{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# High level plotting with iqplot\n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
\n", " \n", " Loading BokehJS ...\n", "
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\\n\"+\n", " \"

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\\n\"+\n", " \"\\n\"+\n", " \"\\n\"+\n", " \"from bokeh.resources import INLINE\\n\"+\n", " \"output_notebook(resources=INLINE)\\n\"+\n", " \"\\n\"+\n", " \"
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\\n\"+\n \"

\\n\"+\n \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n \"

\\n\"+\n \"\\n\"+\n \"\\n\"+\n \"from bokeh.resources import INLINE\\n\"+\n \"output_notebook(resources=INLINE)\\n\"+\n \"\\n\"+\n \"
\"}};\n\n function display_loaded() {\n const el = document.getElementById(\"f7a60a88-36d7-4694-b4f4-43fb25683847\");\n if (el != null) {\n el.textContent = \"BokehJS is loading...\";\n }\n if (root.Bokeh !== undefined) {\n if (el != null) {\n el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n }\n } else if (Date.now() < root._bokeh_timeout) {\n setTimeout(display_loaded, 100)\n }\n }\n\n function run_callbacks() {\n try {\n root._bokeh_onload_callbacks.forEach(function(callback) {\n if (callback != null)\n callback();\n });\n } finally {\n delete root._bokeh_onload_callbacks\n }\n console.debug(\"Bokeh: all callbacks have finished\");\n }\n\n function load_libs(css_urls, js_urls, callback) {\n if (css_urls == null) css_urls = [];\n if (js_urls == null) js_urls = [];\n\n root._bokeh_onload_callbacks.push(callback);\n if (root._bokeh_is_loading > 0) {\n console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n return null;\n }\n if (js_urls == null || js_urls.length === 0) {\n run_callbacks();\n return null;\n }\n console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n root._bokeh_is_loading = css_urls.length + js_urls.length;\n\n function on_load() {\n root._bokeh_is_loading--;\n if (root._bokeh_is_loading === 0) {\n console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n run_callbacks()\n }\n }\n\n function on_error(url) {\n console.error(\"failed to load \" + url);\n }\n\n for (let i = 0; i < css_urls.length; i++) {\n const url = css_urls[i];\n const element = document.createElement(\"link\");\n element.onload = on_load;\n element.onerror = on_error.bind(null, url);\n element.rel = \"stylesheet\";\n element.type = \"text/css\";\n element.href = url;\n console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n document.body.appendChild(element);\n }\n\n for (let i = 0; i < js_urls.length; i++) {\n const url = js_urls[i];\n const element = document.createElement('script');\n element.onload = on_load;\n element.onerror = on_error.bind(null, url);\n element.async = false;\n element.src = url;\n console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n document.head.appendChild(element);\n }\n };\n\n function inject_raw_css(css) {\n const element = document.createElement(\"style\");\n element.appendChild(document.createTextNode(css));\n document.body.appendChild(element);\n }\n\n const js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-3.2.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-3.2.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-3.2.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-3.2.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-mathjax-3.2.1.min.js\"];\n const css_urls = [];\n\n const inline_js = [ function(Bokeh) {\n Bokeh.set_log_level(\"info\");\n },\nfunction(Bokeh) {\n }\n ];\n\n function run_inline_js() {\n if (root.Bokeh !== undefined || force === true) {\n for (let i = 0; i < inline_js.length; i++) {\n inline_js[i].call(root, root.Bokeh);\n }\nif (force === true) {\n display_loaded();\n }} else if (Date.now() < root._bokeh_timeout) {\n setTimeout(run_inline_js, 100);\n } else if (!root._bokeh_failed_load) {\n console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n root._bokeh_failed_load = true;\n } else if (force !== true) {\n const cell = $(document.getElementById(\"f7a60a88-36d7-4694-b4f4-43fb25683847\")).parents('.cell').data().cell;\n cell.output_area.append_execute_result(NB_LOAD_WARNING)\n }\n }\n\n if (root._bokeh_is_loading === 0) {\n console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n run_inline_js();\n } else {\n load_libs(css_urls, js_urls, function() {\n console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n run_inline_js();\n });\n }\n}(window));" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import pandas as pd\n", "\n", "import iqplot\n", "\n", "import bokeh.io\n", "import bokeh.models\n", "import bokeh.plotting\n", "\n", "bokeh.io.output_notebook()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "In this lesson, we do some plotting with a high-level package [iqplot](https://iqplot.github.io/). You should have installed it in [Lesson 0](../00/configuring_your_computer.ipynb).\n", "\n", "We will use [the frog tongue data set from Kleinteich and Gorb](https://doi.org/10.1038/srep05225) that we used in our exercises with Pandas. Let's get the data frame loaded in so we can be on our way." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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dateIDtrial numberimpact force (mN)impact time (ms)impact force / body weightadhesive force (mN)time frog pulls on target (ms)adhesive force / body weightadhesive impulse (N-s)total contact area (mm2)contact area without mucus (mm2)contact area with mucus / contact area without mucuscontact pressure (Pa)adhesive strength (Pa)
02013_02_26I31205461.95-7858841.27-0.290387700.823117-2030
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22013_03_01I11745342.82-8502111.37-0.15783790.0521020-10239
32013_03_01I21556412.51-45510250.74-0.1703301580.524718-1381
42013_03_01I3493360.80-9744991.57-0.4232452160.122012-3975
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" ], "text/plain": [ " date ID trial number impact force (mN) impact time (ms) \\\n", "0 2013_02_26 I 3 1205 46 \n", "1 2013_02_26 I 4 2527 44 \n", "2 2013_03_01 I 1 1745 34 \n", "3 2013_03_01 I 2 1556 41 \n", "4 2013_03_01 I 3 493 36 \n", "\n", " impact force / body weight adhesive force (mN) \\\n", "0 1.95 -785 \n", "1 4.08 -983 \n", "2 2.82 -850 \n", "3 2.51 -455 \n", "4 0.80 -974 \n", "\n", " time frog pulls on target (ms) adhesive force / body weight \\\n", "0 884 1.27 \n", "1 248 1.59 \n", "2 211 1.37 \n", "3 1025 0.74 \n", "4 499 1.57 \n", "\n", " adhesive impulse (N-s) total contact area (mm2) \\\n", "0 -0.290 387 \n", "1 -0.181 101 \n", "2 -0.157 83 \n", "3 -0.170 330 \n", "4 -0.423 245 \n", "\n", " contact area without mucus (mm2) \\\n", "0 70 \n", "1 94 \n", "2 79 \n", "3 158 \n", "4 216 \n", "\n", " contact area with mucus / contact area without mucus \\\n", "0 0.82 \n", "1 0.07 \n", "2 0.05 \n", "3 0.52 \n", "4 0.12 \n", "\n", " contact pressure (Pa) adhesive strength (Pa) \n", "0 3117 -2030 \n", "1 24923 -9695 \n", "2 21020 -10239 \n", "3 4718 -1381 \n", "4 2012 -3975 " ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df = pd.read_csv('../data/frog_tongue_adhesion.csv', comment='#')\n", "\n", "# Have a look so we remember\n", "df.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plots with categorical variables\n", "\n", "Let us first consider the different kinds of data we may encounter as we think about constructing a plot.\n", "\n", "- **Quantitative** data may have continuously varying (and therefore ordered) values.\n", "- **Categorical** data has discrete, unordered values that a variable can take.\n", "- **Ordinal** data has discrete, ordered values. Integers are a classic example.\n", "- **Temporal** data refers to time, which can be represented as dates.\n", "\n", "In practice, ordinal data can be cast as quantitative or treated as categorical with an ordering enforced on the categories (e.g., categorical data `[1, 2, 3]` becomes `['1', '2', '3']`.). Temporal data can also be cast as quantitative, (e.g., second from the start time). We will therefore focus out attention on quantitative and categorical data.\n", "\n", "When we made scatter plots in the previous lesson, both types of data were quantitative. We did actually incorporate categorical information in the form of colors of the glyph (insomniacs and normal sleepers being colored differently) and in tooltips. \n", "\n", "But what if we wanted a single type of measurement, say impact force, for each frog? Here, we have the quantitative impact force data and the categorical frog ID data. One of our axes is now categorical." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bar graph\n", "\n", "To demonstrate how to set up a categorical axis with Bokeh, I will make a bar graph of the mean impact force for each of the four frogs. But before I even begin this, I will give you the following piece of advice: *Don't make bar graphs.* More on that in a moment.\n", "\n", "Before we do that, we need to compute the means from the inputted data frame." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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3IV419.10
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" ], "text/plain": [ " ID impact force (mN)\n", "0 I 1530.20\n", "1 II 707.35\n", "2 III 550.10\n", "3 IV 419.10" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df_mean = df.groupby('ID')['impact force (mN)'].mean().reset_index()\n", "\n", "# Take a look\n", "df_mean" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To set up a categorical axis, you need to specify the `x_range` (or `y_range` if you want the y-axis to be categorical) as a list with the categories you want on the axis when you instantiate the figure. I will make a horizontal bar graph, so I will specify `y_range`. Also, when I instantiate this figure, because it is not very tall and I do not want the reset tool cut off, I will also explicitly set the tools I want in the toolbar." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "p = bokeh.plotting.figure(\n", " frame_height=200,\n", " frame_width=400,\n", " x_axis_label='impact force (mN)',\n", " y_range=df_mean['ID'].unique()[::-1],\n", " tools='pan,wheel_zoom,save,reset'\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that we have the figure, we can put the bars on. The `p.hbar()` method populates the figure with horizontal bar glyphs. The `right` kwarg says what column of the data source dictates how far to the right to show the bar, while the `height` kwarg says how think the bars are.\n", "\n", "I will also ensure the quantitative axis starts at zero and turn off the grid lines on the categorical axis, which is commonly done." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
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console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n", " }\n", " }\n", " }, 10, root)\n", " }\n", "})(window);" ], "application/vnd.bokehjs_exec.v0+json": "" }, "metadata": { "application/vnd.bokehjs_exec.v0+json": { "id": "p1001" } }, "output_type": "display_data" } ], "source": [ "source = bokeh.models.ColumnDataSource(df_mean)\n", "\n", "p.hbar(\n", " source=source,\n", " y='ID',\n", " right='impact force (mN)',\n", " height=0.6\n", ")\n", "\n", "# Turn off gridlines on categorical axis\n", "p.ygrid.grid_line_color = None\n", "\n", "# Start axes at origin on quantitative axis\n", "p.x_range.start = 0\n", "\n", "bokeh.io.show(p)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We similarly make vertical bar graphs specifying `x_range` and using `p.vbar()`." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
\n" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "(function(root) {\n", " function embed_document(root) {\n", " const docs_json = {\"b1b8938c-e08a-4a9c-bef9-78831663d4ce\":{\"version\":\"3.2.1\",\"title\":\"Bokeh 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render_items);\n", " }\n", " if (root.Bokeh !== undefined) {\n", " embed_document(root);\n", " } else {\n", " let attempts = 0;\n", " const timer = setInterval(function(root) {\n", " if (root.Bokeh !== undefined) {\n", " clearInterval(timer);\n", " embed_document(root);\n", " } else {\n", " attempts++;\n", " if (attempts > 100) {\n", " clearInterval(timer);\n", " console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n", " }\n", " }\n", " }, 10, root)\n", " }\n", "})(window);" ], "application/vnd.bokehjs_exec.v0+json": "" }, "metadata": { "application/vnd.bokehjs_exec.v0+json": { "id": "p1041" } }, "output_type": "display_data" } ], "source": [ "p = bokeh.plotting.figure(\n", " frame_height=250,\n", " frame_width=250,\n", " y_axis_label='impact force (mN)',\n", " x_range=df_mean['ID'].unique(),\n", ")\n", "\n", "p.vbar(\n", " source=source,\n", " x='ID',\n", " top='impact force (mN)',\n", " width=0.6\n", ")\n", "\n", "p.xgrid.grid_line_color = None\n", "p.y_range.start = 0\n", "\n", "bokeh.io.show(p)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## iqplot\n", "\n", "Generating the bar graphs was not too painful, even tough we used Bokeh, a low-level plotting library. Nonetheless, we would like to make plots more **declaratively**. We do not want to have to explicitly pre-process the data, set up the categorical axis, etc. We would like to just provide a data set, say which column(s) is/are categorical and which is quantitative, and then just get our plot.\n", "\n", "iqplot generates plots from tidy data frames where one or more columns contain categorical data and the column of interest in the plot is quantitative.\n", "\n", "There are seven types of plots that iqplot can generate. As you will see, all four of these modes of plotting are meant to give a picture about how the quantitative measurements are *distributed* for each category.\n", "\n", "- Box plots: `iqplot.box()`\n", "- Strip plots: `iqplot.strip()`\n", "- Spike plots: `iqplot.spike()`\n", "- Strip-box plots (strip and box plots overlaid): `iqplot.stripbox()`\n", "- Histograms: `iqplot.histogram()`\n", "- Strip-histogram plots (strip and histograms overlaid): `iqplot.striphistogram()`\n", "- ECDFs: `iqplot.ecdf()`\n", "\n", "This first seven arguments are the same for all plots. They are:\n", "\n", "- `data`: A tidy data frame or Numpy array.\n", "- `q`: The column of the data frame to be treated as the quantitative variable.\n", "- `cats`: A list of columns in the data frame that are to be considered as categorical variables in the plot. If `None`, a single box, strip, histogram, or ECDF is plotted.\n", "- `q_axis`: Along which axis, x or y that the quantitative variable varies. The default is `'x'`.\n", "- `palette`: A list of hex colors to use for coloring the markers for each category. By default, it uses the Glasbey Category 10 color palette from [colorcet](https://colorcet.holoviz.org/).\n", "- `order`: If specified, the ordering of the categories to use on the categorical axis and legend (if applicable). Otherwise, the order of the inputted data frame is used.\n", "- `p`: If specified, the `bokeh.plotting.Figure` object to use for the plot. If not specified, a new figure is created.\n", "\n", "If data is given as a Numpy array, it is the only required argument. If data is given as a Pandas DataFrame, q must also be supplied. All other arguments are optional and have reasonably set defaults. Any extra kwargs not in the function call signature are passed to bokeh.plotting.figure() when the figure is instantiated.\n", "\n", "With this in mind, we will put iqplot to use on facial identification data set to demonstrate how we can make each of the seven kinds of plots using the frog data set." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Box plots with iqplot\n", "\n", "As I [discuss below](#Don't-make-bar-graphs), bar graphs are almost never a good choice for visualization. You distill all of the information in the data set down to one or two summary statistics, and then use giant glyphs to show them. As a start for improvement, you could distill the data set down to five or so summary statistics and show those graphically, as opposed to just one or two. \n", "\n", "Box plots provide such a summary. I will first make one using `iqplot.box()` and then describe how a box plot is interpreted." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
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console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n", " }\n", " }\n", " }, 10, root)\n", " }\n", "})(window);" ], "application/vnd.bokehjs_exec.v0+json": "" }, "metadata": { "application/vnd.bokehjs_exec.v0+json": { "id": "p1082" } }, "output_type": "display_data" } ], "source": [ "p = iqplot.box(\n", " data=df,\n", " q=\"impact force (mN)\",\n", " cats=\"ID\",\n", ")\n", "\n", "bokeh.io.show(p)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The line in the middle of each box is the median and the top and bottom of the box at the 75th and 25th percentiles, respectively. The distance between the 25th and 75th percentiles is called the **interquartile range**, or IQR. The whiskers of the box plot extend to the most extreme data point within 1.5 times the interquartile range. If any data points are more extreme than the end of the whisker, they are shown individually, and are often referred to as _outliers_.\n", "\n", "A box plot can use a useful visualization if you have many data points and it is difficult to plot them all. I rarely find that there are situations where all data cannot be plotted, either with strip plots of ECDFs, which we will cover in a moment, so I generally do not use box plots. Nonetheless, I do not find them too objectionable, as they effectively display important nonparametric summary statistics of your data set." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plot all your data\n", "\n", "Box plots summarize a data set with summary statistics, but what not plot all your data? You work hard to acquire them. You should show them all. This is a mantra to live by.\n", "\n", "
\n", " \n", "Plot all of your data.\n", " \n", "
\n", "\n", "Let's do that now." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Strip plots\n", "\n", "A **strip plot** is like a scatter plot; it puts a glyph for every measured data point. The only difference is that one of the axes is categorical. In this case, you are plotting all of your data." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
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We will deal with this in the next lesson when we discuss styling plots." ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "## Spike plots\n", "\n", "A **spike plot** is useful when you want to see how many times a specific value was encountered in your data set. Let's make a spike plot for the number of times specific impact times were observed." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
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console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n", " }\n", " }\n", " }, 10, root)\n", " }\n", "})(window);" ], "application/vnd.bokehjs_exec.v0+json": "" }, "metadata": { "application/vnd.bokehjs_exec.v0+json": { "id": "p1416" } }, "output_type": "display_data" } ], "source": [ "p = iqplot.stripbox(\n", " data=df,\n", " q=\"impact force (mN)\",\n", " cats=\"ID\",\n", ")\n", "\n", "bokeh.io.show(p)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Histograms\n", "\n", "In plotting all of our data in a strip plot, we can roughly see how the data are distributed. There are more measurements where there are more glyphs. We ofter seek to visualize the *distribution* of the data. **Histograms** are commonly used for this. They are typically interpreted to as an empirical representation of the probability density function." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
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Unable to run BokehJS code because BokehJS library is missing\");\n", " }\n", " }\n", " }, 10, root)\n", " }\n", "})(window);" ], "application/vnd.bokehjs_exec.v0+json": "" }, "metadata": { "application/vnd.bokehjs_exec.v0+json": { "id": "p1523" } }, "output_type": "display_data" } ], "source": [ "p = iqplot.histogram(\n", " data=df,\n", " q=\"impact force (mN)\",\n", " cats=\"ID\",\n", ")\n", "\n", "bokeh.io.show(p)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that by default, iqplot includes a **rug plot** at the bottom of the histogram, showing each measurement. The number of bins are automatically chosen using the [Freedman-Diaconis rule](https://en.wikipedia.org/wiki/Freedman–Diaconis_rule)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Strip-histogram\n", "\n", "Strip plots may also be combined with histograms. By default, the histograms are normalized and mirrored, similar to a [violin plot](https://en.wikipedia.org/wiki/Violin_plot)." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
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Unable to run BokehJS code because BokehJS library is missing\");\n", " }\n", " }\n", " }, 10, root)\n", " }\n", "})(window);" ], "application/vnd.bokehjs_exec.v0+json": "" }, "metadata": { "application/vnd.bokehjs_exec.v0+json": { "id": "p2048" } }, "output_type": "display_data" } ], "source": [ "p = iqplot.striphistogram(\n", " data=df,\n", " q=\"impact force (mN)\",\n", " cats=\"ID\",\n", ")\n", "\n", "bokeh.io.show(p)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## ECDFs\n", "\n", "I just mentioned that histograms are typically used to display how data are distributed, but it was hard to make out the distributions in the above plot, partly because we do not have very many measurements. As another example I will generate Normally distributed data and plot the histogram. (We will learn how to generate data like this when we study random number generation with NumPy in a future lesson. For now, this is for purposes of discussing plotting options.)\n", "\n", "Note that iqplot can take a Numpy array as the `data` argument, and makes a plot assuming it contains a single data set." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
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rg.normal(size=500)\n", "\n", "# Plot the histogram\n", "p = iqplot.histogram(x, rug=False)\n", "\n", "bokeh.io.show(p)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This looks similar to the standard Normal curve we are used to seeing and is a useful comparison to a **probability density function** (PDF). However, Histograms suffer from **binning bias**. By binning the data, you are not plotting all of them. In general, if you can **plot all of your data**, you should. For that reason, I prefer not to use histograms for studying how data are distributed, but rather prefer to use ECDFs, which enable plotting of all data.\n", "\n", "The ECDF evaluated at x for a set of measurements is defined as\n", "\n", "\\begin{align}\n", "\\text{ECDF}(x) = \\text{fraction of measurements } \\le x.\n", "\\end{align}\n", "\n", "While the histogram is an attempt to visualize a probability density function (PDF) of a distribution, the ECDF visualizes the **cumulative density function** (CDF). The CDF, $F(x)$, and PDF, $f(x)$, both completely define a univariate distribution and are related by\n", "\n", "\\begin{align}\n", "f(x) = \\frac{\\mathrm{d}F}{\\mathrm{d}x}.\n", "\\end{align}\n", "\n", "The definition of the ECDF is all that you need for interpretation. Once you get used to looking at CDFs, they will become as familiar to you as PDFs. A peak in a PDF corresponds to an inflection point in a CDF.\n", "\n", "To make this more clear, let us look at plot of a PDF and ECDF for familiar distributions, the Gaussian and Binomial.\n", "\n", "
\n", "\n", "![PDF/CDF](pdf_cdf.png)\n", " \n", "
\n", "\n", "Now that we know how to interpret ECDFs, lets plot the ECDF for our dummy Normally-distributed data." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
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" const render_items = [{\"docid\":\"9a39ad8b-f4a8-49aa-9878-bdaad94c06f5\",\"roots\":{\"p2211\":\"bcf52fa1-fbad-407c-af03-2d7959aa847b\"},\"root_ids\":[\"p2211\"]}];\n", " root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n", " }\n", " if (root.Bokeh !== undefined) {\n", " embed_document(root);\n", " } else {\n", " let attempts = 0;\n", " const timer = setInterval(function(root) {\n", " if (root.Bokeh !== undefined) {\n", " clearInterval(timer);\n", " embed_document(root);\n", " } else {\n", " attempts++;\n", " if (attempts > 100) {\n", " clearInterval(timer);\n", " console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n", " }\n", " }\n", " }, 10, root)\n", " }\n", "})(window);" ], "application/vnd.bokehjs_exec.v0+json": "" }, "metadata": { "application/vnd.bokehjs_exec.v0+json": { "id": "p2211" } }, "output_type": "display_data" } ], "source": [ "p = iqplot.ecdf(x)\n", "\n", "bokeh.io.show(p)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that we understand what an ECDF is and how to plot it, let's make a set of ECDFs for our frog data." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
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Unable to run BokehJS code because BokehJS library is missing\");\n", " }\n", " }\n", " }, 10, root)\n", " }\n", "})(window);" ], "application/vnd.bokehjs_exec.v0+json": "" }, "metadata": { "application/vnd.bokehjs_exec.v0+json": { "id": "p2395" } }, "output_type": "display_data" } ], "source": [ "p = iqplot.ecdf(\n", " data=df,\n", " q=\"impact force (mN)\",\n", " cats=\"ID\",\n", " p=p,\n", " show_legend=False,\n", ")\n", "\n", "bokeh.io.show(p)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Don't make bar graphs\n", "\n", "Bar graphs, especially with error bars (in which case they are called dynamite plots), are typically awful. They are pervasive in biology papers. I have yet to find a single example where a bar graph is the best choice. Strip plots (with jitter) or even box plots, are more informative and almost always preferred. In fact, ECDFs are often better even than these. Here is a simple message:\n", "\n", "
\n", " \n", "Don't make bar graphs.\n", " \n", "
\n", "\n", "What should I do instead you ask? The answer is simple: **plot all of your data** when you can. If you can't, box plots are always better than bar graphs." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Computing environment" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Python implementation: CPython\n", "Python version : 3.11.4\n", "IPython version : 8.12.2\n", "\n", "numpy : 1.24.3\n", "pandas : 2.0.3\n", "bokeh : 3.2.1\n", "iqplot : 0.3.4\n", "jupyterlab: 4.0.5\n", "\n" ] } ], "source": [ "%load_ext watermark\n", "%watermark -v -p numpy,pandas,bokeh,iqplot,jupyterlab" ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.11.4" } }, "nbformat": 4, "nbformat_minor": 4 }