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March 18, 2019 12:38
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| { | |
| "cells": [ | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "# Week 2\n", | |
| "## Question 1." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Import the data set and take a look at the first 10 rows." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 89, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/html": [ | |
| "<table>\n", | |
| "<thead><tr><th scope=col>meltpoint</th><th scope=col>burner</th></tr></thead>\n", | |
| "<tbody>\n", | |
| "\t<tr><td>94.10</td><td>b </td></tr>\n", | |
| "\t<tr><td>94.17</td><td>b </td></tr>\n", | |
| "\t<tr><td>94.67</td><td>a </td></tr>\n", | |
| "\t<tr><td>93.83</td><td>b </td></tr>\n", | |
| "\t<tr><td>94.82</td><td>b </td></tr>\n", | |
| "\t<tr><td>94.16</td><td>a </td></tr>\n", | |
| "\t<tr><td>93.96</td><td>a </td></tr>\n", | |
| "\t<tr><td>94.05</td><td>b </td></tr>\n", | |
| "\t<tr><td>93.95</td><td>b </td></tr>\n", | |
| "\t<tr><td>93.66</td><td>a </td></tr>\n", | |
| "</tbody>\n", | |
| "</table>\n" | |
| ], | |
| "text/latex": [ | |
| "\\begin{tabular}{r|ll}\n", | |
| " meltpoint & burner\\\\\n", | |
| "\\hline\n", | |
| "\t 94.10 & b \\\\\n", | |
| "\t 94.17 & b \\\\\n", | |
| "\t 94.67 & a \\\\\n", | |
| "\t 93.83 & b \\\\\n", | |
| "\t 94.82 & b \\\\\n", | |
| "\t 94.16 & a \\\\\n", | |
| "\t 93.96 & a \\\\\n", | |
| "\t 94.05 & b \\\\\n", | |
| "\t 93.95 & b \\\\\n", | |
| "\t 93.66 & a \\\\\n", | |
| "\\end{tabular}\n" | |
| ], | |
| "text/markdown": [ | |
| "\n", | |
| "meltpoint | burner | \n", | |
| "|---|---|---|---|---|---|---|---|---|---|\n", | |
| "| 94.10 | b | \n", | |
| "| 94.17 | b | \n", | |
| "| 94.67 | a | \n", | |
| "| 93.83 | b | \n", | |
| "| 94.82 | b | \n", | |
| "| 94.16 | a | \n", | |
| "| 93.96 | a | \n", | |
| "| 94.05 | b | \n", | |
| "| 93.95 | b | \n", | |
| "| 93.66 | a | \n", | |
| "\n", | |
| "\n" | |
| ], | |
| "text/plain": [ | |
| " meltpoint burner\n", | |
| "1 94.10 b \n", | |
| "2 94.17 b \n", | |
| "3 94.67 a \n", | |
| "4 93.83 b \n", | |
| "5 94.82 b \n", | |
| "6 94.16 a \n", | |
| "7 93.96 a \n", | |
| "8 94.05 b \n", | |
| "9 93.95 b \n", | |
| "10 93.66 a " | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "melt = read.table('melt.dat', header=TRUE)\n", | |
| "head(melt, 10)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "We can visualise the data with various plots. We can also show multiple plots at once by setting the parameter 'mfrow' to a 2 by 2 grid." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 90, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "\n", | |
| " The decimal point is 1 digit(s) to the left of the |\n", | |
| "\n", | |
| " 934 | 76\n", | |
| " 936 | 60\n", | |
| " 938 | 0136912256777\n", | |
| " 940 | 00023599001677\n", | |
| " 942 | 0444889913488\n", | |
| " 944 | 22691288\n", | |
| " 946 | 0770\n", | |
| " 948 | 281\n", | |
| " 950 | 7\n", | |
| "\n" | |
| ] | |
| }, | |
| { | |
| "data": { | |
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CmKCKmgEFK+EFJBiUdInNmQiZDk4hES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\nuYhJAAAAAElFTkSuQmCC", | |
| "text/plain": [ | |
| "Plot with title “Histogram of melt$meltpoint”" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data", | |
| "source": "R display func" | |
| } | |
| ], | |
| "source": [ | |
| "par(mfrow=c(2,2))\n", | |
| "boxplot(melt$meltpoint)\n", | |
| "hist(melt$meltpoint)\n", | |
| "stem(melt$meltpoint)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "We can also use the tilde operator to graph one variable BY another and use optional arguments to label our axis." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 91, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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| |
| "text/plain": [ | |
| "plot without title" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data", | |
| "source": "R display func" | |
| } | |
| ], | |
| "source": [ | |
| "boxplot(melt$meltpoint ~ melt$burner, xlab = 'Burner', ylab='Melt Point')" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Examine some numerical summaries." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 92, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stderr", | |
| "output_type": "stream", | |
| "text": [ | |
| "Summary:\n" | |
| ] | |
| }, | |
| { | |
| "data": { | |
| "text/plain": [ | |
| " Min. 1st Qu. Median Mean 3rd Qu. Max. \n", | |
| " 93.47 93.97 94.17 94.21 94.42 95.07 " | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| }, | |
| { | |
| "name": "stderr", | |
| "output_type": "stream", | |
| "text": [ | |
| "Mean:\n" | |
| ] | |
| }, | |
| { | |
| "data": { | |
| "text/html": [ | |
| "94.2056666666667" | |
| ], | |
| "text/latex": [ | |
| "94.2056666666667" | |
| ], | |
| "text/markdown": [ | |
| "94.2056666666667" | |
| ], | |
| "text/plain": [ | |
| "[1] 94.20567" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| }, | |
| { | |
| "name": "stderr", | |
| "output_type": "stream", | |
| "text": [ | |
| "Standard Deviation: \n" | |
| ] | |
| }, | |
| { | |
| "data": { | |
| "text/html": [ | |
| "0.338608151446459" | |
| ], | |
| "text/latex": [ | |
| "0.338608151446459" | |
| ], | |
| "text/markdown": [ | |
| "0.338608151446459" | |
| ], | |
| "text/plain": [ | |
| "[1] 0.3386082" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| }, | |
| { | |
| "name": "stderr", | |
| "output_type": "stream", | |
| "text": [ | |
| "Length:\n" | |
| ] | |
| }, | |
| { | |
| "data": { | |
| "text/html": [ | |
| "60" | |
| ], | |
| "text/latex": [ | |
| "60" | |
| ], | |
| "text/markdown": [ | |
| "60" | |
| ], | |
| "text/plain": [ | |
| "[1] 60" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "message(\"Summary:\")\n", | |
| "summary(melt$meltpoint)\n", | |
| "message(\"Mean:\")\n", | |
| "mean(melt$meltpoint)\n", | |
| "message(\"Standard Deviation: \")\n", | |
| "sd(melt$meltpoint)\n", | |
| "message(\"Length:\")\n", | |
| "length(melt$meltpoint)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Question 2.\n", | |
| "Now we will conduct a one sample, two sided T test to see if our data is different to the required mu. " | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 93, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "\n", | |
| "\tOne Sample t-test\n", | |
| "\n", | |
| "data: melt$meltpoint\n", | |
| "t = -4.4456, df = 59, p-value = 3.93e-05\n", | |
| "alternative hypothesis: true mean is not equal to 94.4\n", | |
| "95 percent confidence interval:\n", | |
| " 94.11819 94.29314\n", | |
| "sample estimates:\n", | |
| "mean of x \n", | |
| " 94.20567 \n" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "t.test(melt$meltpoint, mu = 94.4)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "We will reject the null hypothesis at .05 significance because our P value is 3.93e-05.\n", | |
| "We would also reject at .01 significance because 3.93e-05 < .01" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "We can also change the level of significance and confidence interval using the optional argument 'conf.level'. Even with conf.level of .99 our confidence interval does not include mu (94.4)." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 94, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "\n", | |
| "\tOne Sample t-test\n", | |
| "\n", | |
| "data: melt$meltpoint\n", | |
| "t = -4.4456, df = 59, p-value = 3.93e-05\n", | |
| "alternative hypothesis: true mean is not equal to 94.4\n", | |
| "99 percent confidence interval:\n", | |
| " 94.08931 94.32202\n", | |
| "sample estimates:\n", | |
| "mean of x \n", | |
| " 94.20567 \n" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "t.test(melt$meltpoint, mu = 94.4, conf.level=.99)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 95, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "\n", | |
| "\tOne Sample t-test\n", | |
| "\n", | |
| "data: melt$meltpoint\n", | |
| "t = -4.4456, df = 59, p-value = 3.93e-05\n", | |
| "alternative hypothesis: true mean is not equal to 94.4\n", | |
| "95 percent confidence interval:\n", | |
| " 94.11819 94.29314\n", | |
| "sample estimates:\n", | |
| "mean of x \n", | |
| " 94.20567 \n" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "t.test(melt$meltpoint, mu = 94.4)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Question 3.\n", | |
| "We can see the confidence intervals for .95 and .99 above or we can access them directly from the result of the t.test as below. We use the $ operator to access a component of the test result." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 96, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stderr", | |
| "output_type": "stream", | |
| "text": [ | |
| "95% interval:\n" | |
| ] | |
| }, | |
| { | |
| "data": { | |
| "text/html": [ | |
| "<ol class=list-inline>\n", | |
| "\t<li>94.1181949058223</li>\n", | |
| "\t<li>94.293138427511</li>\n", | |
| "</ol>\n" | |
| ], | |
| "text/latex": [ | |
| "\\begin{enumerate*}\n", | |
| "\\item 94.1181949058223\n", | |
| "\\item 94.293138427511\n", | |
| "\\end{enumerate*}\n" | |
| ], | |
| "text/markdown": [ | |
| "1. 94.1181949058223\n", | |
| "2. 94.293138427511\n", | |
| "\n", | |
| "\n" | |
| ], | |
| "text/plain": [ | |
| "[1] 94.11819 94.29314\n", | |
| "attr(,\"conf.level\")\n", | |
| "[1] 0.95" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| }, | |
| { | |
| "name": "stderr", | |
| "output_type": "stream", | |
| "text": [ | |
| "99% interval:\n" | |
| ] | |
| }, | |
| { | |
| "data": { | |
| "text/html": [ | |
| "<ol class=list-inline>\n", | |
| "\t<li>94.0893102135013</li>\n", | |
| "\t<li>94.322023119832</li>\n", | |
| "</ol>\n" | |
| ], | |
| "text/latex": [ | |
| "\\begin{enumerate*}\n", | |
| "\\item 94.0893102135013\n", | |
| "\\item 94.322023119832\n", | |
| "\\end{enumerate*}\n" | |
| ], | |
| "text/markdown": [ | |
| "1. 94.0893102135013\n", | |
| "2. 94.322023119832\n", | |
| "\n", | |
| "\n" | |
| ], | |
| "text/plain": [ | |
| "[1] 94.08931 94.32202\n", | |
| "attr(,\"conf.level\")\n", | |
| "[1] 0.99" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "message(\"95% interval:\")\n", | |
| "t.test(melt$meltpoint, mu = 94.4, conf.level=.95)$conf.int\n", | |
| "message(\"99% interval:\")\n", | |
| "t.test(melt$meltpoint, mu = 94.4, conf.level=.99)$conf.int" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "# Week 3" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Question 1.\n", | |
| "Lets read out light data set and check the structure." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 97, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stderr", | |
| "output_type": "stream", | |
| "text": [ | |
| "Warning message in file(file, \"rt\"):\n", | |
| "“cannot open file 'light.dat.txt': No such file or directory”" | |
| ] | |
| }, | |
| { | |
| "ename": "ERROR", | |
| "evalue": "Error in file(file, \"rt\"): cannot open the connection\n", | |
| "execution_count": 97, | |
| "output_type": "error", | |
| "traceback": [ | |
| "Error in file(file, \"rt\"): cannot open the connection\nTraceback:\n", | |
| "1. read.table(\"light.dat.txt\", header = T)", | |
| "2. file(file, \"rt\")" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "light = read.table('light.dat.txt', header=T)\n", | |
| "head(light)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Question 1. \n", | |
| "We have 2 samples brand 1 and brand 2. First we will check the normality of data using QQ plot." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "par(mfrow=c(2,2))\n", | |
| "qqnorm(light$Brand1)\n", | |
| "qqnorm(light$Brand2)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Both samples appear approximately normal so two sample T tests can be appropriate but we must check the standard deviation of samples to determine which test to use. We can use R functions max() and min() to ensure we divide the larger value by the smaller value." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "sd1 = sd(light$Brand1)\n", | |
| "sd2 = sd(light$Brand2)\n", | |
| "max(sd1, sd2)/ min(sd1, sd2)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Standard devation ratio is near 1, much less than our rule of thumb: 2 so we will use a two sample t-test (not modified), we indicate that it is not a modified test by passing the optional argument var.equal=TRUE.\n", | |
| "\n", | |
| "\n", | |
| "Null hypothesis: The means are equal between brand 1 and brand 2.\n", | |
| "\n", | |
| "\n", | |
| "Alternative hypothesis: The means are not equal.\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "t.test(light$Brand1, y= light$Brand2, var.equal=TRUE)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Conclusion: We will reject the null hypothesis at the .05 significance level bceause our P value is 0.03725, which is less than .05.\n", | |
| "\n", | |
| "The brands do not have equal lumens." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Question 2." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Lets read our farm data and check the structure." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "farm = read.table('farm.dat', header=T)\n", | |
| "head(farm, 10)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "We know that we have data from 2 similar fields at each farm, indicating that a paired test might be appropriate. We also know that we are looking specifically for an increase so a one sided test is required.\n", | |
| "\n", | |
| "Lets get the difference between our paired values by subtracting the yield of values that satisfy 'plot == \"unsprayed\"' from the yield of values that satisfy 'plot == \"sprayed\"'.\n", | |
| "\n", | |
| "Then we will look at our differences to make sure they are sane." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "difference =farm$yield[farm$plot == \"sprayed\"] - farm$yield[farm$plot == \"unsprayed\"]\n", | |
| "head(difference)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "qqnorm(difference)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Differences look approximately normal so we can conduct tests on this data. \n", | |
| "\n", | |
| "We use the ~ operator to say that we want the yield column explained by the plot column.\n", | |
| "\n", | |
| "We must pass 'paired=TRUE' to ensure a paired test and 'alternative=\"greater\"' to ensure a one sided test." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "t.test(farm$yield ~ farm$plot, paired=TRUE, alternative=\"greater\")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "We can also do this by separating our data into 2 vectors: sprayed and unsprayed then performing the same test." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "sprayed = farm[farm$plot== \"sprayed\",\"yield\"]\n", | |
| "unsprayed = farm[farm$plot== \"unsprayed\",\"yield\"]\n", | |
| "t.test(sprayed, unsprayed, paired=TRUE, alternative=\"greater\")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "We find the same result with the 2 different ways to do the same test in R." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Conclusion: We reject the null hypothesis with a significance level of .05. P-value = 0.0223\n", | |
| "\n", | |
| "The yield of the sprayed plots were greater than the yield of similar unsprayed plots." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Question 3.\n", | |
| "Lets get our dataset and look at the structure." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "fertile = read.table('fertile.dat', header=T)\n", | |
| "head(fertile)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "There are 2 samples but no indication that these are paired.\n", | |
| "\n", | |
| "Lets check the normality." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "qqnorm(fertile$fertile)\n", | |
| "qqnorm(fertile$nonfertile)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Both data sets appear approximately normal. Now we will check standard deviation ratio." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "max(sd(fertile$fertile), sd(fertile$nonfertile))/min(sd(fertile$fertile), sd(fertile$nonfertile))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Ratio of sd1/sd2 is more than 2. Do we have a large data set?" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "length(fertile$fertile)\n", | |
| "length(fertile$nonfertile)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Our deviation ratio is over 2 and our dataset is small so we will specify that var.equal=FALSE so conduct a modified (Welch) 2 sample T Test." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "t.test(fertile$fertile, fertile$nonfertile, var.equal=FALSE)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Conclusion: Our P value is 0.2129 so we do not reject the null hypothesis." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Other useful R" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## qt(Q, DOF)\n", | |
| "\n", | |
| "QT returns the Tobs or Critical value at a given percentile for a T distribution with given degrees of freedom.\n", | |
| "Use dof = Inf for a normal distribution.\n", | |
| "\n", | |
| "eg. calculating the critical value for an arbitrary confidence interval" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 1, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stderr", | |
| "output_type": "stream", | |
| "text": [ | |
| "conf: 0.97 low CV: -2.20149690107717 high CV: 2.20149690107717\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "#\n", | |
| "conf = .97\n", | |
| "alpha = 1 - conf\n", | |
| "dof = 100\n", | |
| "low_crit = qt(alpha/2, dof, lower.tail=TRUE)\n", | |
| "high_crit = qt(alpha/2, dof, lower.tail=FALSE)\n", | |
| "message(paste(\"conf:\", conf, \" low CV: \", low_crit, \" high CV: \", high_crit, sep=\" \"))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 26, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stderr", | |
| "output_type": "stream", | |
| "text": [ | |
| "conf: 0.99 low CV: -2.5758293035489 high CV: 2.5758293035489\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "conf = .99\n", | |
| "alpha = 1 - conf\n", | |
| "dof = Inf\n", | |
| "low_crit = qt(alpha/2, dof, lower.tail=TRUE)\n", | |
| "high_crit = qt(alpha/2, dof, lower.tail=FALSE)\n", | |
| "message(paste(\"conf:\", conf, \" low CV: \", low_crit, \" high CV: \", high_crit, sep=\" \"))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 43, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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v5RqUeTmFkhkScwnAoh2aQPuqvdIyseK+eaMjV+ml9qk4Q5bwv6dDFAPtpOP0GZ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\nw/3W64Gu43Qr/ad7xybQjm4GEjH4gtSjQckwCynDnck8+ZwjpCv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BG5t9xUgVqX+K4UwARjhaSLf7CHyQ4Pb6nc8W123MdCYAIxwtpGcD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\nRU5ErkJggg==", | |
| "text/plain": [ | |
| "plot without title" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data", | |
| "source": "R display func" | |
| } | |
| ], | |
| "source": [ | |
| "pvals = seq(0,1,len=200)\n", | |
| "plot(pvals, qt(pvals, Inf))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## pt(T, DOF)\n", | |
| "\n", | |
| "PT returns the probability of getting LESS THAN a given T obs at a specified degrees of freedom. That is the CDF.\n", | |
| "\n", | |
| "lower.tail = TRUE => Probability of LESS THAN a given T value. lower.tail = FALSE => Probability of GREATER THAN a given T value.\n", | |
| "\n", | |
| "eg. Calculating a P value from a given T obs." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 40, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "dof = 30\n", | |
| "tobs = 2.66\n", | |
| "\n", | |
| "P_val = pt(tobs, dof, lower.tail = FALSE)\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "We can also plot the **cumulative distribution function** for T using pt." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 41, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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WSMkdv6FiGCSEpM/EEpr8k9GUIChi4l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\n/g/Ow1l5sjdrWAAAAABJRU5ErkJggg==", | |
| "text/plain": [ | |
| "plot without title" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data", | |
| "source": "R display func" | |
| } | |
| ], | |
| "source": [ | |
| "tvals = seq(-4,4,len=200)\n", | |
| "plot(tvals, pt(tvals, Inf))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## dt(t, dof)\n", | |
| "\n", | |
| "Returns the height of the probability function at a given point or points.\n", | |
| "\n", | |
| "eg. We can graph the relative probability of a any T score for any T/Z distribution." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 39, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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Us2faMX3EyWB0UStwMMd5vJNWqRHI3l3FavNS+PMwcJJxELKJK4DeVPVDUELCEb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\nYgAAAABJRU5ErkJggg==", | |
| "text/plain": [ | |
| "plot without title" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data", | |
| "source": "R display func" | |
| } | |
| ], | |
| "source": [ | |
| "tvals = seq(-4,4,len=200)\n", | |
| "plot(tvals, dt(tvals, Inf))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [] | |
| } | |
| ], | |
| "metadata": { | |
| "kernelspec": { | |
| "display_name": "R", | |
| "language": "R", | |
| "name": "ir" | |
| }, | |
| "language_info": { | |
| "codemirror_mode": "r", | |
| "file_extension": ".r", | |
| "mimetype": "text/x-r-source", | |
| "name": "R", | |
| "pygments_lexer": "r", | |
| "version": "3.5.1" | |
| } | |
| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 2 | |
| } |
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