{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# The way you define groups affects your statistical tests" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook is, I hope, a step towards explaining the issue and sharing some intuition about\n", "\n", "* the difference between experiments where classes to be compared are under the control of the experimenter, and those where they are *predicted* or otherwise subject to error\n", "* the importance to interpreting a statistical test of knowing the certainty with which individual data points are assigned to the classes being compared\n", "* the effects of classification false positive and false negative rate, and an imbalance of membership between classes being compared" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Overview: Experiment\n", "\n", "Let's say you have data from an experiment. The experiment is to test the binding of some human drug candidates to a large number (thousands) of mouse proteins. The experiment was conducted with transformed mouse proteins in yeast, so some of the proteins are in different states to how they would be found in the mouse: truncated to work in yeast, and with different post-translational modifications." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Overview: Analysis\n", "\n", "Now let's consider one possible analysis of the data. We will test whether the mouse proteins that bind to the drug are more similar to their human equivalents than those that do not bind to the drug.\n", "\n", "We are ignoring the question of what 'equivalent' means here, and assume that a satisfactory equivalency is known and accepted. We will represent the 'strength' of equivalence by percentage sequence identity of each mouse protein to its human counterpart, on a scale of 0-100%.\n", "\n", "We will test whether there is a difference between the two groups by a $t$-test of two samples. We assume that each group (binds/does not bind) subsamples a distinct, normally-distributed population of sequence identities. We do not know whether the means or variances of these populations are the same, but we will test the null hypothesis that the means are identical (or the difference between means is zero).\n", "\n", "This isn't the way I would want to analyse this kind of data in a real situation - but we're doing it here to show the effect of how we define groups. We'll define *positive* and *negative* groups as follows:\n", "\n", "* ***positive***: mouse protein that binds to drug in the yeast experiment\n", "* ***negative***: mouse protein that does not bind to drug in the yeast experiment" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Python code:\n", "\n", "Let's take a look at what we're actually doing when we perform this analysis. We'll use some Python code to visualise and explore this. Skip over this if you like…" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "%pylab inline\n", "from scipy import stats\n", "from ipywidgets import interact, fixed" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def sample_distributions(mu_neg, mu_pos, sd_neg, sd_pos,\n", " n_neg, n_pos, fnr, fpr,\n", " clip_low, clip_high):\n", " \"\"\"Returns subsamples and observations from two normal \n", " distributions.\n", " \n", " - mu_neg mean of 'negative' samples\n", " - mu_pos mean of 'positive' samples\n", " - sd_neg standard deviation of 'negative' samples\n", " - sd_pos standard deviation of 'positive' samples \n", " - n_neg number of subsampled data points (negatives)\n", " - n_pos number of subsampled data points (positives)\n", " - fnr false negative rate (positives assigned to negative class)\n", " - fpr false positive rate (negatives assigned to positive class)\n", " - clip_low low value for clipping samples\n", " - clip_high high value for clipping samples \n", " \"\"\"\n", " # subsamples\n", " samples = (clip(stats.norm.rvs(mu_neg, sd_neg, size=n_neg), clip_low, clip_high),\n", " clip(stats.norm.rvs(mu_pos, sd_pos, size=n_pos), clip_low, clip_high))\n", " # observed samples, including FPR and FNR\n", " [shuffle(s) for s in samples]\n", " obs_neg = concatenate((samples[0][:int((1-fpr)*n_neg)], \n", " samples[1][int((1-fnr)*n_pos):]))\n", " obs_pos = concatenate((samples[1][:int((1-fnr)*n_pos)],\n", " samples[0][int((1-fpr)*n_neg):]))\n", " # return subsamples and observations\n", " return ((samples[0], samples[1]), (obs_neg, obs_pos))\n", "\n", "def draw_sample_comparison(mu_neg=80, mu_pos=90, sd_neg=5, sd_pos=5,\n", " n_neg=100, n_pos=100,\n", " fnr=0, fpr=0,\n", " clip_low=0, clip_high=100,\n", " num_bins=50,\n", " xmin=50, xmax=100, points=100,\n", " subsample=True,\n", " negcolor='blue', poscolor='green'):\n", " \"\"\"Renders a matplotlib plot of normal distributions and subsamples,\n", " and returns t-test P values that the means of the two subsamples are\n", " equal, with and without FNR/FPR.\n", " \n", " - mu_neg mean of 'negative' samples\n", " - mu_pos mean of 'positive' samples\n", " - sd_neg standard deviation of 'negative' samples\n", " - sd_pos standard deviation of 'positive' samples \n", " - n_neg number of subsampled data points (negatives)\n", " - n_pos number of subsampled data points (positives)\n", " - fnr false negative rate (positives assigned to negative class)\n", " - fpr false positive rate (negatives assigned to positive class)\n", " - clip_low low value for clipping samples\n", " - clip_high high value for clipping samples\n", " - bins number of bins for histogram\n", " - xmin x-axis lower limit\n", " - xmax x-axis upper limit\n", " - points number of points for plotting PDF\n", " - subsample Boolean: True plots subsamples\n", " \"\"\"\n", " x = linspace(points, xmin, xmax)\n", " # Normal PDFs\n", " norms = (normpdf(x, mu_neg, sd_neg), normpdf(x, mu_pos, sd_pos))\n", " # Get subsamples and observations\n", " samples, obs = sample_distributions(mu_neg, mu_pos, sd_neg, sd_pos,\n", " n_neg, n_pos, fnr, fpr,\n", " clip_low, clip_high)\n", " # Plot distribution and samples\n", " plot(x, norms[0], color=negcolor)\n", " plot(x, norms[1], color=poscolor)\n", " if subsample:\n", " h_neg = hist(samples[0], num_bins, normed=1, facecolor=negcolor, alpha=0.5)\n", " h_pos = hist(samples[1], num_bins, normed=1, facecolor=poscolor, alpha=0.5)\n", " ax = gca()\n", " ax.set_xlabel(\"value\")\n", " ax.set_ylabel(\"frequency\")\n", " # Calculate t-tests\n", " t_sam = stats.ttest_ind(samples[0], samples[1], equal_var=False)\n", " t_obs = stats.ttest_ind(obs[0], obs[1], equal_var=False)\n", " ax.set_title(\"$P_{real}$: %.02e $P_{obs}$: %.02e\" % (t_sam[1], t_obs[1]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A perfect experiment:\n", "\n", "First, we're assuming that there are two \"real\" populations of sequence identity between mouse and human equivalents - one representing proteins that bind to the drug in the experiment; one representing proteins that do not bind to the drug in this experiment. We're also assuming that the distribution of these values is Normal.\n", "\n", "Giving ourselves a decent chance for success, we'll assume that the real situation for drug-binding proteins is that they have a mean sequence identity of around 90%, and those proteins that don't bind the drug have a mean identity of 85% to their human counterpart. We'll also assume that the standard deviation of thes identities is 5% in each case.\n", "\n", "These are the \"**real**\", but idealised, populations from which our experimental results are drawn.\n", "\n", "We can see how these distributions look:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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V1T8BGV4HaEw8+eILaNTImdiX6JbuWUr7Wu2pUKoCffsW/NzwRBPvTVTh3GmM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\nlmv4cGfV27NnfQ0jJgxvNZz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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_sample_comparison(mu_neg=80, mu_pos=90, sd_neg=5, sd_pos=5, subsample=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A $t$-test between samples of these populations is not consistent with the null hypothesis: that both means are equal. The reported P-value in the plot title tells us that the probability of seeing this data (or a greater difference between the population means) is $P_{real}$ and is pretty small. No-one should have difficulty seeing that these populations have different means.\n", "\n", "**NOTE:** The $t$-test is calculated on the basis of a 100-item subsample of each population and $P$-values will change when you rerun the cell." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When the experiment is performed, the results are not these idealised populations, but **observations** that are subsampled from the population.\n", "\n", "We'll say that we find fewer mouse proteins that bind the drug than do not and, for the sake of round numbers, we'll have:\n", "\n", "* 100 *positive* results: mouse protein binds drug\n", "* 2000 *negative* results: mouse protein does not bind drug\n", "\n", "And we can show this outcome:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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cdjuUgOjVax7PPw/FReFllsnOzSZxVCI7eu+gU14n4qOrPzBhvuSTOCqRxFGJ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\nNF3Ym3BqzlNLbQYv4ODOVhT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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_sample_comparison(mu_neg=80, mu_pos=90, sd_neg=5, sd_pos=5, n_neg=2000, n_pos=100)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now the frequency of each experimental group is also plotted, as a histogram. The blue group - our negative examples, match the idealised distribution well. The green group - our positives - match the profile less well, but even so the difference between means is visibly apparent.\n", "\n", "The title of the plot shows two $P$-values from the $t$-test, which is again very small. The null hypothesis: that the means are equal, is rejected." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Experimental error in classification\n", "\n", "For many experiments, the experimenter is in complete control of sample classification, throughout. \n", "\n", "For example, the experimenter either does, or does not, inject a mouse with a drug. The 'experimental' sample is easily and *absolutely* distinguished from the control. In this case, $t$-tests are simple to apply, with relatively few caveats.\n", "\n", "This easy distinction between 'experiment' and 'control' samples is such a common circumstance, that it is easy to fall into the trap of thinking that it is always a clear division. But it is not, and it is increasingly less so when the samples being compared derive from high-throughput experiments, as in our fictional example, here.\n", "\n", "When the categories being compared are classified as the result of an experiment or prediction that has an inherent error in classification, then we may be comparing hybrid populations of results: mixtures of positive and negative examples - and this can potentially affect the analysis results." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Where does classification error come from?\n", "\n", "In our fictional experiment every interaction is taking place in yeast, so the biochemistry is different to the mouse and may affect the outcome of binding. Furthermore, the assay itself will have detection limits (some real - maybe productive - binding will not be detected).\n", "\n", "Although we are doing the experiment in yeast, we want to claim that the results tell us something about interaction in the mouse. Why is that? It is in part because the comparison of mouse protein sequence identity to the human counterpart protein implies that we care about whether the interaction is similar in the human and mouse system. It is also because the implication of binding in the yeast experiment is efficacy in the animal system.\n", "\n", "The experiment is an imperfect proxy for detecting whether the drug \"really binds\" to each protein in the mouse. Not every individual binding outcome will be correct. Errors arise in comparison to what happens in the mouse, and also simple experimental error or variation. We can therefore define outcomes for each individual test:\n", "\n", "* ***true positive***: the drug binds in the yeast experiment, and in the mouse\n", "* ***true negative***: the drug does not bind in the yeast experiment, and does not bind in the mouse\n", "* ***false positive***: the drug binds in the yeast experiment, but does not in the mouse\n", "* ***false negative***: the drug does not bind in the yeast experiment, but does bind in the mouse" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Introducing false negatives\n", "\n", "We can look at the effect of introducing a *false negative rate* (FNR: the probability that a protein which binds the drug in the mouse gives a negative result in yeast).\n", "\n", "We'll start it low, at $FNR=0.01$:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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SNRR6IJBDfv5EMjJy/Q6pWU47zRnOfUmNd+HKKsuYvmo61wy/xp/AImRYl2Fs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\ngItrlJkAPAOgqvOBTBHpqqo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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_sample_comparison(mu_neg=80, mu_pos=90, sd_neg=5, sd_pos=5, n_neg=2000, n_pos=100, fnr=0.01)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again, the $P$-value reported by the $t$-test allows us to reject the null hypothesis. But there's a difference to the earlier graphs, as the two $P$-values in the title differ. That is because they represent two different tests.\n", "\n", "* $P_{real}$: the $P$-value obtained with no false positives or false negatives. This is the $P$-value we would get if we could correctly assign every protein to be either 'binding' or 'non-binding' of the drug, in the yeast experiment.\n", "* $P_{obs}$: the $P$-value obtained from our observed dataset, which could contain either false positives or false negatives. This is the $P$-value we would get if the yeast experiment had the same false positive or false negative rate.\n", "\n", "In this case, with *FNR*=0.01, and 100 'true' positive interactors, we should expect approximately one 'true' positive to be misclassified as a 'negative', and the resulting effect on our test to be quite small. This is, in fact, what we see - $P_{obs}$ should be very slightly higher than $P_{real}$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Increasing the rate of false negatives\n", "\n", "If we increase the rate of false negatives to first $FNR=0.1$ and then $FNR=0.2$, we see a greater influence on our statistical test:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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lidWYSpGRAYmJybz5pjNbXvfuv2T58vln9GDy6hmIUMrOjuXGG7vz0ktw8cVJ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\nxsnPMvWH4XQ5L7weQKzp0tJ2kBXUhff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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_sample_comparison(mu_neg=80, mu_pos=90, sd_neg=5, sd_pos=5, n_neg=2000, n_pos=100, fnr=0.1)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_sample_comparison(mu_neg=80, mu_pos=90, sd_neg=5, sd_pos=5, n_neg=2000, n_pos=100, fnr=0.2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now the $t$-test reports several orders of magnitude difference in $P$-values. Both are still very small, and the difference in population means is clear, but the trend is obvious: misclassification moves the reported $P$-value closer to accepting the null hypothesis that both populations have the same mean." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Introducing false positives\n", "\n", "Now let's introduce a *false positive rate* (FPR: the probability that a protein which does not bind the drug in the mouse does so in the yeast experiment).\n", "\n", "Again, starting low, at $FNR=0.01$:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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LKO/Cb2NCyMKFTh9G9+6/jGvwf4T6TZaqqqgoksTEZBITkynqvZb43MZ8/3ot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\npLOK21hKg3UdLGGUIrFzCre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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_sample_comparison(mu_neg=80, mu_pos=90, sd_neg=5, sd_pos=5, n_neg=2000, n_pos=100, fpr=0.01)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The direction of change is again the same: with false positive errors, the test $P$-value moves towards accepting the null hypothesis. Also, the size of this change is (probably - it might change if you rerun the notebook) greater than that which we saw for $FNR=0.01$. \n", "\n", "The increase in effect is because the sample sizes for positive and negative groups differ. 1% of a sample of 2000 negatives is 20; 1% of a sample of 100 is 1. Misclassifying 20 negatives in the middle of 100 positives is likely to have more effect than misclassifying a single positive amongst 2000 negatives.\n", "\n", "This tendency becomes more pronounced as we increase $FPR$:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_sample_comparison(mu_neg=80, mu_pos=90, sd_neg=5, sd_pos=5, n_neg=2000, n_pos=100, fpr=0.1)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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WDUSWM+39U5gyJa3svseECanVqmf5juWsS1jH+V3PD0+gETCq5yi6tujKxHl1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\nntKgnNLSIrZtW1L2Ki4+8j7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ht5y7mNcYXnamtpz3La8yFOcrXtnLOvLPP8BkzkEpRVF2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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_sample_comparison(mu_neg=80, mu_pos=90, sd_neg=5, sd_pos=5, n_neg=2000, n_pos=100, fpr=0.2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With $FPR=0.2$, the $t$-test now reports a $P$-value that can be 20-30 orders of magnitude different from what would be seen with no misclassification. This is a considerable move towards being less able to reject the null hypothesis in what we might imagine to be a clear-cut case of having two distinct populations." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Combining false negatives and false positives\n", "\n", "As might be expected, the effect of combining false positive and false negative misclassifications is greater than either case alone. This is illustrated in the plots below." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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SkQjgOVWt0W/VNxBwerl1k8stj69k35XA4Jqc15j66tln4a67YOvWxjXn59Ch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\nMHfbXM9isCsNY/w89BA88gj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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_sample_comparison(mu_neg=80, mu_pos=90, sd_neg=5, sd_pos=5, n_neg=2000, n_pos=100, fpr=0.01, fnr=0.01)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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kpvdUhiUMY4wx4O5OY42IvAHMAwo861RV3/VdWMYYYwKRm6TRGDiOMzy5N0saxhgTZNx0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\nZcpEwqKzUD3CiWORRMac8He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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_sample_comparison(mu_neg=80, mu_pos=90, sd_neg=5, sd_pos=5, n_neg=2000, n_pos=100, fpr=0.1, fnr=0.1)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_sample_comparison(mu_neg=80, mu_pos=90, sd_neg=5, sd_pos=5, n_neg=2000, n_pos=100, fpr=0.2, fnr=0.2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The effects of class size\n", "\n", "We have seen that the relative sizes of positive and negative classes affect whether $FPR$ or $FNR$ is the more influential error type for this data. The total size of classes also has an influence. In general, reducing the number of class members increases the impact of misclassification, in part because the smaller sample size overall makes it harder to reject the null hypothesis as a 'baseline':" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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6KgXoKiJuEWkA3AjMK1VmHvBbABEZCGQYYw6JSLSIxHnWxwDDgY1+jFUpn3nx\nRWjQIJfevZ2OJLDS0vYxd24Sy5evY8IEq0pubcQ0Ygvd7P38V06H57ghHYfQsqAlSalJTodSI367\n0zDGFIjIJGAJEAq8bozZIiITPdunG2MWisjVIrIDOA3c7tm9FfCJpx93GPCOMeZzf8WqlK+kpcFf\n/wqDB3+G9eMfOIuTpnAody1zkyYQiYuRCVOrfIwjmRuZmzQBgLSDybjKqEopPs/Lb/elVdv4M2UL\nm4ThciVAbCpudyLH+Zljuf/kLvMZ724TWnXtjItCW3FMeWQKGTnW+COuSBdTnzz7syR/n8yEKRNI\nXpN85hu0L3if286xi+NYn7Ke+H7xFcbcP7s/Cw4toHfLsr9R2PnclZWv6jGqyq/PaRhjFhljuhlj\nuhhj/ulZN90YM92rzCTP9nhjzFrPup+NMX08r17F+ypV202eDPfeC40aHQ34uXPIILx/NK4ENzlk\nVL5DGYoa5ONKcONKcFNIXpllis+TF5ZZblmD4TPuxbWpC+dEdmT4cNi3/TZMkb0/ORk5GbjHunGP\ndZ/5A1hanuThHusmr7DsOKvL+9x2jl0cR2ZRZqUxR5pIruh4BQu2L6CIogrPXd4xKitf1WNUlT4R\nrpSPzJ8PGzbAn/7kdCTO28QHZLIf15bOAPTqBWENTrJv1cBK9qz/+rbqS6iEsj1iu9OhVIsmDaV8\n4NQp68nvl1+GyPo3Bl+VFIblsYQHuYbpiLH+xIhA265vsmf5peSdbOVwhM4SEUadO4p1kevYn7nf\n6XCqTJOGUjVkPZOxgvDwdbz5ZvA9k1HagU5r6ca1tGNQifURUYdpO2gl+76aUqPpYeuDFjEtODf3\nXCYvnux0KFWmSUOpGtq58xx2776YceOskWDd7sSzxl0KFifYy4lmexhK2c2Q7S5eQf6plpw+VrUJ\nm+qj3jm9WXdwHfO2le5UWrtp0lCqBoqfyRg6FGLq17QJVWbEsJ35tN7Rn0hcZZYJCS2k7RX/4Wjq\nn8nODO56vDDCmH7NdCYtnERmbqbT4dimSUOpGnj2WQgPzyM+3ulInJfT4hhRNMZ12F1huQyzBIn8\njNf+1PPMMx1TpiQGJMba5oqOV3Blpyv5y1d/cToU2zRpKFVNO3fCP/8JgwbNr/fzZFSmsGEeuc0y\n6MqoSgckLCwMI7blNE7tvhwKbsLt/mVK2GD0n2H/Yfam2SSn1Y0ZIDRpKFUNxsDvfmcNytewYbrT\n4TjKYDhhybKHAAAXA0lEQVQ94AiRB5sSQUNb+0joKbqO+oy92yeQn+/nAGu5ptFNeXrE09w5704K\nbT786CRNGkpVw8yZcOIEPPig05E47wDWzHQRx8puxyhPs27biI5NJSnJD0HVMTf3upmOro5sjKz9\noyVp0lCqig4ehEcegddegzB/DvlZB+SQQSpJxCQ3r9Y8Ga27vMP69XD0aGs/RFd3iAgvjXqJbRHb\nOHTqkNPhVEiThlJVMHlyIgMGbKVVq2+ZOjW4n8kwGLYxj7YMIvRk9UZtDW+QyfDhsGLFtUHbTblY\nm4ZtuCD7Aj7d9ilF5uwhRmoLTRpKVcHatfHk5nZnzJjLgv6ZjLwuJykkj3ZcXKPjnH8+xMRk8Le/\n+SiwOqxLXheiwqNYsXeF06GUS5OGUjalpUFKynDGjtVqqcLwfLLPT6cb1yI1/DMiYvVAe+UVSK4b\nHYj8RhBGnzualftWcjzkuNPhlEmThlI2GAN33QXduiVzzjlOR+MsgyGr3UEit7qIoblPjhkdfYpp\n0+C22yA72yeHrLNckS6GdhzKsphl5BbkOh3OWTRpKGXD66/D4cPQu/dZk0cGnaNtt2BCiojYWrXe\nUpW58UaIj9dRggH6tOpDTFEMT3zzhNOhnEWThlKV2LEDHn0UZs2CkJDa20AZCIfYyKEOG4jZcw5i\nfPdEY3LyKiZMSAT+xfTpJ1m6KIzFi5N8dvy6RkS4OOtiZq6bWevaNzRpKFWBvDy4+WZ47DFrTohg\nVkAOn3ALrXdeSGieb+e4zsuLxO1OpHv3hxk3riFHdj/JqYw4n56jrokyUbx49YvcOudWTuWdcjqc\nMzRpKFWBxx+HFi2suTKC3Zf8iaacS+ODXfx6nq5doVGzNfw0fxJz5pScczzYujeP6zGOhA4J3Lfw\nPqdDOUOThlLl+PprePNN6+nvYB9bKrNxGpv50JpYqRoP8VXVOZ0+pPB0W7J3/g+xscE95Py0q6ax\nOm01s9bNcjoUAIK846BSZZs48d+8/fZELr54Hg89tPPM+uTkdbjdzsXlhKKwfPZ0+Y7f8BnRNA3I\nOUNCCojp/0dSv/6YjuetDMg5a6uYBjHMvn42Q2YN4aK2F9G9WXdH49GkoVQphYWwYMF19OnTiEsu\nubXEtuXLxzoUlTOKKOSU+wDN07rTseOQgJ47NC6VTsOWsnvpPeQNgwa+bUapU85veT7/d+X/ceNH\nN7LqzlVEhUc5FotWTylVyhNPQFFRKFde6XQkztvFl0hhCC12n+/I+VvGryMqbhfz5xP0U8TefcHd\n9GjWw/EpYjVpKOXls8+sNozLLvuIkCD/7chrc5ojbLa61wagHaMsItC265scOwarVjkSQq0hIrwy\n+hWW71nOK2tecSwOrZ5SQW/KFGsSoMxMFwsX3sWQIbPZuPE7evT4f06HViFjDPn5WWeWi4p8NxfD\naY6QNeAwfbid1MLlPjtudYSE5nPDDdaowo3a9HM0Fqc1jGjI3JvmcumMS+nVwpk+4Jo0VNDLyIBz\nzklk0SJISIABA+5k+/b5TodVqcLCPJZ89wcKw3IxpoiMk6nQ7OxyRzI3MjdpAgAH962nVdt4Du5b\nz+ncY8xNmkAkLkYmTD1TPp8sfuQ9otY1peFFbQFI25d85hhpB5OhSflxeZfdk/51if1cuMsseyh3\nLYuTppSIw5vLBePGwTvv/oMP3ppEg7gjHDqUzty5SRw6lM7ixUmMHJlQyRUrX/L3yUyYYsWZvCYZ\n91h3tcqUVdYV6WLqk2V/rmJTHplCRk5GieN6H2N9ynri+8Wfed97YG+GvjaUNj+2qTAOfwjyG3Cl\noKgohI8+gvbtYcAAp6OpmsLofBpd2oHwbjGYcmZ9K2qQjyvBjSvBTV5Y5pl/w/tH40pwk8Mvc62a\nEMMmPqAZPYjY9cssfIVheWeOUUjF/V69yxZFFVS4X3HZ8P7RJeIoS+fOEB73Kns+e47YqBGEhzfB\n5UogPLwJOTkV7lqpPMnDPdaNe6ybvMKyP5+dMmWVzcipfC7bjJyMs47rfYzMoswS7y+95lIGdRrE\n3vP3kl8Y2KkPNWmooLd69QiMgauuCu7nMQyG3IuPE0YEnaidvQDCY1+hYdu9bP7w1xgT3BUll7a/\nlPCscD7Z+klA59/QpKGC2rRpcOBAR66/nqBv+P6Of1HUIo/uXFfj4c79RQS6Xr0ICSki69ATQd2j\nSkRo8WMLcgpyWLxjMYbAXIza+ZOhVAC89x78619w5ZXvEhnpdDTOWsOrrOEVIhc3J4wIp8OpkIQU\ncd71H1GY04s9ywY7HY6jxAg39ryR3Sd2syliU0DOqUlDBaV58+DBB2HJEoiLq7zOuT7LaJ7KNyRy\nK58TkhXqdDi2hDbII7bt3Rxc15ec4791OhxHRYZFcsv5t7A1cmtAhhoJ7kpBFZS+/NKaUOmzz3Tk\n2nR2knbu99zJKprg34EIfS0k7DDxv53F6hfuYMeyPOaSdKZHFcCRI+nOBhhADSMaMixzGH/66k90\natAJd6lear6kdxoqqHz7Ldx0E3z0EfTv73Q0zsqPO8VWPqHDjwm0It7pcKol0nWC2Ha3kbXlPnJS\nJ5/pUeVyJVAUZFOfNCpqxNJbl7Imag0bDm3w23n0TkMFjYULrelE33sPLrvM6Wicldf2FFntjtKH\nCRSdKHA6nBoJbbCbuEvuYNdXswmLvtHpcBx1XvPzGJY5jKU/L0UQ4vD9nCR6p6GCwuzZcPvtVlvG\n0KFOR+Osw2wkq99RYne1pSFtnQ7HJ0LjdhF/2xvkpE9k97LBQd2rqnFRY27tfStLf17KlogtPj++\nJg1V702fDn/4AyxdCoMGOR2NcwyGnO4Z7GQpcV+1Jiy7fnUZi26aTlz7mzjyYy92LhmJ8eF0tHVN\ni5gW3NH3DrZGbOWhpQ/59DkOTRqq3ioogAcegGeegW++gd69nY7IOUUUsp355Lkz6cudhJ6sn+OM\nh4Qdps/tM8k8cA45h2eSl10/P6cdrkgXV2VexXd7v+PWObdSWM6IAVWlbRqqXkpPhxtugPBwa3RU\nl8taXzw4obf6PrGSiShkA28TRgRxX7Qh8vpGTofkV2GROcTf+hYrp7l57d67uOnv7zsdkmMiTSRf\n3PoFt829ja/ivmJ8znhcka4aHVPvNFS9k5JijSHVpw8sWPBLwgBrcMLiqUODYQrR3Swja9whGtKa\nntyAFATHr3xIWAEm9nc06Pg2L909nrRdFzB3bhKLFyc5HVrARYVHMfv62XTM68hra19jR/qOGh1P\n7zRUvVFYCP/+t1Ud9dxzsHJlInfeWbJMfb+rKGYoIoknSOElIpY3ptOIYU6HFHgidLnsJM3dc1j/\n1rMcXbmHJv0eg3CnAws8EaFnbk96ndeLj7d8XKNjBcfXDlXvpabCFVdYT3inpMCNNwbfXUWxLI6y\ns+8SdvMNE1lL2D7npgatDRq130tD9yjys6PY/u6rHDnY0emQHNPB1YG7L7i7RsfQpKHqtNxc+Mc/\noF8/GDXKetq7fXuno3KGCSkiu+VRfmAGjQ67uZWlxNHa6bBqhZDQk/S47hNaDZrBV/Om8OCDnNW2\nFSziImr27IZWT6k6yRjrrmL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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_sample_comparison(mu_neg=80, mu_pos=90, sd_neg=5, sd_pos=5, n_neg=2000, n_pos=100, fpr=0.1, fnr=0.1)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_sample_comparison(mu_neg=80, mu_pos=90, sd_neg=5, sd_pos=5, n_neg=1000, n_pos=50, fpr=0.1, fnr=0.1)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_sample_comparison(mu_neg=80, mu_pos=90, sd_neg=5, sd_pos=5, n_neg=200, n_pos=10, fpr=0.1, fnr=0.1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Some realisations of the last example (`n_neg=200, n_pos=10, fpr=0.1, fnr=0.1`) result in a $P$-value that (at the 0.05 level) rejects the null hypothesis when there is no misclassification, but cannot reject the null hypothesis when misclassification is taken into account.\n", "\n", "**Misclassification of samples into categories can prevent statistical determination of category differences, even for distinct categories**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The general case\n", "\n", "All our examples so far have been single realisations of a fictional experiment. The results will vary every time you (re-)run a cell, and quite greatly between runs, especially for some parameter values.\n", "\n", "Let's look at what happens over several hundred replications of the experiment, to pick up on some trends." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Python code\n", "\n", "As before, ignore this if you don't want to look at it." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def multiple_samples(n_samp=1000,\n", " mu_neg=80, mu_pos=90, sd_neg=5, sd_pos=5,\n", " n_neg=100, n_pos=100,\n", " fnr=0, fpr=0,\n", " clip_low=0, clip_high=100):\n", " \"\"\"Returns the distribution of P-values obtained from subsampled\n", " and observed (with FNR/FPR) normal distributions, over n_samp\n", " repetitions.\n", " \n", " - n_samp number of times to (re)sample from the distribution\n", " - mu_neg mean of 'negative' samples\n", " - mu_pos mean of 'positive' samples\n", " - sd_neg standard deviation of 'negative' samples\n", " - sd_pos standard deviation of 'positive' samples \n", " - n_neg number of subsampled data points (negatives)\n", " - n_pos number of subsampled data points (positives)\n", " - fnr false negative rate (positives assigned to negative class)\n", " - fpr false positive rate (negatives assigned to positive class)\n", " - clip_low low value for clipping samples\n", " - clip_high high value for clipping samples \n", " \"\"\"\n", " p_sam, p_obs = [], []\n", " for n in range(n_samp):\n", " samples, obs = sample_distributions(mu_neg, mu_pos, sd_neg, sd_pos,\n", " n_neg, n_pos, fnr, fpr,\n", " clip_low, clip_high)\n", " t_sam = stats.ttest_ind(samples[0], samples[1], equal_var=False)\n", " t_obs = stats.ttest_ind(obs[0], obs[1], equal_var=False) \n", " p_sam.append(t_sam[1])\n", " p_obs.append(t_obs[1])\n", " # return the P-values\n", " return (p_sam, p_obs)\n", "\n", "def draw_multiple_samples(n_samp=1000,\n", " mu_neg=80, mu_pos=90, sd_neg=5, sd_pos=5,\n", " n_neg=100, n_pos=100,\n", " fnr=0, fpr=0,\n", " clip_low=0, clip_high=100,\n", " logy=True):\n", " \"\"\"Plots the distribution of P-values obtained from subsampled\n", " and observed (with FNR/FPR) normal distributions, over n_samp\n", " repetitions.\n", " \n", " - n_samp number of times to (re)sample from the distribution\n", " - mu_neg mean of 'negative' samples\n", " - mu_pos mean of 'positive' samples\n", " - sd_neg standard deviation of 'negative' samples\n", " - sd_pos standard deviation of 'positive' samples \n", " - n_neg number of subsampled data points (negatives)\n", " - n_pos number of subsampled data points (positives)\n", " - fnr false negative rate (positives assigned to negative class)\n", " - fpr false positive rate (negatives assigned to positive class)\n", " - clip_low low value for clipping samples\n", " - clip_high high value for clipping samples \n", " \"\"\"\n", " p_sam, p_obs = multiple_samples(n_samp, mu_neg, mu_pos,\n", " sd_neg, sd_pos, n_neg, n_pos,\n", " fnr, fpr, clip_low, clip_high)\n", " # plot P-values against each other\n", " if logy:\n", " p = loglog(p_sam, p_obs, 'o', alpha=0.3)\n", " else:\n", " p = semilogx(p_sam, p_obs, 'o', alpha=0.3)\n", " ax = gca()\n", " ax.set_xlabel(\"'Real' subsample P-value\")\n", " ax.set_ylabel(\"Observed subsample P-value\")\n", " ax.set_title(\"reps=%d $n_{neg}$=%d $n_{pos}$=%d FNR=%.02f FPR=%.02f\" %\n", " (n_samp, n_neg, n_pos, fnr, fpr))\n", " # Add y=x lines, P=0.05\n", " lims = [min([ax.get_xlim(), ax.get_ylim()]),\n", " max([(0.05, 0.05), max([ax.get_xlim(), ax.get_ylim()])])]\n", " if logy:\n", " loglog(lims, lims, 'k', alpha=0.75)\n", " ax.set_aspect('equal')\n", " else:\n", " semilogx(lims, lims, 'k', alpha=0.75)\n", " vlines(0.05, min(ax.get_ylim()), max(max(ax.get_ylim()), 0.05), color='red') # add P=0.05 lines\n", " hlines(0.05, min(ax.get_xlim()), max(max(ax.get_xlim()), 0.05), color='red')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The perfect experiment\n", "\n", "Assuming $FNR=0$ and $FPR=0$, i.e. no misclassification at all, the *observed* and *real* subsample $t$-test values are always identical. We plot $t$-test $P$-values results for 1000 replicates of our fictional experiment, below:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/usr/local/lib/python2.7/site-packages/matplotlib/collections.py:590: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison\n", " if self._edgecolors == str('face'):\n" ] }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_multiple_samples(n_samp=1000, mu_neg=80, mu_pos=90, sd_neg=5, sd_pos=5, n_neg=2000, n_pos=100)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The red lines in the plot indicate a nominal $P=0.05$ threshold. \n", "\n", "The vertical line indicates this for the 'real' data - that is to say that points on the left of this line indicate a 'real' difference between the means of the populations (we reject the null hypothesis) at $P=0.05$.\n", "\n", "The horizontal line indicates a similar threshold at $P=0.05$ for the 'observed' data - that which has some level of misclassification. Points below this line indicate that the experiment - with misclassification - rejects the null hypothesis at $P=0.05$.\n", "\n", "Here, there is no misclassification, and all points lie on the diagonal, accordingly. The two populations we draw from are quite distinct, so all points cluster well to the left of and below the $P=0.05$ thresholds. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The effect of $FNR$\n", "\n", "We saw before that, due to the small relative size of the positive set, the effect of $FNR$ was not very pronounced. Running 1000 replicates of the experiment, we can get some intuition about how increasing $FNR$ affects the observed $P$-value, relative to that which we would see without any misclassification." ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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uQA9ccEtw6yNfxG1L/DGwCJhHbm4PunSpYvz4Yi6++CgTSSMkLBRE4I0i3+Ei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\nJpSGYRgN8P8KlinhgTUUWwAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_multiple_samples(n_samp=1000, mu_neg=80, mu_pos=90, sd_neg=5, sd_pos=5, n_neg=2000, n_pos=100, fnr=0.01)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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kP4HAOezb909KSkZRV7eSefOGo/osmzf/jcbGWn7zm58xfnzKN+Y0jF4nFqEM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\nl/b29Uya5PbEDjevw/dFg4mkYaQ3aS+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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_multiple_samples(n_samp=1000, mu_neg=80, mu_pos=90, sd_neg=5, sd_pos=5, n_neg=2000, n_pos=100, fnr=0.1)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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CvB7XyfVIOn2SXmTyB4FmEXlORP5CVaNAIjL508CtFpl8cnbubOfAgSDbtg1y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\n83lnXT8VTCCNOYENJudNuL7DL6pqj4j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GUv2SAUBfoAWoz33qSRFtiWElHYBHgF05ohto\neyvwHDAhX+9PW7Q7tzh0J1MvXp9d+N5duC7bfwA/SZpZmo+k8RXktRvT9knbdfmzKjevJ20/9Lfd\nXGYOj1fQt4UL7WVgBzCz9JBI0qDC3m7QzQgnWVucj5hsbyaVyK0jRWlLJR0EDpAKNQG8CuwDviXt\nSRblVHsSfB3wiaTDQBPwnu3fSXVYBuWl8HySgy5xApgv6RjJqa4kOZIvJB0CdgHP5r6LSUvhRlJp\n1+KT9qJe1fZAr89yFxTkFu9/FJiXbdJM2uPsSGd2KLGJ5Iw3FNreAd6S1ESyVzm9y9rL9nHgFWBb\nnsM20tZD0A2JfJJBzaH0v6MTnQphBcEVJSLJoBaJv+zBVSMiySAIgipEJBkEQVCFcJJBEARVCCcZ\nBEFQhXCSQRAEVQgnGQRBUIVwkkEQBFX4F1R/RNa5ezwnAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_multiple_samples(n_samp=1000, mu_neg=80, mu_pos=90, sd_neg=5, sd_pos=5, n_neg=2000, n_pos=100, fnr=0.2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The effet of increasing $FNR$ is to move the reported $P$-values away from the $y=x$ diagonal, and towards the $P=0.05$ threshold. Even with $FNR=0.1$, almost every run of the experiment misreports the 'real' $P$-value such that we are less likely to reject the null hypothesis." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The effect of $FPR$\n", "\n", "We also saw earlier that, again due to the small relative size of the positive set, the effect of $FPR$ was greater than that of $FNR$. \n", "\n", "By running 1000 replicates of the experiment as before, we can understand how increasing $FPR$ affects the observed $P$-value, relative there being no misclassification." ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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utMD1oofNnWhrcBJtGV5Cp7J6gGIgghbXl4ADQDlQCXwTPVQ/B/jT59rE431M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\nzOaY2RzgaGAMYb23kxEXScdpDEppUT4JTDOzrrz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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_multiple_samples(n_samp=1000, mu_neg=80, mu_pos=90, sd_neg=5, sd_pos=5, n_neg=2000, n_pos=100, fpr=0.01)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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47rKeN4m2GhvRrnctWiDdaLEuAwKIHMUwHBhGGq93AocjQirlAm5HKTd+/x6y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\nAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_multiple_samples(n_samp=1000, mu_neg=80, mu_pos=90, sd_neg=5, sd_pos=5, n_neg=2000, n_pos=100, fpr=0.1)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Ip0614/ePL9/DNsyJEcj5YURyhZg9dtfRMUAk8hCdnT1Eo4WMjk7Q0RGho2OEvr5Pc+aM\nkErVYNsRoASlhrGsCTKZKyil6O5+mZ6eArzeXYTDKeLxUVKpehxHENmLyFmUagGO4DiQTGawrAyw\nmWSyH8sqI5V6gWBQGBw8A6QYHDzN5s0PUlFRTkWFh4GBp9i0aZL771e0tt41pyVYVVXKoUPQ1naG\nTEYYHT3L1q1vu5arCTqxvbv7u0v+jA03xwjk/DEiuULMHrtTynK3y4wk7zqi0WaeffZVpqbuIpMZ\nBsrIZC4BfuLxHyLSiFJTQBKdix9hdPQClrUdr3cricRJLKsPCAFHgTQ6P78XxxkFhnGcy/h8TXi9\nlaTT44jECIdbiER2MTU1RF/fRRoaijh48B7C4aNcuNDD3//9iygFtbUB3vnOvezevfVaX6qqSq8J\n6MjIOMePD7v316RSPdTXlyzRkzXcDiOQuWFEcpHMJydwrmNmj92J6PfxeIwnnxwgna5EpIdYrA+/\nfxuFhZsZGRkHurGszdh2JxBFqctAACgCLNLpXsAHdAEj6OntglJ+wEFPe68DqoCrwAtY1t2IBHCc\nCQoKztPU9DaGho6STFokEhGGh5PE42MkEn0kEpc4dmwficR+wOLcuQ46O5/lgx/kOqHMUl4eobW1\nmM7OHmxb8HgUzc3FVFRM5u0zMMwfI5C5YyqTL4Cs6A0NxWhrG6a5+W5KSrQwxuPt1yVYz1WNJxgc\nYOdOH6dPp68bkzx69Cg+XwsjI2VMTka4evVluruPMjpag9d7kFSqF9tOksmESadfwbJqcZwEWhTr\ngWrgGeAsuv7HLiCDFtFXgYvutiQwhM6yOglUYFkpPB4/Xm+aior7GBu7iMezCcfZjm2XoNQ5lDqF\nZfVQXr6V8vKHCQRKSaXSTE4+wZ139vMLv/DAtT8S089onLa2CXbsmB5rnf2MDMvDkgukSSY3wPUB\nl3PnehC5m1On2tm1C0pKSm+Y1vfJTz7P+fObcZwxLMumsfEy+/Y10NFxkYaGEp5//p+xbUVxcTGh\n0BjBYIzBwW6GhyN4vSHGxyux7W0kEh1oC3AIER/Qh0g1WgBL0BbjOaAGmAQ2ASl0XeU4MAaMApfd\nfxvd1wja0jyEbXsQUfT3n8fvryeZ7EekH8fpQWQUj2crmcweRkYEx+nG6x0nmSzGsnbR1TVCPN7C\nkSPt7Nw5cu0PQDgMzc3DnD37HLt2lVBRUciBA0YglxtjQS6cNSeSIlIH/Dn613021ymLi2VmwMVx\nhFhsmIEBuHLlOFu31tLUVInfr/+I/u3ffp+nnrJJpwsBoaDAz8DAKfr6jvPa195LOl1EKrUJiFFd\nXUkiUc/UVIjKSsG2K3j11fMotRelBrCsMmx7DO0yP4fPN47jhNCiWOBu9zJdatOLdrkVehwyCBSi\nhXOXe54f2AIUoNQQIs2kUqNAhmTyJFpgU4CNz9eIxxPHti0mJ6+STu/C57tKIFCL44zS0xPj6NF2\nWltr+da3nqOl5eFrz6ykpJQDBx4mFDrDQw/tWMJPxzAXRiAXx5oTSWA38FWl1N+7pdSWlZkBl6mp\nYTo7ffh8LShVSDpdy6lT7YRCY5w8eYHPfvYko6NvQqQKny+EbWdwnE7Aum7sMZFI09HxfWxbceWK\nh9HREaLRWoaGzuHxPMDU1Fk8nhq8XhvLCpFKJXGcImy7B+1C+9wWFQBRdJCkDC2KGXe/hbYirwJN\naJf7IvorcDfwDRznKjAMlKJddwuoBE6TTkdQqgBQKKWw7UmUmmBy8huInCeT8fCVrxymo6ORLVvS\ncz67TGbdeGBrBiOQi2fNVSZHD7p9TUR+kekak8vG9QGXlOvygmVlx0AjjI728aUvxUgkNuP37yeZ\ntInHh7AsRSbjJ53uYGCgnHS6gatXY1y82MfUVAqfDxKJJiyrhnB4B6nUeVKp0wSDD5HJlOI4Q6TT\nx4AJbNtGP6JqYDvahc4AnUACPfX9fqAYmAK+hrY2LXefQovqmLs/AAhQjh7fPA7sRY9d1gE2jrOJ\nQOCHQBDLqiIe/w5Qh8/304gUkUx6eOGFbzM5eZ7XvvYnb3h2s2fnGJYWI5D5YSUtyceATwKfz25w\nK5P/BTMqk4vI17i+Mvk7gI+4RXv/Efib5Wz0zGTpUKiQxsYQvb0vU11dQCDQQ3NzMb29Dj7fTgoK\nrpJKTeHzeYnF4ijVj+NcRikvbW3C1NSL9PZeJJmsIp3ux7K2ITKMnu1ykVQqg22HUSoNJEinYyj1\nOjddyO++9qDFsRg9AhEG+tFW5BfR7nQnevxxF/ojL0ALZRptdX4FLaDD7v5epsVUgEtAAseZJJNJ\nEw6XEA5fJJmcQuRORMZIp+M4jh+f7wE6Ok7x7LNPEgzW0dRUSUlJKfF4OwcOVC7DJ2QAI5D5ZM1V\nJheRp4DfE5F3o3+9y8rMZGm/v4vS0hD79m25FrkFOHNmiu7uAUKhCMPDJ0gmSxGxEdmOZcXxeIbp\n7BwjFhsmlWpEqSKUOkAmM4EWsB5E0ni9211h6sS2e4E70YKn0KIWAsbRgliP/jiTaPf6LNr19qAF\ncpt77Sr0Y9uPLrqURovjFsBGW5SVaAEudK8ZdY/zYtujeL1FjI93Y1mV+HwHUCqBUg5KnWZqKkw0\n2sDOnffQ2TnGmTMn2LcvzKFD202wZpkwAplfVtuY5G0rkyulXgEevd2F9uw5wKZNtezZ08xb3vLj\nORXdvV3uYzZZurW1wo101wG60vcPfvB12tp6EQmTySQoLJxgfPwkHs8uksnjeL1pt8rOKyhV444r\nvgulYkxHr/eTSv0Lfn8AkTJsexQtfAm0iCn08kBJt0UptLuNe1wD2m2uRVuESbS1aaOtzQhwBT0+\n2QO8ES2gHuA8WngjaHG8gI6abwZK8Hheg+N4sax+lKoBxgkGCwgECkgmNxOPP4dtT3LpUq9rRb6e\nUOiMEchlYiUEcr0X3V1tIpm3Qas//MPnAZ2Tt3Pn/N28XOshioxy6tSTjI9P0d19mfPnIyj1VoaH\nB4nHM8Rir5JOl5DJTOI4ZYgU4vE0AhdwHFAqiBY8H9qiE5QaRqkE6XQftn0ZPeYYAu5Ci1whcAQt\nmB3oRPI+tFjG0cK3Ay2QXWhxrQBeQothIdotP4O2SC+iBbQe2Accdq8XRQvkPei0onNkMkkSCS8i\nQ4TDW7Cs5ygoOEQ8foV4fBzLitHc/DrS6ZZrqVHZaL9haVkpC/Ja5f+PfxwOH0ZkfX3eq00ke9G/\n1Cz16F/8gpmZtzgf5qqHONc1psX0ILt2wdGjJ3n11RGmpu4jlfIxMlJCMtmBbf8Yfn+GZDKC41QT\nj3cSjz/PtMV3Au3+htBCNIC2+jqw7YPuti70eOKLaAvxCvAa4IfoRzSKdo8voMWxBC2MU2iBPYN+\njNuBg24PfogWyPuZNta/w/SMHMu9RznaNbeBMZQ667Z7FMvaRHFxF6nUk3i9frzeYqLRQq5cCaNU\nD42NDXR1dVNbO69Hb1gExsVeOlabSC5JZfJcUk+GhmKcO9dzbVmEpib9w599jayYjowM09ExwDPP\nnGJgoAzbjpNKebGsnaTTl7CsWmy7F8dRgB+lWlDqBbQV+DJalAbRAjaOtiavoAP/u9DWXBtauHrc\n/SXo4Mzd7v/96HFEG3gFHfGuQluPV9HWZRla8NqZzqN8G3qMsx0ttj/GdCnPIFpcFTrCPY7+SMbJ\nZO4jEEgQiaRQqpqmJn290dGrBAKbEdnM1atDwBS2fYbW1vvn/fwNuWMEcmnZEJXJ55t60t8/TFvb\nMCJ3X9vW1tZDayvU1NxYXDZbUNbvb2FiIoZIhGQygeP48HgAPNh2BssKY1lBYIpMJo22FO9DC1Qc\nbUCPoMcQQ+gphRNoyzGIFrDL6I/rHrSoDqGt0ShaCCfQYnnIPb7bvX4902OX1Wir1Oce60VbnBl0\nZlUYnfpTho5qN6KFdwod2AkAXWQy3yccLiIYTOLzKSYnh7Esh/Lye0kmA4yNvYzIKGVlm4hGbTMe\nuYQYgVx6VuyJKqXepZSqUUoFlFL1SqnH3O1PKKV2KKW2KaX+aLH3icfbaW2tmNexJ08O0Nx8N6lU\n+7Vtfn8dZ88+f+0a/f3DPPlkOy+91MlTT7WRTjcAEA578PuDWNYkHk/cHVecxHG+AzhYVtCt8P0S\nWpROo8cCy4EWtPjtRAtTPbAVbcXtRAvpi+gxxzb0GOZL6Fkz2XHIy+65DlrgshHqfrQ7L+77FvTf\nH9DW4Sa0AB5Ai2kDcC/wMPrr0eie04sW471YVim2XcnYWBrb3ksqtZ2JiS28+uoxRkaEgoLtlJTs\nIhY7zejoFN/+9lmefLKd/v7heX0OhvlhBHJ5WG3udt7w+8/i9aqc5gnbtkVJSSm7dkFX15lrVWu2\nbSucscSqdrNrays5fvwlJiamaGyETZtKGBvrIx6HePwZMpkgRUUFJJNTpFIDZDI/QqkE2uLbj7bW\nRt1XOVrwsnjR1lsS7fL60FZgHO1en0ZHn59zt+vlFXRiePYPQsY9xu9eaxA9ZXEn2joEbW3egxbW\npHsNP9qqLUEHeZLu9WNoMS0jkxkmHu/H73+AVOoKImmSyToymT1cvXqMyclTNDV58HprGR/3kko1\nA2bZhnxiBHL5WLci+aY3Ned8zszZNHoMUXAcdc1dnxnUKSkpZfPmInp7E1y92ktNDQwPJykqaqC3\nt42CgnvJZLpIpSbo738Fka1uubI6tDh50YGRk2hxguliFMNoNzo77TCKFrKDaCvwDnR02wMcQ7vp\nGfeaNtpq9DFtgdajRe4kWliDaEtzMzp6nR13bEKPg3ahrc+029YraAszirZcvaTTNhMTrxAIjFFW\nVkMs1odIKZYVpabmLkZGjlBUVEN5+dS1Z5prEM0wN0Ygl5d1K5ILYffuSh5//DkuXIji92sxTKV6\nGB6eoL9/+IZCubt2bQMGCIXKsSzF3r1buHjxCI6jSCYv4/P5uHxZ0dz8KJcunWVqyo9SKbRQnkZb\nk5PoYMmL6GBLGTpKPYS23DxoEexD5zBm60BOoQM/2bzJSbTANaKF7Cx6fDGOtjbvQIvnIFowY2g3\nuhNtPY6ihfi4e/xetFjb7v4itMX7IjCISAylthEK1WPbW/B6XyIUUkCGYDBOIgEFBYri4oLrnpmZ\nv704jEAuP0YkZ1BVVUo0alFYGMG2e68ViI1G62hrO4PHc33wJuua9/e/SCpl4fcXUVdXTiSyjUym\nhStXxhEZJZ1WBAJR0mkhk2nAcQRtrfWjrbei7BXRohhBi+VBtKjdgRawmLsdtDiG0HmNe9zjnkW7\n833u8bvQFqWDFtY6d1sF8HfoGaGN7ntBC7dCT3EMoi3ZTWiXux0t3rvxetNY1l14PC/h9W4HIBTa\nz9TU49TX382mTWV4vWEs6yqNjVuue2Zm/vbCMQK5MuQkkiISAuqVUmeWqD0rTnFxlDvvrLtheyYj\n7N1bcd0iVwDB4ACPPLKFb37zApcvJ7DtnUQiCQYH24EaIpFyJifHsayrpFJD6IBLtozZJvQ44jZE\ndgNJlHoVLZIPoS3HMrRrHUYLXnZWTDU68HIaaGZaAJV7zSq05TeJdpvvd49PoF3prKt9F9pirESn\nD9lM52160C72INqdb8TnG8fj0UGpUGgCkW4ymSv4/dsJhfzU1Eyg1JO0tAh+fyfR6J3XnpWZv71w\njECuHPMWSRH5SXSBiQDQJCL7gI8rpW4s97KGmb2sQhavV92wyJXXq2hq0hXGq6vv5sUXX0KknKGh\nISoq4OrVH9DYGOb8+e8yMbEJLVgHmC5hdgIteGcRqcRxspHqrEtqo624AFrgJtEW4QB6nHA/8D20\nuz6FFrusCw/aSvQzXUotm2CeRAdxqtFRcQdtze4EnkYL7Rm0WDtoAe3FsobcMmmXKCzcR3PzTkIh\nB8u6TCzWRl2djz17wjQ0NF2rvj4wMP2sTLHdhWEEcmXJxZL8GDoU+jSAUuq4iGy55Rl5QEQ2A/8V\nKFZK/bSIvBWdaV2EzqPM67J7s5dEhestoJmLXAE8+aQ+tqAAN5DTg8cjpFKDPProfnp6bHy+Lg4f\nfgXL+imU2gQ4KDWBDtzoedeOM4m2AIfcK7+Idse96ETzJPrx16Dd4H9FT0mMMF2953508KcC7ZoX\noN3kCXSJt3XUAAAgAElEQVRKUTapPLuMQxod1PGgxTLpXi/htq0QUPh8x8lasZb1MjU1LRQWBrFt\n2LKlhEikmo6Or1BT4+XixWMkEhH27KmhsnIbu3cbUVwMRiBXnlxEMq2UGp01L3NusyuPKKUuAe93\ny6KhlHoceFxEosCfAnkVybmsxVtZQDODOdlAjt/fgtcLTU3VBALHSCYtnnnGYnJyBO0GF6OtRS/a\nooyhrbcWtPZn8yBD7rHZRPJz6PScKbSAbUaPR55Gi1iAbO1HLX7nmK7287foKYuX0WOfQ+jgTA9a\nMMNuW9JoF7wf8ODxjOP3byUY7CQYrKGg4BL19XtJJkexrB6uXGknFIqwaVMDgcA2amvrSKXaSSQq\nOXJkwKT8LAIjkKuDXETylIj8LOAVke3Ar6GnacyLRRTZvRkfQdeezDuzrcVbMdM9n5lj6fP1EArF\nuPfeUrq6qgmFJojFAqRSXpTKJlUXoIUpm8t4Cm3Flbrb70VbfWm02AnaGjyOjnhnC1eAtjafRYtw\n1oocRYvvCNpi7UUL6Si6dNoQ2vI8417rCHAHlhXB4/EiUkIgUEpBAYRCw4TDFrYdwLaL8XqLiEZD\n9Pc/Q23tZs6ff5mKCgiHO5mcnF7OwrLO8eij1xVyMswDI5Crh1ye/K8yvdTeF9CDZL+ew/mPAY/M\n3DCjyO4j6BDuu0Rkp4j8OxH5nyJSM/siovkE8IRS6kQO978t2dk0ucwQ2b27knh8eoZOSUkpzc2K\nn//5fTz00A76+9NUVW0jHPYg0oZOufG5rxfRopUtKrEZbU3uQUe9+9DiGUFbjhbaSqxzz4uihW4U\n7apvRYvfTrQVmU0jqnfPEbQVWegeU4B21QNu671ABMtKUlBQjM93AcvqQ6QDv7+PVOosDQ2vJ5Ua\nxHHK6e0dY3TUQ39/B+HwDmKxECdOdBOLNZBOt5BOt3D8+KSZaZMjRiBXF/O2JJVSk8DvuK+cWUSR\n3VLgvwN7ReRD6KjEQ0CRiGxTSv31Qtozm1xLpGW5nXuu53jH2bXrLnp6vkMikZ0j7aCtux1owbqM\nFsNatOAlgDejXekgOgk8iv4blQ3miHvuWbToTqHd5Cr0OGQNOm1nEh0BF7SgJtACXeHevxTLuoxS\ndyDSg2UNATsJh+vxeJIUFl6goOAKRUU1RKNbCQaHGRs7Qzx+Bq93gIqKg4RCUXp6BggE7mdsbIjC\nQp3qU1DQTFvboHG554kRyNVHLtHtp+fYrJRSr1/E/edTZHcY+I+zzvvkIu45J/MtkTYXt3LPPR6H\niYlxrlwZZfv2/8T58xdIJFqw7U683gLS6adRKlvqbDPaVT6GzpHswrLGgUYcpwj4ETqtJ4MeZ/wv\n7l3K0Y8uibY+i93/h9Hu+Wvc4xzgKNqq/B7aRS9GxIPPN0VBQTGOM45SZyksTBONRohEFHffXUdB\nwb+lu/s8Xu8ZPB7B6x0lnQ6jVBXDw69QWRklkxnHsiCd7qWiYguplF7OIpOZnnVjuDlGIFcnuYxJ\n/taM/weBt6N/rYthyTKLH3zwQZqammhqapouCnoLZs+mybLYGSK7d1fy2GMv4PEcIBwuoqIiSn9/\nH6lUEdCNx1NAJuMBjmNZhYiMYdsTQDeWFQKu4jjPopduKEePeHwXbUl+Cy2uJ9HLAim0WHrRghhH\nW4vZJRqqgBa83nvIZGxEAiiVpLj4DgoKpqiv3wkECAYLaWjYw44dZRQXexgdtTl3bhDH8VNcrPD7\nK+jsdPB6d+I4F9ixYxOjo69SWjpAPB6mtHSKsrIxGht1mTmvt29Rz3AjsJYF0lQmd1G6COJMjorI\nsUXeP+9FdrMcPnw4p+NvlR+5GKqqSnnggTq+8IVzWNYmqqpCKDXGxESKyckYEMfrTSCyB9u+ANRh\nWWGU0tXGHaccy6rCcTrQ1mM3etzxGbQADqCj4E+ijfBsBaGvot3qiLttHMu6hLYuJ/H79dIOljWM\nxxPEsiaYnHyKu+/2U1W1i8LCMhobi2lrG8Pvr6OsrJjLl58DLPr6XiQY3E802k5ZmY+qqmqqqqpJ\npY6RSl1h//4D19b8MQnkt2ctCySYyuTXcMcGs1joiq9FNzl8vixJkd2FcLv8yFyZuU7O2FiKN75x\nM6+88goez06GhweZmrJJJp/GcRxgOx5PMY7jAy5jWWV4vV2k03VADKXSWNYUjrMFbSFeRgdkutHj\njhF0zuQQ2qo8jg7+2OiIeSeQwestw+OJkcn8K35/HQUFESzrCj7fKEVFk2zZEqKycgvxeC+pVD8T\nEzvw+3WhEL+/l9e+dgvj4xni8ats2RKnsXEnAJ2dPdi2EImM8+Y3NzEw0GcSyOfJWhfIjUAu7vZL\nTLvHen0BeN98T17OIrsLIdf8yFsxOwhUXV3O8ePH2bOnmm9+85t0daVIJGIoFUVXAz+HbceAESzr\ntfh8Pfj9DSgVJ5NJolQfXu9+LEvhOC+41uVlHGcUkRqUCgMT7tTGPehZo2Xo6YRJLMuHz9eBz3cV\npaCk5B6UiuD1KoqKumhtrWdwsIvx8QkGB1Ps37+f4uJCnnjiW9TVTVJcHGL7dr00LIDH00Vr6/TU\nzazVGArF2L176yI+hY2FEci1QS7udtNibqSUmtNCVEo9wfSaAStKLvmRs5lpOZ440UFNzb0UuAVw\nSkpK2bJlG4cPP8n582MEg/eRSnVi21uBJkTuQqlvYVl1iITdH8smLMuDx5NEqSNYVjm6srkg0ofX\nW41SFYi04jijZDKliDRhWTF3emMQqMHv7ycSCaJUnMnJNizrAdJp7eYHg1NUVx/kypVLeDy17Nu3\nH0hz9OgLNDSU4veXY1le7rxzx3V93b69iHg8f1b3RsQI5NrhtiIpIm/nFgEWpdQ/5bVFa5DZlmMi\nAW1tY7S2TltZo6MewuEWQqHLxGLF+HwHsO0RsjmKIi2InELEIRAAxxlHZBMi7UAcx/knlPIg8hLB\n4KN4vZtJJi+5Y6leYBKR01jWFsCH47wITCESx+OpI532Ewjsw+vd4waGbFKpYS5ePE5NjbBnzzYg\nTWfnAD7fG7l8uYeKih2cPfstdu2qvWZFxuPtHDqkK//MtrpBT9O82VK8Bo0RyLXFfCzJf8Oto9Ab\nXiRnpw+JOPj9dXR29hCNFjI6OsG5c4P09l4hHu/HtpsRKcCywjjOKEqNu/mJ48DXCIXqCIUiXL78\nKl7vIH7/DlKpKI4zhdd7Ab+/A9suxOMpIZN5Fb8/glKbUaqGTOZxfL5yRMI4Tgjb7iGT2UEiYePz\nNVNUVEY8XojjTBEMNmBZz1FZmaGw0ENPzwA+n+6H4wiRSCE7duyhv/9FqqoabxiCmHv1yNzyTDca\nRiDXHrcVSaXUzy9DO9Y0s9OHmpoqOXWqHa9XC2Rb2xjJ5CTFxXvYvHkbr7zyNF7vu0mnx1DKh1Ln\nXMEaoKhoB4WFx2lpuUwwOEg8fh+pVDHDwwm83ggez2vx+TzE4y/iOILfb+PzeclkdGWgcPiNZDLj\niOzE42lHqRSWFcCyqrBth/Hxc4jcQSCQIhIJIHKVLVvejEgH6fQ4IpBITDExMUA6PciWLSHq60tu\nW+l9MXmmGwUjkGuTXOtJvgU9fTCY3aaU+v18N2o5mTmWuFAXcXb60MxivL29QmFhPfffX097exKR\nWlKpfVy8+A+EQlVMTcUIBl9DINBNKFRCKCREo3dRVdVNeXkzIyNNnDnTTSIRxLIsvF4f8XgH4fAh\nksl+iop2Egg8i8dTy+XLgxQU9DM1dQHLyhAM1uLxxIEA6bSDZUXw+YSpqVdJJK6STCa5444Mvb3d\nNDYKmzcHuXChh/7+Dmpr66ivr8TvD3Hq1Hfp7x++5XNZqjzT9YIRyLVLLilAf42e7Pt64NPAT6On\ngKxZFusiZgV2aChGW9t3aG6++9rYXTA4wM/93F2cODF0bSGsaHSCH/3oNOPjE0QiivLyITo7x0kk\nOonHLZTaDJQQiwX4znfOs317gF27ygkEwly9Gqa7e5x4fIJQqJJE4hiZTD9KXSQS2YzjXGHbth1M\nTUWALkSKSaeHsawMqdRRIpH7SSZfZmqqAduuAiKEQl2Ewy1Eo1EuXz7K/fdX09t7nnvvfTORiB5L\nTaXa2bXrrttOLVyqPNP1gBHItU0uluRrlVK7ReQVpdTHReTP0FM+1iyLcRFnCmw4DDt2THD27PPs\n2lXoCoNw4oSOdFdXlyPio62tg/7+NJWV91BaWkcoVMbg4A/w+VrIZEKMjwtebyWO4wX2MTY2xKVL\nh7GsO0gkFEVFacbHnyMa3U0weC+VlXH8/kKUGiIajZBKpRkb+z6bN+/h4sVxvN7tOM4g4fBm4vEn\n8HrHCQQKmZoaoqBgC4FACT5fC1eufJeWlq2MjU3S0ODDttvxeovxeNS11J9MZuiWzyPfeabrBSOQ\na59cRDLu/jslIrXoEtmb8t+k5WMxLuJsgY1GC2luPsCpU9/DtiMEg3U0NZVTU1PND35wBJ+vkdFR\nH5Z1H4lED11dk2zdup3y8lbOnn2ZeHw/Hs9WkskklnWegoJigsEybPs4jnOGTKacYLCcaLSKgoJ9\nZDJDVFfrNb/Hxsqx7ZeoqBilsLCEyclzbNoU4OrV0wQCpUxODlNUtJdUqp2WllbGxnzEYg6WdZXh\n4ZeJRiGd3sWpU+eBUsbGRqirs6msrKezcwoRHzU1t7YI85lnul4wArk+yEUkvy4iJeglHF50t306\n/026njkqk1vAf0PX+3pBKfX5hV57MS7ibIHNBmguXYrg87WglNDWdpz772+ipGQbAwPdiFj4fBFq\naorp729kYGCKxsYm+vqeZXKyHcexEYkTiRRTVlbmjh06HDz4VmKxCfr6zhOJFDI2NkBpaQFe7xRe\nbzle7zBbtjTj842yc+c9XLx4mbNnQ8RiIQYGBqioqGBsLE0qVUJ3dzdFRXUUFnqprNzC+Ph5/P56\nurrGKCioR+QqZ870c+HCCM3NPhobNzM8/Dx79zbd9pksJs90vWEEcv0w709OKfX7SqkRpdRX0cUO\nW5RSv7tkLZu+7yWl1PtnbHorunpQikXO855dCxK0i9jaWnGTM6aZLbAdHWOk06X09yfJZOqw7VpE\nHuKZZy7iOBmamhppbq5l8+Y6IpFCRNS1NJu77trKpk1XiUR8FBdXUltbjc93kVBogkzmCp2dP8Dv\n7+Atb9nGgQPN3H13PWVlY2zZMoLIs1hWFyMj57CsCZRKI+KglDA6OoDX20Ig4CMa9RIO2wD4fBcp\nLc0QDBbiOOdRygcECYcTXLo0RnHxj2FZ2xgd9dLXd5zNm5sYGFhsLZONgxHI9UUugZtXgC8CX1JK\nXUBXT5g3eaxM3gz8UCn1aXdJh6dyacdMFuMizh6Dcxyht/clysquT5WxrEYGB/spLq6koUGnBvn9\nLVRWFtPXd5FUapB77tnHjh1NfPvbTxMONwKQTHpobCwmEnkDfv9uUql2lEoTjfp44YWnSSSKmZpK\nkkop6up83HPPmxDx8dJLz7N5cxOZTDtQj22PU1oaIJMZpKSknGAwSSTSQ2XlCJcvP8vevRlGRx3K\nykL09w/h8bQgEqKgoIxNm4StW+9kfPyMiVLPEyOQ649c3O2fRBeg+LKIKLRgflkp1TXP8x9D14G8\n5h7PqEz+BnRFoGMi8jV08Yz9wJ8opWbX2epBW5GQhzV2FuoizhbYUKiThoZqbLuWzs4hvN5yACxL\nUVw8QjAYp6ND4TjjdHV9F59vgJoaC58vTG9vN9u3F/HHf3yIgYEMx451k8lU09BQgYiP5547y+ho\nOZcu/YhkEsbGFBUVUYaGkmQyNiUlerg4Gi1k//4DXLnyHK9/vfCP//gkZWVvIhQKUFFRSSp1mcJC\niEYVr3lNiNbWNwHwyU8eR+ROlNI/6Eymh9LSYixrDADbFhOlngdGINcnuczd7gA+AXzCXePmd933\nnnmev9jK5PtE5LeBPwc+KSIPAIfn2/6lYKbA7t1b7opNK42NMDAwRDJ5htraIrZvj+A4hSQSESKR\nQiyrgJGRJPv3H7qupFhlZQm7d5eSyQgDA9V0dIwxPh7nwoVeYrEhYrFOoJbCwh0oFQHSWFYZsdgg\nXV2DlJSUEo0WUlnZyJve1Mx9923my1/uwOttweMZo7GxmkCgl0OH9l/3h+Gd72ziy1/+Ll4vVFR4\niMc9eL1jVFQUA5DJdNLaetdyP941hRHI9UuuyeRNaGvyHeg6XB9c5P0XWpn8/dyGXIvuLpaqqtJr\nYuPxlODxjNDUVIzPdxmloLr6NVRX62OPH5/A73/LtWmLcH3q0djYKG1tIfz+Oi5e7GF8fDfJ5BCp\nlB+lihgacojHk4TDxThOEVeu9DA2lrzWlqzVt3v3ViorS2hrG3SHEyZpbb1xOCF73A9+cI7jxzux\n7TogSUGBkMk8zzvescUEZG7BRhdIU3TXRUR+hC6D/WXgp5VSF/Nw/yXz4XItupsPsmXCvvzlDrZs\nuQOPR9HYuJP29mMEAsPXEs2zbq1tXz/Olx33E3HQyzjA8HAS2y5mYqIXj6eKeLwYkTsYHDxFWVkJ\nExND+P1FDA1dAm7MTZzvcEJVVSmPPnoPDzwwPENUY7S27jMCeQs2ukCCKbo7k/cqpdoBRCRf+ZFL\nVpl8pejvT3PgwEPXbQsGm6+5w5AVQfB4rv8bkbUAi4pK2bWrnK6uM3i9F4nHLxKN3oVl9ZHJDJBO\nt+PxlJFMOpSUDOP1tlNV5RAKnVl0bqJJ45k/RiA3BrmMSc7MlfkmOrCyWFZNZfJ8MVeCelNTMadP\nt6NXJtQFMI4f/x7NzQeuHTPTAvR4HEpKSikpKWViQjh6dBTLKsXjmaKsLILIOXy+4/h8QmvrVnbt\nup/a2kEeemjHDfc2LA1GIDcOOY1JziBne3q1VybPF3MlqOuoczGhkI6E19Yq9u27+TIHM9OLWlur\nOX26k5GRVyktDWNZPoqLi7jjjoMEAucIhys5c+YEBQWh2xahMOQHI5AbC1Eq92FBEfkVpdRfLkF7\n8oKIqIX0Kx/MVTRDF6q9uRs8VyUi4NrYYHd3N6dOTRKN3oXHoygu9nDx4ovYdprKyjtoaKigpKT0\ntvcxLB4jkLdABJRCRFBKrZuByduKpIg0o6cibgNeAX5TKdW7DG1bMCspkqBFbzr4oWhtrbilQM5H\nVGdfc3h4hGDw4A3XC4XOGLd7iTACeRs2sEgeBT4H/ABdpfxepdTblqFtC2alRTIXnnyynXi85Ybt\ntxO7b3/77LUSbDPx+8/etkCuIXeMQM6DdSqS8xmTjCilsoUs2kXk+FI2aKOx0EpEpn7j8mEEcmMz\nn087KCL73dddQEH2/yKSjwj3hmahYreY4hyG+WME0jAfd/sw1yd9y8z3SqnXLUnLFsFacrcXEuiZ\nee58xz4NuWMEMkfWqbu9oOj2amctiSQYsVuNGIFcAEYkVwYReSu6xFoR8Bngh8D/BZLAYaXUP8xx\nzpoSScPqwgjkAjEiubKISBT4U3TlnxGl1DdE5ItKqZ+Z41gjkoYFYQRyEaxTkVy2b4CIfFZE+kXk\n5Kztj4hIu4icc0uh3YyPoGtP1jE9v9teouYaNiBGIA1zMe9vgYhYIvLvROT33PcNInLgdufN4DHg\nkVnXzBbdfQS9nve7RGSne5//KSI1ovkE8IRS6gRaIOtybb/BcCuMQBpuRi5zt/8SXQn89cDvo2t5\n/SW6ivhtWUTR3V8DHgKKRGSbu/0vROQngK/l0H6DYU6MQBpuRS4ieY9Sal82mVwpNSwivkXefz5F\nd/8cXY18Jr+4yPsaDIARSMPtyUUkU657DICIVLD4NWaWLLqy3JXJDWsPI5D5Yb1XJp93dFtE3oNe\ntuEu9FzuR4GPKKW+PO+baXf7X7OrJYrIQeBjSqlH3PcfBpx5rJh4u/uY6LbhlhiBXALWaXQ7l6K7\nfyciL6LHB0GPHS629uO6K7prWP0YgTTkwnymJc6e+pH9C6Hg2kJdt7/RjKK7wADTRXd/nOl1tz+j\nlPqj+Tf/pvcylqRhToxALiHr1JKcj0h2cPOxQ6WU2pLvRi0WI5KGuTACucRsVJFcixiRNMzGCOQy\nsE5FMpclZQV4G3A/Oqp9VCn1z0vVMIMhXxiBNCyGXKLb/xfYCnwBPS75TuCCUupXlq55C8NYkoYs\nRiCXkXVqSeYiku3AHUopx31vAa8qpW5ce2CFMSJpACOQy846FclcvjXngYYZ7xvcbQbDqsMIpCFf\n5DLjpgg4LSLPo6PdB4BjIvKv6Cj3Ty5FAw2GXDECacgnuYjk791in/FtDasCI5CGfJNzCpCIFDFD\nXOebTL5QZlcmV0p9V0TC6OK7H1NKfWOOc8yY5AbECOQKs07HJHMJ3PwH4OPoZROyhS2WLZk8W5lc\nKfV+Efk4MAGcNiJpACOQq4J1KpK5fJN+C2hVSjUqpTa7r3kLZL4qk4vIw8CrwGAObTesY4xAGpaS\nXL5NF4H4Iu6Vr8rkh4CDwLuBX3KT3A0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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_multiple_samples(n_samp=1000, mu_neg=80, mu_pos=90, sd_neg=5, sd_pos=5, n_neg=2000, n_pos=100, fpr=0.2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see the same progression of 'observed' $P$-values away from what would be the 'real' $P$-value without misclassification, but this time much more rapidly than with $FNR$ as $FPR$ increases. Even for this very distinct pair of populations, whose 'true' $P$-value should be ≈$10^-40$, an $FPR$ of 0.2 runs the risk of occasionally failing to reject the null hypothesis that the population means are the same.\n", "\n", "As before, combining misclassification of positive and negative examples results in us being more likely to accept the null hypothesis, even for a very distinct pair of populations." ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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22693QRllvIVTUFDKypVw4cIpiotr6Ol5kXB4hxvLsZRksgSvdxvJ5Em83gEK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\n/YCLgFtr0JoB/Bx4nfyfuBMdUhGQc3Kbjs/L5ub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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_multiple_samples(n_samp=1000, mu_neg=80, mu_pos=90, sd_neg=5, sd_pos=5, n_neg=2000, n_pos=100, fpr=0.2, fnr=0.2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A more realistic population?\n", "\n", "The examples above have all been performed with two populations that have very distinct means, by $t$-test. How powerful is the effect of misclassification when the distinction is not so clear.\n", "\n", "Let's consider two populations with less readily-distinguishable means, as might be encountered in real data:\n", "\n", "$\\mu_{neg}=85$, $\\mu_{pos}=90$, $\\sigma_{neg}=6$, $\\sigma_{pos}=6$\n", "\n", "Over 1000 repeated (perfect) experiments, pretty much all experiments reject the null hypothesis that the means are the same, at $P=0.05$, but some (rare) experiments might falsely accept this:" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Fe38j8fD7CzjrrLvZufNIoCewFLco1MU4JZvtQB1gGE2aLGPDhomxM9ZIWEJx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\nDcMwPP4/iNR3Ct4zGw4AAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_multiple_samples(n_samp=1000, mu_neg=85, mu_pos=90, sd_neg=6, sd_pos=6, n_neg=1000, n_pos=50)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "In a single realisation of a perfect experiment with no misclassification, the reported $P$-value is likely to very strongly reject the null-hypothesis:" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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osBVJe8F4YLFMGp2BFVHzK4HjQ5TpDHQKUVeq4R58gQsLoaDgx2n7\ndsjPD6Zt2yAv78dp8+Zgys2FGTOOJifnVIqKmlFQYGzfbphtZfXq4EvesmXwNzn5WwYNOovWraFV\nK0hMbMMrr1zJ+vX9+fRT+PRTmD59FoccUnW85budoO66nhynmB2UUEgJOyimgMIWeeQwlyLyI9M2\ntmasZDr/ppCt7GAr6/vO5Q2uo4Bc8tnAdjaw8ZJv+QtNSCWdNDqw9fC1rOALWtKFAziBIxjKp+//\nnWuHTCYh6r9YzrdD6HjCMXWyPdJwJSfD4YfDv/8ddEe1ahV0W5WWzuGss8aRm8vOqaCgO998E+yE\nbdh4N8VfNychYQujry0hoWgT5y+HBctuYOGKJDZ+35YvX+lB3pKDePFFSEuDNSt6krSgLRvXlbB0\nKaSmQpMmP/5NToaEOr7ALpZJI+w1Bnt0e2L7X563J9XDq2JrKnzLq6gS/V51ryN/y67YcK94Kpqx\nmL9mT8cdSksjy0vBEoK9ocRESEwIvkAJiZCUGCxLSHSSkoLRXxMTgy9ZUhtIbg+57TdSnF9EUqLR\nKrGUdCtm8+Yc0jsGP3zbIlP+YdP4qtNbu7TGqpNmUtTJ8Mj86pSZjOWsSAkHnDWDZvMsg3bWW3PG\nHJ4mM1IiKPPDWQt4ghMjy0pxSll/zlIe5ajIfAm55/+HB+iGU0IpxWxnEyWXFnEv6ZRSRAlFlF5T\nxD3egkRSSKIJSTRl+2m5vM5QkmlGCs1JphnbuqxhJV/RhBak0IKkbU05kJNJJZ2mtKUZbZn01q+5\n5pI3SSQZgLEfDOGCq5/a5Z94St7oXRJGY5NQmkDekhxse+O9JLiip0CWHWGUWblyNFdddQYAE7Lu\nwHt/z5YpeZx967V8NymXG675Azf/1/tsX78/2/K3MfOrzez4vhUjR86lR48jmT3zAuYvSCN/nXP2\n18FO4Y4dwVRQEOw0JiUF/6+Tk2FH4YMkPwdwV623y2L1dCcz6w+MdPfBkfnfAaXRJ7TN7FEgy91f\niswvAk4h6J6qsm5keSO/+E1EpHbcvVY77LHcFZoGdDezDGA1cDkwtFyZicBw4KVIksl19xwz2xCi\nbq03WkREaidmScPdi81sOPAuwWWzT7j7QjO7KfL+GHefZGbnmNkygp6O66qqG6tYRUQknJh1T4mI\nyL5nrzpLZWbZZjbHzGaa2dTIsjZm9r6ZLTGz98ys6gux9xGRy5NfM7OFZrbAzI5vjG1hZodGvg9l\n02Yz+0UjbYvfmdl8M5trZi+YWZPG2A4AZnZHpB3mmdkdkWWNoi3M7EkzyzGzuVHLKt32yPdmqZkt\nMrMzq1v/XpU0CC7NyXT3o929bEjP3wLvu3sP4MPIfGPwL2CSu/cEegOLaIRt4e6LI9+Ho4FjCUYW\nGE8ja4vI+b+fA8e4+5EE3bpX0MjaAcDMjgBuAI4D+gDnmtkhNJ62eAoYXG5ZhdtuZr0Izhn3itR5\n2MyqzgvuvtdMwHdA23LLFgHtI687AIviHWc9tEMrYHkFyxtdW5Tb/jOBzxpjWwBtgMVAa4JzlW8C\nZzS2dohs5yUEQw+Vzf8R+E1jagsgA5gbNV/htgO/A+6MKvcO0L+qde+NRxofmNk0M/t5ZFl7d8+J\nvM4B2scntHp1MLDOzJ4ysxlm9m8za07jbItoVwAvRl43qrZw943AP4HvCa44zHX392lk7RAxDzg5\n0iXTDDgHOIDG2RZlKtv2TgQ3T5cpu8G6Untb0hjgQTfE2cBtZnZy9JsepMrGcGY/CTgGeNjdjyG4\n8myXQ+1G1BYAmFkKcB7wavn3GkNbRLpfRhDsYXYC0szs6ugyjaEdANx9EfA34D1gMjALKClXplG0\nRUVCbHuV7bJXJQ13XxP5u46g37ofkBMZrwoz6wj8EL8I681KYKW7fxOZf40giaxthG1R5mxgeuS7\nAY3ve9EX+NLdN7h7MTAOOIFG+p1w9yfdva+7nwJsApbQ+L4T0Srb9lVAl6hyB0SWVWqvSRpm1szM\nWkReNyfov55LcIPgtZFi1wKVPxx4H+Hua4EVZtYjsmgQMJ+gH7tRtUWUofzYNQWN73uxiGCE6KZm\nZgTfiQU00u+EmbWL/D0QuAh4gcb3nYhW2bZPBK4wsxQzOxjoDkytakV7zX0akQ0aH5lNAp5393vM\nrA3wCnAgkA1c5u65Fa9l32FmfYDHgRTgW4IbIxNpnG3RHPgPcLC7b40sa3TfCzP7DcEPQikwg+AK\nohY0snYAMLNPgbZAEfBLd/+4sXwnzOxFguGY9iM4f/En4A0q2XYz+z1wPVAM3OHu71a5/r0laYiI\nSPztNd1TIiISf0oaIiISmpKGiIiEpqQhIiKhKWmIiEhoShoiIhKakoZIHTOzvHjHIBIrShoidU83\nP8k+S0lDpBpmdo+Z3Ro1P9LM/mBmH5jZ9MiDwc6voF6mmb0ZNf+QmV0beX2smWVFRmx+p2xcIJGG\nTklDpHovA5dFzV8KPA1c6O7HAqcRDEteHQfczJKBB4GL3b0vwUNz/rdOIxaJkaR4ByDS0Ln7LDNr\nFxkdtB3BqKk5wKjI8PylQCcza+fu1Y2casChwOEEz4aBYMyw1THbAJE6pKQhEs6rBE+E6wC8BFxN\nMCDcMe5eYmbfAanl6hSz69F89Pvz3f3EGMYrEhPqnhIJ52WC4dcvIUggLYEfIgnjVOCgCur8B+gV\nGXY6HTidoItqMbC/mfUHMLPkyLOaRRo8HWmIhODuC8wsjeDhVzlm9jzwppnNAaYBC6OLR+qsMLNX\nCB4/+h3BcOW4e5GZXQI8YGatCP4f3k/w/AuRBk1Do4uISGjqnhIRkdCUNEREJDQlDRERCU1JQ0RE\nQlPSEBGR0JQ0REQkNCUNEREJTUlDRERC+/+oMy3J1wq2lAAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_sample_comparison(mu_neg=80, mu_pos=90, sd_neg=6, sd_pos=6, n_neg=1000, n_pos=50)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "### What is the impact of misclassification?\n", "\n", "Now, we increase the level of misclassification modestly:" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Fy9WJqoYolzVCIYPR0VGcTg2HQ8M0I4yM+Egm/UAHHs8p4DuYZj0TE6doaPhA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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_multiple_samples(n_samp=1000, mu_neg=85, mu_pos=90, sd_neg=6, sd_pos=6, n_neg=1000, n_pos=50, fnr=0.01, fpr=0.01)" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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oGElNc6Pr5zGMHJCipsagWHyWdPppCgUDRfEBk+j6oxSLXhznIlKeR1U/TiaT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yYiV4vIN93f70rVUTmqvcnx/nfpIPq6kjz+SyLS7L6nDSJyUQB9+KCIPNb/kUamYkKY+bylqnNx\nLKum4Fg/pYLSXUyfS1n0Xq9FcTwX5wIfBH4iIqMC75WRVZgQZiZN8TtUtQtYARwNICLHi8gyEXlV\nRJ4QkTHu/q+IyAoRWSUifxKRsqhmwovc78UpqYpBRL7ujpJeE5H73H0xIy53ZDrJ3SwSkXtFZI2I\nPBg+l4j8LKqd69x9Z4rIyyJSJyJPi0h1VPt3i8g/RGSjiHxaRH4hIq+LyBIRKXKP2ygi17r7XxGR\noxP0/2g35lW3vem9vL/ivqfNODW1R8a185KIHBO1vUxE5onIe0TkRfcaXhCRmgR96PX9EpHPuX3/\nl4jcnOro3gge+yAyEFXt4VsnIqU4Zpz1IlIM3ACcpY6P4Z3Aj91DH1LVE1T1OOANoMfCPqp6maq+\nnODUlwPHqeocur3m4kdc0dvTgZtU9RhgH3CJiFQBn1TVWW47P3KPfU5VT1TVeTiuzN+JamcKjsvz\nx3FMQp9W1WOBNlyvSPe8e9z9N+IY4Mb36RbgUvc9+TbwmwTXGEFEjgKOwqmnjWYxjtEqIjIWGKOq\ndUAjsMC9hv8FfpKg2YTvl4jMdNt8vzsa7cJxyDYygFw0Zs01jhaRf+GIxTOq+jcRqQVmAUtFBBxr\n9W3u8bNF5BqgAigHnvBwrteB+0TkzzhLFvTHFlV9yf39XhzH418B7SJyO/BX9wdgoog8AIzBcTR5\n292vwBJVPSwi9UCBqj7pvraa2NFa2DT2fhzL+AgiMhR4P/Cg+55ArEFt5FDgXBE5CWdU/FVV3RN3\nzAPAUzju1+fgLIEAziJHvxeRqW6/ixO9Kb2c81TgeOBVt39lwI4k440BxoQw81mvqnNFZCTwDxGZ\nD7QDDar6/gTH3wV8XFVXi8gXcZ6DJctHcRYTOhP4vojMBjqJvXMojfo9evQjgLqCdgLOH/7ZwNfc\n328AfqGqf3Unaq6Oiu3ACe4SkUNR+7vo/TsaP/IqAHa7o62+UJwV874e6bjIRJx1TwB+q6q3iMi7\n7vWfg+vCjTO6fUZVPyUiRwLLErTf1/t1t6p+r5/+GWnAbo2zBFV9F2ddjZ/g2CONEpETAUSkOOqZ\nVjmww719/hzdgiH0gTjDlEmqugxnjYoKnCUHNgLz3GPm4YxMw0wK9wE4H3jOHZmNUNUlOOu/zHFf\nH073qPVL0afu59KjXz836t8Xo14XVd0PbBBnqYLwmsXH9tJezDlVdYuqznV/bnF3L8Z5VDBcVesT\nXMOiXvq7kZ7vlwLPAGeHJ2ZEpCrqWauRZkwIM5/IyEdV/wxU46xYdjZwrYisAv6Fs+AOOEtDvgI8\nj/OMMLqdvmZYC4F7xFmasw74taruw1lPo8q9bf1vHBEOsxb4bxFZgyOcv8URi8dE5DWc1dW+4R57\nNc5t66s4y6ZGz2BH96uvZ5KVbruXRrUbHX8B8GX3PanHeeYYT3/vQ5g/4QjuA1H7fg78VETqcN6v\nRP1O+H6p6hs4y7U+5V7DUziPCYwMwPwIjaxAnNzK49VZNMgwAsVGhEa2YP9jGwOGjQgNw8h7bERo\nGEbeY0JoGEbeY0JoGEbeY0JoGEbeY0JoGEbeY0JoGEbe8/8BNoOhYD4pjngAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_multiple_samples(n_samp=1000, mu_neg=85, mu_pos=90, sd_neg=6, sd_pos=6, n_neg=1000, n_pos=50, fnr=0.05, fpr=0.05)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And now, at $FPR=FNR=0.05$ we start to see the population of experiments creeping into the upper left quadrant. In this quadrant we have experiments where data that (if classified correctly) would reject the null hypothesis are observed to accept it instead. This problem gets worse as the rate of misclassification increases." ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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PC24rIrwd8xB+lLiWcftqpHa5RcrrMZYXChmmpwt4TngP09Oz1Ov2aixrqVRs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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_multiple_samples(n_samp=1000, mu_neg=85, mu_pos=90, sd_neg=6, sd_pos=6, n_neg=1000, n_pos=50, fnr=0.1, fpr=0.1)" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/usr/local/lib/python2.7/site-packages/matplotlib/axes/_base.py:1166: UserWarning: aspect is not supported for Axes with xscale=log, yscale=linear\n", " 'yscale=%s' % (xscale, yscale))\n" ] }, { "data": { "image/png": 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Q3t4VjZA6fHiDRjGlAI/HQ1NTU1raTsTE1JiWOyuKoqyRTEVMbQSyMoMQkR9nhWxoY8xX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\n5ejRRvL5HI7TgOu6iDRQLjuYZhgIkMuNYVkZHGc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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_multiple_samples(n_samp=1000, mu_neg=85, mu_pos=90, sd_neg=6, sd_pos=6, n_neg=1000, n_pos=50,\n", " fnr=0.1, fpr=0.1, logy=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "At $FPR=FNR=0.2$ " ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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EzlssXThJKLIFkUlgpUHYdehGCNtJsOTpw+UKEAp5yIcClBI5nEIc0zTx+Zqo\nkR6krCWZdCiVOhDksawshrEfKVvQhRuPpxvHqaFYPIvjbMFxxhGiEymLKHKbRS3/XERFgCdRmlwR\nZe5WSuiaUdrdSPmYWpSpW0T5BltQRJpDmcvjKA1zC2p1hy0obS+LItoGFKnOIkQ9ut6MEEUsK4Fh\n2Pj9gmi0hpqadkZGRoFdOBroWghd1/D4M/haDFq27sS2+/H7+6jdUcuWsE4yaSPEIfyH2jiwq37d\nQQ79x8NwnX6Rhn8EntyxGgTZWjaBNV2//Pup9hOs4r2Cil+opeWxVaKrtMfyeuN0dEQJBEK0tWU4\neXKAePwSUurs2GHQ1dXM1NQcs7OL1Nc7xOMv0NR0BK/Xj64HKRSep6ami29+cxRNq6NUSuDxSLLZ\nIoVCAcdxozrA1JPPS7zeJhznXWzbTSpVj9+vUSym8fn24fGApk2Ty51F13M4TguqYmIZ0zyJ0lWC\n6LoPXU8BSTyep3CcIo6zQKl0BhVwaEGZrTVcbl6wiNLaRlABizjqp2CiTGQbRZSVz9FQ3WGSKBKc\nRQVJ3kSRXn1528XyPsoc93hMfD4/UgZxnGl03YuUO3G5fgZdf4fGxhIzM+cIhbysrHwPn+9T2HYW\nt7uBQuEHbN3ahs/nIharpbbWYM+ey/W+xeIsUkpOn15E1+M0NrqYny/dNOBxs3SpCgFWfIDvdRN4\nLR5Yc1gI8XHgo6i7+8+llD+6zj7yQZXvbuHHPx5e7R69spJmcjKJbQv8/nf57Gcf5syZOLOzrasE\nOT9/gXffnUDXDQ4dqgQRGtm1K8w770wyO+vCcQQezyTbtjXw3HMXEcJHbW0Ny8vLXLqUJpmsoVRq\noFhM4HK1Yppv4vf7se00DQ07Mc0Z0ulGTHOYWOxRQqEwxeI8hpHD4/EwPT1HqbQNy1ohl1tEiMPY\n9hQwj6YV8HgCCOHHcRbQNAvDWCGXa6RUAiEOIuUCQsSQ8l2UD24KRVY7ULmFl1DJ2DFUas0+lB/v\nNPBtVIBjK5fN4zyaNoOUC0jZhCJKB+WD/DCQw+0O4XL9Ldu3h7BtQSx2mLGxYVKpbhxHQ9Mm0fU8\n9fUfIpM5hmH0kM+PImWKYjFJf/8n2LIlQH29xujo8zzzzON0dTUDMDv7JmDT3HwIUL0fBwYG2L//\nAJGIqvzI54c5cuRaIpyfT5RzBFW61K5d9QSDnusT4FWdpavm8H0GKeV3gO8IISLAf0RVu1dxC6wt\no6s41gHfNWXEAAAgAElEQVTc7uzqD+bYsRO43U+SySRYXCwRDjfg9ZaYm1sgFpuntTVNJHKUmpoI\nXq9Kpu7vf5jJyRytrXVoWobu7h0MDZ3AcXYSCo2xtPQmuVyWQiGO2x0hFuvFMCwSiTNo2hLRaAvp\ntIZt5ykUUrS1hbCsZYTQqavzYBgpJiayeL0fxnGWcbt1HCeKrrsoFr9LILATywoj5TSFQj+6DqXS\nu0g5ALiQ8i2UH68V5SOs5PgdR5m99ajuMBoqjy+HCnjoCNEERBCiFseZRYgEmpbEsvIon+BS+bxB\nVN2wjpQ5QiE3sZiFrteTSHiQsg6vd0c5bchG1zXS6QlMc4Xm5jr8/k5SqZ/g97eTy73B4KBJQ4Ob\n/fubKBQGcbvTGIYkGrXxeg+tfo8TE3GCwSeZnJxe/T6vF/CAa9Ol3s8aYAX3nASFEF9GaXTxylrD\n5e3PAP8Jdef+mZTyD29wit8F/uSuT/Q9gpuV0YH6kezaFeL8+REmJ6fw+/vo7AwTDIZYWnqT5eU6\nxsff4YUXztDcXEOhoHPw4GNEozHGx/NY1jCtrfsA8HojNDa2USrZtLR4uXRphXS6g0xGksnkkTKL\nlJVUmAYsa5ZgcA8uVx7bhkgkQ6GwQCzWQKFgo/xwtbjdNqY5SyDQSi6XxLYzmOYymhakVKrHtn1I\nOYMQreUcwyiOswjsRtMWkLIX5Q+M4DgpdP0gtj2Kyv9zUMbFDJrWiePUoohwsdzB2kAIiZST6HoC\nKT9QXgukFiEeRohFNM3EcSYpFNLoeivx+LvkcnUI0YRpJhBiHE3bhRAeLEtD198hmTxDoeBjaWkE\naKS9/ZP4fEWi0RrOnn2en/1ZsbqmzLPPjq62xwKQUhGXbV+pqN2qZX6VABXuB6m/gmr6torygut/\nUt6+E/i0EKJPCPE/CSH+XyFEi1D4Q+AHUjWVq2Id2L27gXx++Ipt+fwwu3bVr76vq6thz54dbN3a\nSXd3G8FgiHh8moGBRZaXd7G4uI9Q6PMsLu5l585DLCxMkM2ewO9/l8cf78LtVuutC6EId2lpgq1b\nd9He3kQgUADeRIgMQqxg223k8x4WFp5F02Ikk69hWSVyuQuUSh7m5y9gWdPU1zfj99dTU1OL1+tQ\nW7sbr3cXHk8bhuGiVApiml40rYDjpJByN15vN4HAbjQtDjQh5XmkzOI4CRynhONcABLY9grK/A2j\nAiSNaFoUKd9BCBBiECmLaNo5hEgi5QlsO4Su9xMMdqPrYTStH1XzfAEpa3C7n8Ht3k4+v51I5CFK\npVeR8nWKxb9EiFoMI4/HY2Gap9G0DpaWZrHtw+RyPmz755mausTycoqzZ2eJx/fy938/wvx8Arj2\nQVa5zld3BbpZy/wqAV7GPZd8IwuuSym/JqX838qLlX8eeBL4lBDif/7pzvrBhSqja8DvH8HtHsXv\nH7nGd1QhysqPC2B4+G0aGo6wshLHMFR1gte7h/Pn0xw48CT19WE++9mHaWoq0d/fgMczQktLilLp\nf9DVpTM/P8Xyslqwqb//Cfbv34euG0ip4XY/jdfbh8fThaYtk81+DV0folhcpLn5cZqbW8lmT7J9\newKv93lcLommtWBZWbLZ76Jpj6DrH8a2WzHNJJo2hsdTg64HgDC2nURKP5p2FCmfQIiPopKdBapS\nREOVs9nAIrq+jK4LhPBgGF1ADCHyaFoJKWfRtG48noNI2Uw+P4jKD3RQ1R9BhGimVCpRKKyQy5VY\nXPSRz6vSQCH8lEozCJFB0xbxeMJksw62DUtLf42u58jlpnGcCImEjmU1s7SURYgmjh+PMz+fuOZB\n1tXVQCbzPJ2d4dVtVz/Y1qJKgFfinpvDN8B1F1xfu4OU8o9QqUxVXIVblUbdqna0Um+saecYGHgB\nn6+H+novuu7Hspaoq+tY3deyVJnd0NBFFhbSDA6qpSQDgQA7dkBjo4fvf38YKR/G76/F7w+RSmXw\nev14vQVMsx4hTCzLIRiM4fN9ACHiPPbYJxkfH2RhwaGm5hBNTeByLdLScpITJ75LqXSGTOYSfv8+\nslkbXQ9jGAa6/gSW9Twu13lsexGfL4aUeTTtIFKm0TQHx2lFBUG+XP47imE0oushTDOKlG8AMfz+\nrUgZwTTncRyJpvXhcr2NEL04zpvoeguOU0LKbRiGF8epx7LGcRwbw1hE03Sy2TbyeSgWe9C0Blyu\nAkI8gZQzuN1TaJobXe9D04p0dT3F2NhfEAjEyOXmcbkMNG2RaLSOUslZ9fM9+eSOK+rBW1sl+/Z1\nEY9fumV9eJUAr8X9SoKbFtI9evQoXV1ddHV1cfTo0Z/KmiD3EhspjboZGhtjfOpTBzl8WEUTx8fn\nKBanaWz04nL5V/crlXIMDiYRIsbAQANu9yOY5jCBgIuhoQnc7nb27v0Ik5M5oEB9/SLZbB3z88fR\ntAJNTR3k8w653By53Os0NW3D7w8RCPiZmzuLEE8xN7cESGpri/T3P00mM8TIiIUQdeTzy0hpUyx+\nA59vN+Dg823FtqeJxfbjcmmkUjEs6ySwFdsuomkgRA7HceHzbUPKS0g5gm2XMIxGLCuCEL0Ui++g\naaqTtds9i22fRQiJy2UihBeVYN2Lx5PBcYYpFgO43XUIcRbDSOL378VxXCwuDlJT04WutyLEGQzj\ndSxrG+l0imBwOzBIJNKK2+2hpuYAKysv4vU+gctVJBqto1h8nq1bVY10xc+3kSYIFWyEAI8dO8Yx\nYOJXf5WJiYkNfc6DhvuVBO9owfW1uJsLo99vmJ9P8NXVJOjh1SToG0UK14PKj62hweDLXx4B9jE5\nOYzL1Uuh8DZtbT7Ueh8u3G6Vx+Z29zIw8CPa2p5iauondHT46eyEeBx0vUAwOIOUNdh2N7OzGl5v\nhq6uHhYWEiwtvUmpNMY77zyH2+3CNJ1ycAIWFsaZmTlDLqeh613Ydg2wEyEcXK7TSHmGQKAGyzpH\nIFCDy/Uc+XwNuj6G4zyBEKWy/y+IpnnKzU1fQNdrMc1h4BAulw/DiGJZo9h2HY4zj2EUgVocp7e8\nGHsLjnOMYHAMywqiadvwem1McwXTTOM4U7hcfjTtEqnUu0iZwTS7sawAUvrw+WKY5gKWFScS6WBp\nKUAms4JpFvH5WnGcCUqlv8TrbcbtjtLXt4WWFg9w+0tjblQDPHr0KEcBvvpVoLr4+r3Afb3g+v2I\nigZYKPRjWaqrcCUJOhqN3fHi2rt3b+XXfg1++MOTeDxZEomTfOhDraysWLS07OfMmUuMjQ0jpYYQ\nDoWC6kFXWeUsEPDT3e3HMIps2VLD8eNDRKMhLOsVLGsbCwsr5PMa9fVR9u79h5w5cwrbbicW85JK\njZNMJohGdc6enSKTcaFpddTU1LCyMoHL1Yem9SGEhde7SG/vHmx7mcXFJM3NnSwvCyYmTmGanYCN\n40wjZQ7DiCGERKXMJJHy+xSLEArtR9P8COGnWLyArjdiWb1Y1ki54qOO2tpuDGOGpqY92HYer7eJ\nQqGbXM4hlfpjfL4UUkbxeOpwuyOYpo0QbkyzBtNcJBjsQtM8GEYLbncatzuNab5OJOIlFFpk9+6P\nkUzO0tPzOInEGdLpFV57bZi9e2uYn09s6IFWNYFvjntOgg/iguv3IyrF8Zp2WWF2u3uZmhohGo1t\nyuLau3dvZffurVds+/GPh7l0CaamVlCLESksLb1NJpOguTmCaV5u567rEo9nhqef3oLXe4DduxO8\n8MIQuVwRv7+d2tp6AoEGhAiRy5mk0y9QU/MQ27b1ATA0dIJUykWhMI0QTbhciwiRRNPq8HodHnqo\ni927O2lr0/nGN86j6zUYRgBdd5WjuA5SrqBpQ3g89Xi9LTjOQYrFaQyjD5frFIGAQNc9JBLn8HhW\nsG0b2+7HMJ5AJUyfxuVK4fO5EOJdPJ56FhYmsG2LbHaGjo5eDh16jGPHzhCPa+XqmUsIcQHDqME0\nVygUvkln504s6zQNDfvI50fp7o6xfbtDa+tRFhbG2L9f59Klb2EYHkKhPXR29uDzhTbk3qgS4K1x\nz0nwQVxw/X5EJQm6qyvM4OD0qmlq2+KKTtKbjd27Gzh27C1aWx9ncnIRw6jDsqbp6fkgU1PP8ou/\n+DGkLDE1NUIud5He3jCHD28FVAlXNNpLd/cWTDNLseintraGqakkjhPBtgW5XJxc7k0cZxzbLpFK\nJclkopRKuzGMdqS00LSXcLnG8XpNstk0mUyQ6WkPmpZncfFtZmen8Xh+A4/HRtN0SqVhQqFulpe/\ng5SPo+sufL5mTLOAEHuBWUKhraRS57BtL4bxKLbdiaa5cRyJ230IeJtiMYtlpbDtGny+VjweL7W1\n9bhcQ1y6dJZsNo5tC1wuQSjkxTRXygsmxWls/Bn6+g5RKCRIJhcIBAqk09+jUKjj7bc1mpqCxGLN\nxGJBfL4DV1zz9bo3qgS4PtxzEqxic1DJHYtEQuzaBZOT0+VyuEmOHHn4tvyB64FKro4xMHABTZsn\nkTCJRFy4XD7a2gSXLp3AcRx6e2s4fHj/FfOoRDg9not4PJLGxkPE40ksy08+b5FORzCMD+D3d5BM\nPk8qNVKuIT6Kpi1jWTNADMd5BF3/Fi7XdpJJkxMnHBoaXNTXtzA29g6WFaVYXMTlagDyuN2NrKxM\nIEQHPt/DAJRKo7jdufJ5TxMIrGAYo0jZimWZSPkStt2KYQQRQpDLjRGL9WGanQQCfcAoPl8Q23aj\naTlyuSDt7e2cO7eCZZXweiMEAs04zkmCQQ23OwiA1xvDMHKEw1E0rQGv92FqapTWfPLkNIXCKR55\nJL1aCVJBNRF681AlwfcI1hbHV8rhVP3o3SPACnRd5cf19n4YgEwmwdjYAH19+9i5U+UUXp2gDZeD\nLrt21fO1r73Fyy8/x/g4pFJFSqUY4bAAimXtTcflqqdQCOH1NmBZNqXSDFLOI0QOlytLTU09xWIn\ntj3L/LwPeIPOzp2cPDmFlDFMM43fb1AqJfH5eigUTiNlsZwP2I2mvUptbYzGRj/NzUVMM8rQ0CRC\nPIyqFDGwrDeRMoXH04NpFgiH3VjWJOFwiELhAl7vFtzudmw7SUNDK9PTo6ysrGCaH8Dv9+D17sXn\nO0FLywRerw1Impt9SOkhHm+4YhU4t7uNeHyMycnkNSRYTYTePFRJ8D2Cja4lsplQZVvB1ffxeBzD\n2INKIla4lQmXTheJx11ksy0UCjpg4nIVaWpqJJ32oGlRTNMhmRxF10sEg82USgGkLCGESSiUpq2t\ni3PnxsjlZshkLPz+JjTNJBTqIZd7Da/3ZxEiBwQolV6hvb2OUul1THMbbncal6tEJLJANGowNZUm\nlWqns/OjzM6msCyn3JzhUXT9W9TUJInFDPL5LO3t3UQiIUqlHPF4ESEkuu7g9Yaoq8uVE67zhEKC\ncBi2b99LODzBE0/sWZX/9ddfoK4ues11qauLkc+PorpVK9zMvVElwI2jSoLvIdxO7tiNsJG1KMLh\nCDU1BY4ffxHb1llenqO//3F8vsAV+93IhDt+/DwDA17c7oM0NJS4dGmJUqmZYjFLsZglGs2h62oN\nEtMskcl8k1LpKKVSBl33omk/IRrtBdxYlg8IYVk2S0sWS0sFLMvG729D9djIYxhT1NZuob4+RC6X\no1QaIRbzksvFaWiI4nbXUSzWomk2sVgzwWANi4uLZDLn8PkKdHT4eeyxDwElRkcnSKUWiURC+P0e\namtHgDStrRESiZfp6tqG4+wgmz1PNJpi61Y//f1bcLlK+P2XH1h79/o5ezZIqXTtte3tzV6xbzUR\nenNRJcEqrsFGE64nJy9y4kQd0eiHALCsYUZHi0QiKVTxj8KNTLjTp+dYWmpC02owDIjFdObm5slk\n5tA0g56ehzDNJKVSmsOHP8j3vjdKJvM2udwYmmai6z4cZ4GZmXEs6xLQQDZ7Dr//ZygUzqNpJpo2\nRjjcg9ebwO+vY2rqJfr6niYWcxDCzdzcG+zf383Bg/sYH1/EtnWGh1dIJrMYhpdwuA1NW6S/P8zu\n3R3ADG53Lz09MDNzCl1/g64uL11dIRyniebmQ6yspHnhhQGy2TH6+vz097esmrXFokS1eRNIKent\nrWd5eYELFy5H0k1zmvb2WQ4f3l4NgtxFVEmwimuw3rUoKpiaWkHXL5NdJNLA7OwACwu+1W03M+Hm\n59MYRg+FQpFstghohMMRNG2ILVuKNDbm2bYtxI4du/nhD8d4+ultXLw4Szbbh9vdQ6GQZ2lpmvn5\n54hGd5LPz6JpfnT9LELUYttJ2tqOkMu9REtLDZOT5+nt/SCBQD2OI7DtYfbs6aO5uY5oNMbERByf\nz08k4mN09BiBwKNomoPHI1hZGaGt7WHC4RBTUyMYhqClRfLZz35k9dqonn0juN2Cj37UQyJh0tx8\n2fSt9AP0eC5f47Nnh3nssXpisUXOn/8xQgi2bq3h8OGtVQK8y6iSYBXXYG3PwbW4kTnr80Xo7Gxg\nYWEExxGEQpLGxi4s6wRud90NTbiKyZ3N5kgmR0ilFvF6K7mGKYLBWT7zmUPYdgDb1pifL9HeHqW3\ndx8DAz5KpcskUigYvP22G8vSiURChELbKRSSTE2Nkcm8Sam0QFeXRn29jWH0sW1bP8FgJdjQysWL\nL6+2ourqamB8/B0SCQ91dftxuXJY1kVcrnO0tzeQTOp0dcWIRmPXDT5db0H7tb7aq/sBqmvYSzw+\nwqc+dUWJ/C1RJcA7R5UEq7gGt+o5eO12m2AwRjB4JcnV1Iyt9sBbi/n5BC+9NMrp0zm83h5qa3fj\nci2j6ymk/C4ulw+vN0V//w5eeCHBgQMPrx47OPgcO3akV3voVRAO+9i3r5nx8QVcrloyGZ10OkA0\nuoMtWyyi0SYc5xStrYKGhnbcbkWA2WyO+fkcxaLJ6OhJtmxpJhqN4fdbCDGNpi2gaTpbttTT0/OP\ncbuHMYxh3O7cuoNPV5Pi1f0AK9hoVU+VADcHVRJ8H+NGwY+brUVxPRw4UMsf/dFf4/M9gRCSxkY/\nUr7GL//ytYt2V/yNw8MRNO1QmQxyRCJJAoEuNG2alpY2wmGTYNCFYVz5w+7peYTR0RO4XJfNb9Oc\npqcnDIQxzbN4PHW89to4UjZh22dxu1solSb5wAcOUCiM0dzcyuDgNKVSjMnJHIZRh2E4HDx4gNHR\n12lt1VleXmTnzqMYhorKWpaqxPH7w2zb5qDrDpalceaM6p24kYDURh8y10OVADcPD+waI+tBdY2R\nG+N6wY+161Jcby2K6/3QK+eZm3MxMDBGqaQBc/z6r/fyoQ89fM3+lTVOTp0axbIua4mjo6/jcm0D\nRunt7aCzU61hsrg4S1dX5xWr4mWzJzAMycBAFp+vh87O8GpeZF+fi3jc4tvfPsmZMzqx2D78fj/1\n9WHc7hm6u6eJxdooFlt54YXzJJMBEokBdu6sp6mphUjExZkzr1EsdpLNbqFQkASDighdrmnq69+k\nr6+N5uZHr3vdbnSt1z5sGhtdnD1buuG1vxV+agRYXWPkxhBC+IF2KeXIJs+nip8SbhX8WG+6TeU8\n3d3Q3X25rthxrn9rVPyNaxu2AnR01KJpBUKhWvbsaWN5OcH582fp6noGy1Kma6UhRGtrmCef3LHa\n5suychjGpStM07femiQS+chVn95LOn2RT3yigcHBSzQ1XSSf97Fv31MEgzGWl9O88spxkkkwjAAr\nK+dwu+tpbS1SUxMhm32BujrB7GyYubn1delZ+7BZXk4wMRGnUBinq0ugaUlCoeiGcjqrGuDmY8Mk\nKIT4BeA/oNYq7BJC7AN+T0r5C5s9uSruHjYa/Nis81RMwa6uBoaGLqeDhMM+GhpmicUc3O5R5uYm\neeKJx5meTqJWgFMNIc6d+xFPP600zJsRdWdnjIGByzXUUEk5ia4e99Zbk2zf/tTq+NTULInEPhYX\nX6a9fT9u9zxLSyMUCtNs3+6jqclNNHp4Q116Kg+J5eUEQ0Nx3O5edL2XeHyaSCTD3r116zalqwR4\nd3A7muCXUF2eXwSQUg4IIa51/lRxX2Mz/FK3c56KvzEa7aW/n2saK6wlBNNsJhJJr9ZB67pk27bo\nukijri7Irl3hK47t6QlTX59d3edqokwkcuRyIWprO8nn3yGf30Yw+EEM422SySHa2/eTy2Vxu9Xx\n6+nSU3lITEzEryiJs22xoT6PVQK8e7gdEixJKVeuarJ4/V9CFfctNhr8uN3zXC/4cuRIw2oeXWsr\n7Nq1/xoiWNsQIhIJsbKSZmIiycTECj/+8fBNK1gq80okZtiz58p57dp1Wb6ridLlShIOt+PxxCgU\nPLhcF5FSoGlD1NcHicV6WVkZYHz8bQyjDSEkLS25m163ihxXR7MriyKtR/OuEuDdxe2Q4JAQ4jOA\nIYTYDvyvwKubO631QQgRAI4BX5JSfu92zrGR8rD3Ejar1vhm57lx5UkDTz6546bnXUuuKytpBgeT\nQIb+/v3k87Fb9tRbj3xXE2Uul+all14iHD6ClAYuVw2WNUxLy1ZCoRSZTJr5eY1IpIHz56dwHI25\nuZ/wcz/32BWJ0tcGQYZZqzNcjmbfWvOuEuDdx4ajw2Xi+T+Bitf5WeDfSCkLmzy39czl94A0cPZ6\nJHir6PCtIqRV3BkqkeCr4feP3JIEgdUI9ZtvXsSy2unoqCcaja0GGDyeGR5+uPWOHlxro+DpdJIz\nZ2YYGallft6DlGH8/mW6u2HHjnpeeWUC294KGBhGG6XSMJ2dDQSDA3zuc2qt5evdT319LkZGFq8b\nzb7ZvXbPCbAaHb4+pJRZ4P8ov+4Yt7v4uhDiKVRfdO/tfvZGy8OquDGup1FvRvBFSoltCxxH/RjX\nBhikDJHPt97WQlIVXB1cOXx4Ky+/fIFXXjnH228vEwy2Eww2EYlEaWp6h3j8HTStF00boaWlgWAw\nhmH0Mji4gJTyivtJmfBBxsaGeeSRNn7lV+qIx7Or0eyuLhdnzsQ5fXrxGivknhPg+wi3Ex1+8Tqb\npZTyiducw1eAPwb+Ys1nVBZf/zBq0aU3hRB/BzwC7EdFp48AAdTi7HkhxPc3mhS4WRHS9ztuZPZC\nCp/v2v3XE3xZe07HCVIqtTE0NIyUK3g8quSs4le7VYrKRtwdjY0x/v/2zjxcrqpM9783gZCQBExo\n0wRCZLohjEKgEb1wg9LeGxsVmR+mVsSh7RZvKyK0YppuB5rGp/GCCg0yc4WA0Cgog+BNi4AQCDMk\nzZQwKUEwSGJCSM53/9i7cionVedU7dp1qnbt9/c89Zzaq2qv9e1ae79njd+3337Q1zeePffcksWL\n32DNGvHUUw+yyy7j+e1vp66zvrFiR3LP9N83lS78qFFT6Ov7EytWTOPJJ9ddh1nPScW4cRtZAIeR\nLGOCJ1e9Hw0cShJ1OhMRcWcaUKmatcHXASRVgq//C3BF+p3T0s8+DryaZVV0XjOkZadWi3rlykk8\n9dSTrFlzO6NHT1m7pq7RyZfqPPtDBkzn+edvZ+rUdcfVoPY/rqzhRytljxlDlTPTLXnrrXk8//wi\npH4RrNixwQbLee21N1i48EX6+sSzzy5hs812YNSo2mJdrxcyb96D3HrrxRbAYSRLd/j+AUm/ljQv\nJ3sqDBl8vcqeywbLaLC4w3nNkJadgS3qSpd14433Ztq0TVi8+A0WLnyIPfYYy8yZQ7uFGphndciA\nkSNfZaONEuGp9rZc6x9X1uGOej2E8eM35cgjJ3LNNXewwQbT1y672Wijl5g0aUOeeaaPZcuWMWrU\ndN5+GxYv/hOTJy9g7723XptHRaxrlbFy5XKuvPLf2H//GR0XQMcdHgRJ1XfPCJIu6ia5WZSQW1Ns\nsLjDnfTG3EsMbFFX1sSNHPni2iUuMIWNN258rHVgnpV8pk/fnr6+ZYwZM7Sn5azDHYP1EHbddTsm\nTZpQtaVwObvsMolHH13C5Mn78NZbi3nggTtZsmQJEVOYPFlMmDBxnTxqlbFy5XIuu+xUttpqSscF\nEBx3eCjm0y9Sq4FFwAl5GZSSW/D1ocjTG3NZGdiijhixXncVmhtrrddKnzkz2ZrXyD+urMMdQ/UQ\nat0zDz30e5YufZMXXxzJVlvtx4QJr7N48RJeeWUlS5e+uXY2uJJHdRkVAdxss7HMnn1SxwWwbHSF\nA4V0TPDGyuywpA2AhcABJMHX7wOOajb2sB0oDB/VS00efngxkyfvs15woEaXxtTKczAnDoOdn3UJ\nVLNl3377Au65ZxyrVvW3UJcte52lSx9g+vQR7LXXlPXyeOWV15k3bzEXXvhvbLHFFGbPPonJk/+s\n4etrOyVZItOwCEo6lEG6qRFxfSYDqoKvA0voD77+IfqXyFwUEWdkyNsi2AG6af1lq0LaTDnnnPMQ\nI0b0L5JYtWoBO+88iT//89/X9KvY9ctgLIIDvihdyuAieHxONuWGRbBzDJf4dBPXXvsbFi6csHav\ncmVxd60WcNcLIFgEewGLoBlOGm0BF0IAwSI46EnSh0kWKa/drRER/5yjXblgESwGvbR/e6gWcGEE\nECyCdU+Q/h0YA3wAuBA4HLg3IvKeIW4Zi2D3003jh+2mUAIIpRHBLLXwvoj4a+D1iPgnYB+g8Sk/\nY6qov6D51Q5Z1B4KJ4AlIktNrEj//knSliRrBTfPzyRTJsqwf9sC2N1kWSx9k6QJJE4MHkjTLszP\nJFMmen3/tgWw+2lpdljSaGB0RCzNz6T88Jhg99PLY4KFF8CSjAlmmRh5BLgamBMRz7TFqpywCBaD\nXlxTWHgBBItg3ROSLW5HAkeQLJ6+GrgmIp7P27hWsQiaTtATAggWwYZOTmKMfB04JiJG5mZVTlgE\nzXDTMwIIpRHBrMHXt6a/NbgG+Ep+JhlTTHpKAEtEFn+C9wKjgGuAwyPi2dytMqZgWACLS5YxwekR\nsSB9v3lE/K4tluWAu8NmOOhZASxJd7jp2qoIYMrPc7TFmMLRswJYIjKNCVbRsf8MSvx9fxMYD9wf\nEXOK8CEAABdySURBVJcPcYopEcPhlMEC2Bu0Wmud3CnyMZKATKtok+t9U0wqC7BXrJjOqlXTWLFi\nOv/5n0t45ZXXcyvDAtg7NFxzkqZJ+omkxyVdJWnLiPhBqwZIuljSK5IeHZA+S9ICSU9JOqXGqdOA\nuyLiy8DnWrXD9A7tdspgAewtmqm9i4GbSOIMzycJmJ4HlwCzqhOqgq/PIvFbeJSkHSUdJ+lsSVuQ\ntP4q2/Vqb0A1paSdThksgL1HM2OC4yKi0v1dIOnBPAzIGnxd0vXAuZL2A+bmYYvpDdrllMEC2Js0\nI4KjJc1I3wsYkx4LiIiYn6NdQwZfj4gVwKeGymiw4OumNxkqZGYWyiaAZQq+3kygpbmsG2hJ1ccR\n8f7MRqwfcvNQYFZEfDo9PhZ4T0Sc2GS+XidYUvJ0ylA2AVxLSdYJNtwSjIj922jHQIYt+LrpTWoF\nSM9CaQWwRHRrjd4P/DdJW0saRbJP+acdtsmUDAtgOeh4rabB1+8Gpkl6QdLxEbEa+DxwK/AEie/C\nJztppykXFsDy4LjDxgzAAphSkjHBpmtX0oh0vd7s9HiqpL3zN82Y4ccCWD6y1PAPgPcCR6fHy9I0\nYwqNBbCcZHGg8J6I2KOyWDoiXpe0Yc52GTOsWADLS5aaXpVuawNA0jvxtjVTYCyA5SZLbZ8L/Acw\nSdK3gbuAM3K1yphhwgJoMs0OS9oROCA9vKNbl694dtgMhgVwCEoyO9zMtrmBy+8rP0hAMjaYo125\nYBE09bAANkBJRLCZiZH5rLt3uJoAtm3dHGPajwXQVOPF0qZUWACbwC3B2qSxPQ4B9iWZFf51RPxH\n3oYZkzcWQFOLLCE3zwO2A64iGRc8EngmIv42f/Nawy1BU8ECmIGStASziOACYKeI6EuPRwBPRMT0\nwc8cfiyCBiyAmSmJCGa5G54GplYdT03TjOk6LIBmKLJsm9sEeFLSfSSzwnsD8yTdSOJm/6N5GlgP\nSVOAc4A/AP8VEWcOR7mmOFgATSNkEcHZg3w2nH3PXYHrIuL/poGYjFmLBdA0SuYlMpI2oUpEsy6W\nlnQxcCCwpBJjJE2fBXwXGAn8cGBLT9KmJN6mVwNXRMSlNfL2mGAJsQDmREnGBLNMjHwW+CfgLfod\nJ0REZFosnYbMXAZcXhVoaSSwEPhLkngj84CjgL2AGcBZwBHAA2nIzmsj4vAaeVsES4YFMEdKIoJZ\nusMnA7tExO/zMKCFuMO/BGZLOhp4Lg9bTLGxAJosZBHBZ4EVeRsygEbiDj8CHNZmO0xBsACarGQR\nwVOBeyTdA6xK0yIivpCfWflNsDj4eu9jAcwfB18f7ATpfuBXwKMkY4IiEcHLMhuxfvD1fYDTI2JW\nevwPQF+zy2A8Jtj7WADbiMcE6zIyIr6UuyXrsjbuMPAyyda8o9pcpikYFkCTB1numpslfVbSZEkT\nK6+sBjjusMmCBdDkRZbu8CJqjNlFxDY52ZQb7g73JhbAYaIk3WH7EzSFwgI4jJREBLOMCSJpF2An\nYHQlLSIuz8soY2phATTtIItT1dOBmcDOwM+ADwG/BiyCpm1YAE27yHInHUayne23EXE88G7gHbla\nZUwVFkDTTrLcTSsiYg2wOnVisATYKl+zjEmwAJp2k2VMcJ6kCcCFJOv5lpMscTEmVyyAZjhoaXZY\n0jbA+HQfb9fh2eHiYgHsAkoyO9z0nSXpv0salx7uC3xC0rvyNcuUGQugGU6y3F3nA8slvRv4EvAM\nnhk2OWEBNMNNljtsddrH/Bjw/Yj4PjA+X7NMGbEAmk6QZWLkTUlfBY4F9ku9QG+Yr1mmbFgATafI\ncqcdSeJa/5MR8TsSB6hn5WqVKRUWQNNJMs0OS5pM4gK/D5iXimHX4dnh7scC2MV4drg2kj4F3Asc\nQrJ75F5JJ+RtmOl9LICmG8jiSuu/gPdGxGvp8WbAPRExrQ32VZe7DfA1YNOIOFzSWOAHJF3zuRHx\noxrnuCXYpVgAC4BbgnX5PUmIzArL0rS2EhHPRcSnqpIOAa6JiM8AH213+SY/LICmm2h4dljSSenb\np0m6wDekxwcBDe8YyRpsvQZbAg+n79c0Wr7pLBZA0200cweOB8aRLI6+gcS7dAA/IQnD2SiXALOq\nE9JlNt9L03cCjpK0o6TjJJ0taYsa+bxIv+MGP0kFwAJoupGOeJauEV3uvcA/VkWXOxUgDbZeOWci\n8G0SN14XAueSCOdK4M6IuKpGOR4T7BIsgAWkJGOCWZyq/r8ayRERH2jBjkaCrb8O/M2A8z7ZQplm\nmLAAmm4my46Rk6vejwYOBVa3aEfbmmsOvt5ZLIDFxMHXm81EmhcRf9HE97emDcHWa5Tj7nAHsQAW\nHHeHazMgxvAIYC9gkxbtcLD1HsMCaIpClu7wfPq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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_multiple_samples(n_samp=1000, mu_neg=85, mu_pos=90, sd_neg=6, sd_pos=6, n_neg=1000, n_pos=50, fnr=0.2, fpr=0.2)" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ZH/cRjQqcTsnRo3twuRo5dao743WZZKyksGEuKsEL3QylDC9Bdg/iGeAvgVdR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\nU/UVYATH0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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_multiple_samples(n_samp=1000, mu_neg=85, mu_pos=90, sd_neg=6, sd_pos=6, n_neg=1000, n_pos=50,\n", " fnr=0.2, fpr=0.2, logy=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## What does this all mean?\n", "\n", "If we know that our experiment may involve misclassification into the groups we are going to compare, then we need to consider alternative statistical methods to $t$-tests, as misclassification can introduce quantitative (effect size) and qualitative (presence/absence of an effect) errors to our analysis.\n", "\n", "The likelihood of such errors being introduced depends on the nature of the experiment: number of samples in each group, expected false positive and false negative rate, and the expected difference between the two groups. We need to have at least an estimate of each of these quantities to be able to determine whether a simple test (e.g. $t$-test) might be appropriate, whether we need to take misclassification into account explicitly, or whether the data are likely unable to give a decisive answer to our biological question.\n", "\n", "A further point to consider is whether the initial assumption of the question/experiment is realistic. For instance, in our fictional example here, is it truly realistic to expect that our drug will only bind those mouse proteins that are most similar to their human counterparts? I would argue that this is unlikely, and that there are almost certainly proportionally as many proteins highly-similar to their human counterparts that do not bind the drug. As misclassification can tend to sway the result towards an overall false negative of \"no difference between the groups\" where there is one, it may be difficult to distinguish between faulty assumptions, and the effects of misclassification." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Does misclassification always give an overall false negative?\n", "\n", "No.\n", "\n", "Sometimes, data that should not reject the null hypothesis can be reported as rejecting it: an overall false positive. These are the points in the lower-right quadrant, below:" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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WTgqFYlfJhW8gVR83blTxrW+d54UXBjl5UvMNbNcPAonVaC9e3IsQD3H58jKL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\nzpxZxDQ9WKkQ6DmMZ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gMPRcSvwBxgWD79cwWpcapZBVwhaSWpQZlKehN9VdJn\nwELg6rzuFNLpn0XAOjp+oqqaq6trHrvncidVyq2+/lzg4lwnbaRrGp11Vw81L5EaolmVZfcBd0ta\nTKqvUu5ifUXE58AtwPy8D/NJp9tskPN8EGY9TOm7IWMjTWpvNmD4CMKs57kXZgOSjyDMzKzIRxBm\nZlbkBsLMzIrcQJiZWZEbCDMzK3IDYWZmRW4gzMys6D+Zp4D0ofg/rwAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_multiple_samples(n_samp=1000, mu_neg=85, mu_pos=89, sd_neg=7, sd_pos=7, n_neg=150, n_pos=20,\n", " fnr=0.1, fpr=0.15, logy=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that, apart from the overall sample size (170 mouse proteins instead of 2000) the parameters for this run are not very different from those we have been using." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Interactive examples\n", "\n", "The cells below allow you to explore variation in all the parameters we have modified above, and their effects on reported $P$ values:" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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hdbQNV1peyhetv+C0x0/j8kGX879n/S9dk7qy5cAW1u5dS+pzqUwfOR0/9fQlbzxT/Qf1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\ntgPl5cfPq62tyvLJyanHrVO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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "interact(draw_sample_comparison,\n", " mu_neg=(60, 99, 1), mu_pos=(60, 99, 1),\n", " sd_neg=(0, 15, 1), sd_pos=(0, 15, 1),\n", " n_neg=(0, 150, 1), n_pos=(0, 150, 1),\n", " fnr=(0, 1, 0.01), fpr=(0, 1, 0.01),\n", " clip_low=fixed(0), clip_high=fixed(100),\n", " num_bins=fixed(50), xmin=fixed(50),\n", " xmax=fixed(100), points=fixed(100),\n", " subsample=True, negcolor=fixed('blue'),\n", " poscolor=fixed('green'))" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "interact(draw_multiple_samples,\n", " mu_neg=(60, 99, 1), mu_pos=(60, 99, 1),\n", " sd_neg=(0, 15, 1), sd_pos=(0, 15, 1),\n", " n_neg=(0, 150, 1), n_pos=(0, 150, 1),\n", " fnr=(0, 1, 0.01), fpr=(0, 1, 0.01),\n", " clip_low=fixed(0), clip_high=fixed(100))" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.10" } }, "nbformat": 4, "nbformat_minor": 0 }