumPy." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "15.50977277891788" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.std(sample_height_array, ddof=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Measures of Distribution Shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**z-score** is defined as below, used for measuring how many standard deviations away from the mean.\n", "\n", "\\begin{equation}\n", "z_i = \\frac{x_i-\\bar{x}}{s}\n", "\\end{equation}\n", "\n", "Note that $z$ has subscript notation $i$ which means each observation has its own $z$-score. \n", "\n", "
Actually，measuring how many standard deviations away from the mean (or hypothesis) is the fundamental philosophy of frequentist statistics, it asks one important question: how far away from the mean is far-away? If it is far enough, very likely the mean we are looking at right now is not the 'real' mean of the random mechanism that generates the observation.
\n", "\n", "Here is the example of calculating $z$-score for an randomly generated array. So you can see for a standard normal distribution, it would be fairly hard to stray $2$ standard deviations away." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 0.09, -0.59, 0.6 , -0.91, 1.06, -1.44, 0.78, -1.58, 0.69,\n", " 1.3 ])" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = np.random.randn(10)\n", "z = (x - np.mean(x)) / np.std(x)\n", "np.round(z, 2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Chebyshev's Theorem" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Chebyshev's Theorem** is used as the last resort of deduction when we have absolute _no knowledge_ of a sample and its distribution. It guarantees minimum proportion of data that must be within $z$ standard deviation from the mean, where the $z$ is $z$-score. But the downside of the theorem is that it only addresses the symmetric distribution.\n", "\n", "\\begin{equation}\n", "p \\geq 1-\\frac{1}{z^2}\n", "\\end{equation}\n", "\n", "For instance, the average height of people in Helsinki is $174cm$, with a standard deviation of of $4cm$, so the question is how many people (percentage) are within $166cm$ and $182cm$? Note that this range is symmetrically $2$ standard derivations away from its mean. Thus according to Chebyshev, we know that" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "z_l = (166 - 174) / 4 # lower z-score\n", "z_u = (182 - 174) / 4 # upper z-score" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Because it is a symmetric range, $z$-score on each sides are equal, we can calculate the probability as below and print the conclusion." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "At least 75.0% of people are within 168cm and 182cm in Helsinki.\n" ] } ], "source": [ "p = 1 - 1 / z_l**2\n", "print(\"At least {0}% of people are within 168cm and 182cm in Helsinki.\".format(p * 100))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If you think of Chebyshev as a function, then the only variable is $z$-score. Now we define a Chebyshev function and plot it against $z$-score.\n", "\n", "Because $z$-score means how many standard deviation away from the mean, from the graph we could conclude that no matter what types of distributions we are investigating, it is guaranteed that $\\pm 2.5$ standard deviation range would cover at least $84\\%$ of data." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def chebyshev(z):\n", " return 1 - 1 / z**2\n", "\n", "\n", "chebyshev_array = []\n", "for z in np.arange(1, 21, 0.5):\n", " chebyshev_array.append(chebyshev(z))\n", "\n", "fig, ax = plt.subplots(figsize=(9, 9))\n", "ax.plot(np.arange(1, 21, 0.5), chebyshev_array)\n", "ax.scatter(2.5, chebyshev(2.5), s=100, color=\"red\", zorder=3)\n", "ax.text(2.5 + 0.5, chebyshev(2.5), r\"(2.5, {}%)\".format(chebyshev(2.5) * 100))\n", "ax.set_title(\"Chebyshev's Theorem\")\n", "ax.set_xlabel(\"z-score\")\n", "ax.set_ylabel(\"Probability\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However in practice we are more likely to deal with data of (semi)bell-shape distribution, they are regular and easier to make deduction. So **Empirical Rules** apply.\n", "\n", "* 68% of data within 1 standard deviation of the mean\n", "* 95% of data within 2 standard deviation of the mean\n", "* 99.7% of data within 3 standard deviation of the mean\n", "\n", "These empirical numbers are from normal distribution." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Measures of Association Between Two Variables" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With similar notation, the **population** and **sample covariance** is defined as:\n", "$$\n", "\\sigma_{xy} \\frac{\\sum(x_i-\\mu_x)(y_i-\\mu_y)}{N}\\\\\n", "s_{xy} \\frac{\\sum(x_i-\\bar{x})(y_i-\\bar{y})}{n-1}\n", "$$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Generate two random arrays, then evaluate a covariance matrix. The values on the diagonal presents the variance, the off-diagonal presents the covariance." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 0.88955858, -0.00649224],\n", " [-0.00649224, 0.07885574]])" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = np.random.randn(300)\n", "y = np.random.rand(300)\n", "np.cov(x, y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Correlation Coefficient** is normalized version of covariance, just like the standard deviation is the normalised variance, some statistics textbook calls it Pearson Product Moment Correlation Coefficient.\n", "\n", "$$\n", "\\rho = \\frac{\\sigma_{xy}}{\\sigma_x\\sigma_y}\\\\\n", "r_{xy}=\\frac{s_{xy}}{s_xs_y}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the sake of everyone's sanity, not to cluster the lecture notes with repetitive codes, some of them were transported in to ```plot_material.py``` module. Take a look inside if you are curious.\n", "\n", "What we did below was basically generating eight linear regression plot $Y = \\beta_1+\\beta_2X+u$ with different parameters. The correlation coefficient $\\rho$ is displayed in the graph, therefore you could observe that the correlation coefficients are affected by size of parameters $\\beta_2$ and scale of error term.\n", "\n", "The reasons are:\n", "
    \n", "
  1. The more significantly $\\beta_2$ differs from $0$, the more significant linear relationship the model has, therefore the relatively larger correlation between $X$ and $Y$.
    2. \n", "
  2. If the parameters $\\beta_1$ and $\\beta_2$ kept constant, the larger scale of the error term, the more dispersed the data are, therefore lower correlation as well.
    3. \n", "
      " ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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      " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import plot_material\n", "\n", "plot_material.reg_corr_plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will dive much deeper into linear regression in our econometrics training sessions." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Different Types Of Correlation Coefficient" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The correlation coefficient above is the **Pearson correlation**, which assumes a linear relationship between two variables. However, there are other correlation coefficients which also measures nonlinear correlation, such as **Spearman correlation** and **Kendall's $\\tau$**." ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "data": { "image/png": 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      " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X = np.linspace(-10, 10, 200)\n", "Y = 1 / (1 + np.exp(-X))\n", "df_dict = {\"X\": X, \"Y\": Y}\n", "df = pd.DataFrame(df_dict)\n", "\n", "df.plot(x=\"X\", y=\"Y\", kind=\"scatter\", figsize=(16, 7))\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 67, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
      \n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
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      " ], "text/plain": [ " X Y\n", "X 1.000000 0.936137\n", "Y 0.936137 1.000000" ] }, "execution_count": 67, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.corr(method=\"pearson\")" ] }, { "cell_type": "code", "execution_count": 62, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Pearson coeffcient: 0.9361365508325603\n" ] } ], "source": [ "print(\"Pearson coeffcient: {}\".format(sp.stats.stats.pearsonr(df[\"X\"], df[\"Y\"])[0]))" ] }, { "cell_type": "code", "execution_count": 63, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Pearson coeffcient: 1.0\n" ] } ], "source": [ "print(\"Pearson coeffcient: {}\".format(sp.stats.stats.spearmanr(df[\"X\"], df[\"Y\"])[0]))" ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Pearson coeffcient: 1.0\n" ] } ], "source": [ "sp.stats.stats.kendalltau(X, Y)\n", "print(\"Pearson coeffcient: {}\".format(sp.stats.stats.kendalltau(df[\"X\"], df[\"Y\"])[0]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice the difference, that Pearson and Kendall produce a perfect correlation coefficient, it is because the latter two are rank tests." ] } ], "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 }