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<!DOCTYPE html>
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<title>C Statistical tables | Fundamental statistical concepts and techniques in the biological and environmental sciences: With jamovi</title>
<meta name="description" content="This is an introductory statistics textbook for students in the biological and environmental sciences with examples using jamovi statistical software." />
<meta name="generator" content="bookdown 0.37 and GitBook 2.6.7" />
<meta property="og:title" content="C Statistical tables | Fundamental statistical concepts and techniques in the biological and environmental sciences: With jamovi" />
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<meta property="og:description" content="This is an introductory statistics textbook for students in the biological and environmental sciences with examples using jamovi statistical software." />
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<meta name="twitter:title" content="C Statistical tables | Fundamental statistical concepts and techniques in the biological and environmental sciences: With jamovi" />
<meta name="twitter:description" content="This is an introductory statistics textbook for students in the biological and environmental sciences with examples using jamovi statistical software." />
<meta name="author" content="Brad Duthie" />
<meta name="date" content="2024-02-11" />
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<div class="book without-animation with-summary font-size-2 font-family-1" data-basepath=".">
<div class="book-summary">
<nav role="navigation">
<ul class="summary">
<li><a href="./">Statistical Techniques</a></li>
<li class="divider"></li>
<li class="chapter" data-level="" data-path="index.html"><a href="index.html"><i class="fa fa-check"></i>Preface</a>
<ul>
<li class="chapter" data-level="" data-path="index.html"><a href="index.html#why-this-book-is-important"><i class="fa fa-check"></i>Why this book is important</a>
<ul>
<li class="chapter" data-level="" data-path="index.html"><a href="index.html#book_chapters"><i class="fa fa-check"></i>Book chapters</a></li>
</ul></li>
<li class="chapter" data-level="" data-path="index.html"><a href="index.html#jamovi"><i class="fa fa-check"></i>Jamovi statistical software</a></li>
</ul></li>
<li class="part"><span><b>I Background mathematics and data organisation</b></span></li>
<li class="chapter" data-level="" data-path="Week1.html"><a href="Week1.html"><i class="fa fa-check"></i>Part I summary</a></li>
<li class="chapter" data-level="1" data-path="Chapter_1.html"><a href="Chapter_1.html"><i class="fa fa-check"></i><b>1</b> Background mathematics</a>
<ul>
<li class="chapter" data-level="1.1" data-path="Chapter_1.html"><a href="Chapter_1.html#numbers-and-operations"><i class="fa fa-check"></i><b>1.1</b> Numbers and operations</a></li>
<li class="chapter" data-level="1.2" data-path="Chapter_1.html"><a href="Chapter_1.html#logarithms"><i class="fa fa-check"></i><b>1.2</b> Logarithms</a></li>
<li class="chapter" data-level="1.3" data-path="Chapter_1.html"><a href="Chapter_1.html#order-of-operations"><i class="fa fa-check"></i><b>1.3</b> Order of operations</a></li>
</ul></li>
<li class="chapter" data-level="2" data-path="Chapter_2.html"><a href="Chapter_2.html"><i class="fa fa-check"></i><b>2</b> Data organisation</a>
<ul>
<li class="chapter" data-level="2.1" data-path="Chapter_2.html"><a href="Chapter_2.html#tidy-data"><i class="fa fa-check"></i><b>2.1</b> Tidy data</a></li>
<li class="chapter" data-level="2.2" data-path="Chapter_2.html"><a href="Chapter_2.html#data-files"><i class="fa fa-check"></i><b>2.2</b> Data files</a></li>
<li class="chapter" data-level="2.3" data-path="Chapter_2.html"><a href="Chapter_2.html#managing-data-files"><i class="fa fa-check"></i><b>2.3</b> Managing data files</a></li>
</ul></li>
<li class="chapter" data-level="3" data-path="Chapter_3.html"><a href="Chapter_3.html"><i class="fa fa-check"></i><b>3</b> Practical: Preparing data</a>
<ul>
<li class="chapter" data-level="3.1" data-path="Chapter_3.html"><a href="Chapter_3.html#exercise-1-transferring-data-to-a-spreadsheet"><i class="fa fa-check"></i><b>3.1</b> Exercise 1: Transferring data to a spreadsheet</a></li>
<li class="chapter" data-level="3.2" data-path="Chapter_3.html"><a href="Chapter_3.html#exercise-2-making-spreadsheet-data-tidy"><i class="fa fa-check"></i><b>3.2</b> Exercise 2: Making spreadsheet data tidy</a></li>
<li class="chapter" data-level="3.3" data-path="Chapter_3.html"><a href="Chapter_3.html#exercise-3-making-data-tidy-again"><i class="fa fa-check"></i><b>3.3</b> Exercise 3: Making data tidy again</a></li>
<li class="chapter" data-level="3.4" data-path="Chapter_3.html"><a href="Chapter_3.html#exercise-4-tidy-data-and-spreadsheet-calculations"><i class="fa fa-check"></i><b>3.4</b> Exercise 4: Tidy data and spreadsheet calculations</a></li>
<li class="chapter" data-level="3.5" data-path="Chapter_3.html"><a href="Chapter_3.html#summary"><i class="fa fa-check"></i><b>3.5</b> Summary</a></li>
</ul></li>
<li class="part"><span><b>II Statistical concepts</b></span></li>
<li class="chapter" data-level="" data-path="Week2.html"><a href="Week2.html"><i class="fa fa-check"></i>Part II summary</a></li>
<li class="chapter" data-level="4" data-path="Chapter_4.html"><a href="Chapter_4.html"><i class="fa fa-check"></i><b>4</b> Populations and samples</a></li>
<li class="chapter" data-level="5" data-path="Chapter_5.html"><a href="Chapter_5.html"><i class="fa fa-check"></i><b>5</b> Types of variables</a></li>
<li class="chapter" data-level="6" data-path="Chapter_6.html"><a href="Chapter_6.html"><i class="fa fa-check"></i><b>6</b> Accuracy, precision, and units</a>
<ul>
<li class="chapter" data-level="6.1" data-path="Chapter_6.html"><a href="Chapter_6.html#accuracy"><i class="fa fa-check"></i><b>6.1</b> Accuracy</a></li>
<li class="chapter" data-level="6.2" data-path="Chapter_6.html"><a href="Chapter_6.html#precision"><i class="fa fa-check"></i><b>6.2</b> Precision</a></li>
<li class="chapter" data-level="6.3" data-path="Chapter_6.html"><a href="Chapter_6.html#systems-of-units"><i class="fa fa-check"></i><b>6.3</b> Systems of units</a></li>
<li class="chapter" data-level="6.4" data-path="Chapter_6.html"><a href="Chapter_6.html#other-examples-of-units"><i class="fa fa-check"></i><b>6.4</b> Other examples of units</a>
<ul>
<li class="chapter" data-level="6.4.1" data-path="Chapter_6.html"><a href="Chapter_6.html#units-of-density"><i class="fa fa-check"></i><b>6.4.1</b> Units of density</a></li>
<li class="chapter" data-level="6.4.2" data-path="Chapter_6.html"><a href="Chapter_6.html#mass-of-metal-discharged-from-a-catchment"><i class="fa fa-check"></i><b>6.4.2</b> Mass of metal discharged from a catchment</a></li>
<li class="chapter" data-level="6.4.3" data-path="Chapter_6.html"><a href="Chapter_6.html#soil-carbon-inventories"><i class="fa fa-check"></i><b>6.4.3</b> Soil carbon inventories</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="7" data-path="Chapter_7.html"><a href="Chapter_7.html"><i class="fa fa-check"></i><b>7</b> Uncertainty propagation</a>
<ul>
<li class="chapter" data-level="7.1" data-path="Chapter_7.html"><a href="Chapter_7.html#adding-or-subtracting-errors"><i class="fa fa-check"></i><b>7.1</b> Adding or subtracting errors</a></li>
<li class="chapter" data-level="7.2" data-path="Chapter_7.html"><a href="Chapter_7.html#multiplying-or-dividing-errors"><i class="fa fa-check"></i><b>7.2</b> Multiplying or dividing errors</a></li>
<li class="chapter" data-level="7.3" data-path="Chapter_7.html"><a href="Chapter_7.html#applying-formulas-for-combining-errors"><i class="fa fa-check"></i><b>7.3</b> Applying formulas for combining errors</a></li>
</ul></li>
<li class="chapter" data-level="8" data-path="Chapter_8.html"><a href="Chapter_8.html"><i class="fa fa-check"></i><b>8</b> Practical. Introduction to jamovi</a>
<ul>
<li class="chapter" data-level="8.1" data-path="Chapter_8.html"><a href="Chapter_8.html#summary_statistics_02"><i class="fa fa-check"></i><b>8.1</b> Exercise for summary statistics</a></li>
<li class="chapter" data-level="8.2" data-path="Chapter_8.html"><a href="Chapter_8.html#transforming_variables_02"><i class="fa fa-check"></i><b>8.2</b> Exercise on transforming variables</a></li>
<li class="chapter" data-level="8.3" data-path="Chapter_8.html"><a href="Chapter_8.html#computing_variables_02"><i class="fa fa-check"></i><b>8.3</b> Exercise on computing variables</a></li>
<li class="chapter" data-level="8.4" data-path="Chapter_8.html"><a href="Chapter_8.html#summary-1"><i class="fa fa-check"></i><b>8.4</b> Summary</a></li>
</ul></li>
<li class="part"><span><b>III Summary statistics</b></span></li>
<li class="chapter" data-level="" data-path="Week3.html"><a href="Week3.html"><i class="fa fa-check"></i>Part III Overview</a></li>
<li class="chapter" data-level="9" data-path="Chapter_9.html"><a href="Chapter_9.html"><i class="fa fa-check"></i><b>9</b> Decimal places, significant figures, and rounding</a>
<ul>
<li class="chapter" data-level="9.1" data-path="Chapter_9.html"><a href="Chapter_9.html#decimal-places-and-significant-figures"><i class="fa fa-check"></i><b>9.1</b> Decimal places and significant figures</a></li>
<li class="chapter" data-level="9.2" data-path="Chapter_9.html"><a href="Chapter_9.html#rounding"><i class="fa fa-check"></i><b>9.2</b> Rounding</a></li>
</ul></li>
<li class="chapter" data-level="10" data-path="Chapter_10.html"><a href="Chapter_10.html"><i class="fa fa-check"></i><b>10</b> Graphs</a>
<ul>
<li class="chapter" data-level="10.1" data-path="Chapter_10.html"><a href="Chapter_10.html#histograms"><i class="fa fa-check"></i><b>10.1</b> Histograms</a></li>
<li class="chapter" data-level="10.2" data-path="Chapter_10.html"><a href="Chapter_10.html#barplots-and-pie-charts"><i class="fa fa-check"></i><b>10.2</b> Barplots and pie charts</a></li>
<li class="chapter" data-level="10.3" data-path="Chapter_10.html"><a href="Chapter_10.html#box-whisker-plots"><i class="fa fa-check"></i><b>10.3</b> Box-whisker plots</a></li>
</ul></li>
<li class="chapter" data-level="11" data-path="Chapter_11.html"><a href="Chapter_11.html"><i class="fa fa-check"></i><b>11</b> Measures of central tendency</a>
<ul>
<li class="chapter" data-level="11.1" data-path="Chapter_11.html"><a href="Chapter_11.html#the-mean"><i class="fa fa-check"></i><b>11.1</b> The mean</a></li>
<li class="chapter" data-level="11.2" data-path="Chapter_11.html"><a href="Chapter_11.html#the-mode"><i class="fa fa-check"></i><b>11.2</b> The mode</a></li>
<li class="chapter" data-level="11.3" data-path="Chapter_11.html"><a href="Chapter_11.html#the-median-and-quantiles"><i class="fa fa-check"></i><b>11.3</b> The median and quantiles</a></li>
</ul></li>
<li class="chapter" data-level="12" data-path="Chapter_12.html"><a href="Chapter_12.html"><i class="fa fa-check"></i><b>12</b> Measures of spread</a>
<ul>
<li class="chapter" data-level="12.1" data-path="Chapter_12.html"><a href="Chapter_12.html#the-range"><i class="fa fa-check"></i><b>12.1</b> The range</a></li>
<li class="chapter" data-level="12.2" data-path="Chapter_12.html"><a href="Chapter_12.html#the-inter-quartile-range"><i class="fa fa-check"></i><b>12.2</b> The inter-quartile range</a></li>
<li class="chapter" data-level="12.3" data-path="Chapter_12.html"><a href="Chapter_12.html#the-variance"><i class="fa fa-check"></i><b>12.3</b> The variance</a></li>
<li class="chapter" data-level="12.4" data-path="Chapter_12.html"><a href="Chapter_12.html#the-standard-deviation"><i class="fa fa-check"></i><b>12.4</b> The standard deviation</a></li>
<li class="chapter" data-level="12.5" data-path="Chapter_12.html"><a href="Chapter_12.html#the-coefficient-of-variation"><i class="fa fa-check"></i><b>12.5</b> The coefficient of variation</a></li>
<li class="chapter" data-level="12.6" data-path="Chapter_12.html"><a href="Chapter_12.html#the-standard-error"><i class="fa fa-check"></i><b>12.6</b> The standard error</a></li>
</ul></li>
<li class="chapter" data-level="13" data-path="Chapter_13.html"><a href="Chapter_13.html"><i class="fa fa-check"></i><b>13</b> <em>Practical</em>. Plotting and statistical summaries in jamovi</a>
<ul>
<li class="chapter" data-level="13.1" data-path="Chapter_13.html"><a href="Chapter_13.html#reorganise-the-dataset-into-a-tidy-format"><i class="fa fa-check"></i><b>13.1</b> Reorganise the dataset into a tidy format</a></li>
<li class="chapter" data-level="13.2" data-path="Chapter_13.html"><a href="Chapter_13.html#histograms-and-box-whisker-plots"><i class="fa fa-check"></i><b>13.2</b> Histograms and box-whisker plots</a></li>
<li class="chapter" data-level="13.3" data-path="Chapter_13.html"><a href="Chapter_13.html#calculate-summary-statistics"><i class="fa fa-check"></i><b>13.3</b> Calculate summary statistics</a></li>
<li class="chapter" data-level="13.4" data-path="Chapter_13.html"><a href="Chapter_13.html#reporting-decimals-and-significant-figures"><i class="fa fa-check"></i><b>13.4</b> Reporting decimals and significant figures</a></li>
<li class="chapter" data-level="13.5" data-path="Chapter_13.html"><a href="Chapter_13.html#comparing-across-sites"><i class="fa fa-check"></i><b>13.5</b> Comparing across sites</a></li>
</ul></li>
<li class="part"><span><b>IV Probability models and the Central Limit Theorem</b></span></li>
<li class="chapter" data-level="" data-path="Week4.html"><a href="Week4.html"><i class="fa fa-check"></i>Part IV Overview</a></li>
<li class="chapter" data-level="14" data-path="Chapter_14.html"><a href="Chapter_14.html"><i class="fa fa-check"></i><b>14</b> Introduction to probability models</a>
<ul>
<li class="chapter" data-level="14.1" data-path="Chapter_14.html"><a href="Chapter_14.html#an-instructive-example"><i class="fa fa-check"></i><b>14.1</b> An instructive example</a></li>
<li class="chapter" data-level="14.2" data-path="Chapter_14.html"><a href="Chapter_14.html#biological-applications"><i class="fa fa-check"></i><b>14.2</b> Biological applications</a></li>
<li class="chapter" data-level="14.3" data-path="Chapter_14.html"><a href="Chapter_14.html#sampling-with-and-without-replacement"><i class="fa fa-check"></i><b>14.3</b> Sampling with and without replacement</a></li>
<li class="chapter" data-level="14.4" data-path="Chapter_14.html"><a href="Chapter_14.html#probability-distributions"><i class="fa fa-check"></i><b>14.4</b> Probability distributions</a>
<ul>
<li class="chapter" data-level="14.4.1" data-path="Chapter_14.html"><a href="Chapter_14.html#binomial-distribution"><i class="fa fa-check"></i><b>14.4.1</b> Binomial distribution</a></li>
<li class="chapter" data-level="14.4.2" data-path="Chapter_14.html"><a href="Chapter_14.html#poisson-distribution"><i class="fa fa-check"></i><b>14.4.2</b> Poisson distribution</a></li>
<li class="chapter" data-level="14.4.3" data-path="Chapter_14.html"><a href="Chapter_14.html#uniform-distribution"><i class="fa fa-check"></i><b>14.4.3</b> Uniform distribution</a></li>
<li class="chapter" data-level="14.4.4" data-path="Chapter_14.html"><a href="Chapter_14.html#normal-distribution"><i class="fa fa-check"></i><b>14.4.4</b> Normal distribution</a></li>
</ul></li>
<li class="chapter" data-level="14.5" data-path="Chapter_14.html"><a href="Chapter_14.html#summary-2"><i class="fa fa-check"></i><b>14.5</b> Summary</a></li>
</ul></li>
<li class="chapter" data-level="15" data-path="Chapter_15.html"><a href="Chapter_15.html"><i class="fa fa-check"></i><b>15</b> The Central Limit Theorem (CLT)</a>
<ul>
<li class="chapter" data-level="15.1" data-path="Chapter_15.html"><a href="Chapter_15.html#the-distribution-of-means-is-normal"><i class="fa fa-check"></i><b>15.1</b> The distribution of means is normal</a></li>
<li class="chapter" data-level="15.2" data-path="Chapter_15.html"><a href="Chapter_15.html#probability-and-z-scores"><i class="fa fa-check"></i><b>15.2</b> Probability and z-scores</a></li>
</ul></li>
<li class="chapter" data-level="16" data-path="Chapter_16.html"><a href="Chapter_16.html"><i class="fa fa-check"></i><b>16</b> <em>Practical</em>. Probability and simulation</a>
<ul>
<li class="chapter" data-level="16.1" data-path="Chapter_16.html"><a href="Chapter_16.html#probabilities-from-a-dataset"><i class="fa fa-check"></i><b>16.1</b> Probabilities from a dataset</a></li>
<li class="chapter" data-level="16.2" data-path="Chapter_16.html"><a href="Chapter_16.html#probabilities-from-a-normal-distribution"><i class="fa fa-check"></i><b>16.2</b> Probabilities from a normal distribution</a></li>
<li class="chapter" data-level="16.3" data-path="Chapter_16.html"><a href="Chapter_16.html#central-limit-theorem"><i class="fa fa-check"></i><b>16.3</b> Central limit theorem</a></li>
</ul></li>
<li class="part"><span><b>V Statistical inference</b></span></li>
<li class="chapter" data-level="" data-path="Week5.html"><a href="Week5.html"><i class="fa fa-check"></i>Part V Overview</a></li>
<li class="chapter" data-level="17" data-path="Chapter_17.html"><a href="Chapter_17.html"><i class="fa fa-check"></i><b>17</b> Confidence intervals (CIs)</a>
<ul>
<li class="chapter" data-level="17.1" data-path="Chapter_17.html"><a href="Chapter_17.html#normal-distribution-cis"><i class="fa fa-check"></i><b>17.1</b> Normal distribution CIs</a></li>
<li class="chapter" data-level="17.2" data-path="Chapter_17.html"><a href="Chapter_17.html#binomial-distribution-cis"><i class="fa fa-check"></i><b>17.2</b> Binomial distribution CIs</a></li>
</ul></li>
<li class="chapter" data-level="18" data-path="Chapter_18.html"><a href="Chapter_18.html"><i class="fa fa-check"></i><b>18</b> The t-interval</a></li>
<li class="chapter" data-level="19" data-path="Chapter_19.html"><a href="Chapter_19.html"><i class="fa fa-check"></i><b>19</b> <em>Practical</em>. z- and t- intervals</a>
<ul>
<li class="chapter" data-level="19.1" data-path="Chapter_19.html"><a href="Chapter_19.html#confidence-intervals-with-distraction"><i class="fa fa-check"></i><b>19.1</b> Confidence intervals with distrACTION</a></li>
<li class="chapter" data-level="19.2" data-path="Chapter_19.html"><a href="Chapter_19.html#confidence-intervals-from-z--and-t-scores"><i class="fa fa-check"></i><b>19.2</b> Confidence intervals from z- and t-scores</a></li>
<li class="chapter" data-level="19.3" data-path="Chapter_19.html"><a href="Chapter_19.html#confidence-intervals-for-different-sample-sizes-t--and-z-"><i class="fa fa-check"></i><b>19.3</b> Confidence intervals for different sample sizes (t- and z-)</a></li>
<li class="chapter" data-level="19.4" data-path="Chapter_19.html"><a href="Chapter_19.html#proportion-confidence-intervals"><i class="fa fa-check"></i><b>19.4</b> Proportion confidence intervals</a></li>
<li class="chapter" data-level="19.5" data-path="Chapter_19.html"><a href="Chapter_19.html#another-proportion-confidence-interval"><i class="fa fa-check"></i><b>19.5</b> Another proportion confidence interval</a></li>
</ul></li>
<li class="part"><span><b>VI Hypothesis testing</b></span></li>
<li class="chapter" data-level="" data-path="Week6.html"><a href="Week6.html"><i class="fa fa-check"></i>Part VI Overview</a></li>
<li class="chapter" data-level="20" data-path="Chapter_20.html"><a href="Chapter_20.html"><i class="fa fa-check"></i><b>20</b> What is hypothesis testing?</a>
<ul>
<li class="chapter" data-level="20.1" data-path="Chapter_20.html"><a href="Chapter_20.html#how-ridiculous-is-our-hypothesis"><i class="fa fa-check"></i><b>20.1</b> How ridiculous is our hypothesis?</a></li>
<li class="chapter" data-level="20.2" data-path="Chapter_20.html"><a href="Chapter_20.html#statistical-hypothesis-testing"><i class="fa fa-check"></i><b>20.2</b> Statistical hypothesis testing</a></li>
<li class="chapter" data-level="20.3" data-path="Chapter_20.html"><a href="Chapter_20.html#p-values-false-positives-and-power"><i class="fa fa-check"></i><b>20.3</b> P-values, false positives, and power</a></li>
</ul></li>
<li class="chapter" data-level="21" data-path="Chapter_21.html"><a href="Chapter_21.html"><i class="fa fa-check"></i><b>21</b> The t-test</a>
<ul>
<li class="chapter" data-level="21.1" data-path="Chapter_21.html"><a href="Chapter_21.html#one-sample-t-test"><i class="fa fa-check"></i><b>21.1</b> One sample t-test</a></li>
<li class="chapter" data-level="21.2" data-path="Chapter_21.html"><a href="Chapter_21.html#independent-samples-t-test"><i class="fa fa-check"></i><b>21.2</b> Independent samples t-test</a></li>
<li class="chapter" data-level="21.3" data-path="Chapter_21.html"><a href="Chapter_21.html#paired-sample-t-test"><i class="fa fa-check"></i><b>21.3</b> Paired sample t-test</a></li>
<li class="chapter" data-level="21.4" data-path="Chapter_21.html"><a href="Chapter_21.html#assumptions-of-t-tests"><i class="fa fa-check"></i><b>21.4</b> Assumptions of t-tests</a></li>
<li class="chapter" data-level="21.5" data-path="Chapter_21.html"><a href="Chapter_21.html#non-parametric-alternatives"><i class="fa fa-check"></i><b>21.5</b> Non-parametric alternatives</a>
<ul>
<li class="chapter" data-level="21.5.1" data-path="Chapter_21.html"><a href="Chapter_21.html#wilcoxon-test"><i class="fa fa-check"></i><b>21.5.1</b> Wilcoxon test</a></li>
<li class="chapter" data-level="21.5.2" data-path="Chapter_21.html"><a href="Chapter_21.html#mann-whitney-u-test"><i class="fa fa-check"></i><b>21.5.2</b> Mann-Whitney U test</a></li>
</ul></li>
<li class="chapter" data-level="21.6" data-path="Chapter_21.html"><a href="Chapter_21.html#summary-3"><i class="fa fa-check"></i><b>21.6</b> Summary</a></li>
</ul></li>
<li class="chapter" data-level="22" data-path="Chapter_22.html"><a href="Chapter_22.html"><i class="fa fa-check"></i><b>22</b> <em>Practical</em>. Hypothesis testing and t-tests</a>
<ul>
<li class="chapter" data-level="22.1" data-path="Chapter_22.html"><a href="Chapter_22.html#exercise-on-a-simple-one-sample-t-test"><i class="fa fa-check"></i><b>22.1</b> Exercise on a simple one sample t-test</a></li>
<li class="chapter" data-level="22.2" data-path="Chapter_22.html"><a href="Chapter_22.html#exercise-on-a-paired-t-test"><i class="fa fa-check"></i><b>22.2</b> Exercise on a paired t-test</a></li>
<li class="chapter" data-level="22.3" data-path="Chapter_22.html"><a href="Chapter_22.html#wilcoxon-test-1"><i class="fa fa-check"></i><b>22.3</b> Wilcoxon test</a></li>
<li class="chapter" data-level="22.4" data-path="Chapter_22.html"><a href="Chapter_22.html#independent-samples-t-test-1"><i class="fa fa-check"></i><b>22.4</b> Independent samples t-test</a></li>
<li class="chapter" data-level="22.5" data-path="Chapter_22.html"><a href="Chapter_22.html#mann-whitney-u-test-1"><i class="fa fa-check"></i><b>22.5</b> Mann-Whitney U Test</a></li>
</ul></li>
<li class="part"><span><b>VII Analysis of Variance (ANOVA)</b></span></li>
<li class="chapter" data-level="" data-path="Week8.html"><a href="Week8.html"><i class="fa fa-check"></i>Part VII Overview</a></li>
<li class="chapter" data-level="23" data-path="Chapter_23.html"><a href="Chapter_23.html"><i class="fa fa-check"></i><b>23</b> Analysis of variance</a>
<ul>
<li class="chapter" data-level="23.1" data-path="Chapter_23.html"><a href="Chapter_23.html#the-f-distribution"><i class="fa fa-check"></i><b>23.1</b> The F-distribution</a></li>
<li class="chapter" data-level="23.2" data-path="Chapter_23.html"><a href="Chapter_23.html#one-way-anova"><i class="fa fa-check"></i><b>23.2</b> One-way ANOVA</a>
<ul>
<li class="chapter" data-level="23.2.1" data-path="Chapter_23.html"><a href="Chapter_23.html#anova-mean-variance-among-groups"><i class="fa fa-check"></i><b>23.2.1</b> ANOVA mean variance among groups</a></li>
<li class="chapter" data-level="23.2.2" data-path="Chapter_23.html"><a href="Chapter_23.html#anova-mean-variance-within-groups"><i class="fa fa-check"></i><b>23.2.2</b> ANOVA mean variance within groups</a></li>
<li class="chapter" data-level="23.2.3" data-path="Chapter_23.html"><a href="Chapter_23.html#anova-f-statistic-calculation"><i class="fa fa-check"></i><b>23.2.3</b> ANOVA F statistic calculation</a></li>
</ul></li>
<li class="chapter" data-level="23.3" data-path="Chapter_23.html"><a href="Chapter_23.html#assumptions-of-anova"><i class="fa fa-check"></i><b>23.3</b> Assumptions of ANOVA</a></li>
</ul></li>
<li class="chapter" data-level="24" data-path="Chapter_24.html"><a href="Chapter_24.html"><i class="fa fa-check"></i><b>24</b> Multiple comparisons</a></li>
<li class="chapter" data-level="25" data-path="Chapter_25.html"><a href="Chapter_25.html"><i class="fa fa-check"></i><b>25</b> Kruskall-Wallis H test</a></li>
<li class="chapter" data-level="26" data-path="Chapter_26.html"><a href="Chapter_26.html"><i class="fa fa-check"></i><b>26</b> Two-way ANOVA</a></li>
<li class="chapter" data-level="27" data-path="Chapter_27.html"><a href="Chapter_27.html"><i class="fa fa-check"></i><b>27</b> <em>Practical</em>. ANOVA and associated tests</a>
<ul>
<li class="chapter" data-level="27.1" data-path="Chapter_27.html"><a href="Chapter_27.html#one-way-anova-site"><i class="fa fa-check"></i><b>27.1</b> One-way ANOVA (site)</a></li>
<li class="chapter" data-level="27.2" data-path="Chapter_27.html"><a href="Chapter_27.html#one-way-anova-profile"><i class="fa fa-check"></i><b>27.2</b> One-way ANOVA (profile)</a></li>
<li class="chapter" data-level="27.3" data-path="Chapter_27.html"><a href="Chapter_27.html#multiple-comparisons"><i class="fa fa-check"></i><b>27.3</b> Multiple comparisons</a></li>
<li class="chapter" data-level="27.4" data-path="Chapter_27.html"><a href="Chapter_27.html#kruskall-wallis-h-test"><i class="fa fa-check"></i><b>27.4</b> Kruskall-Wallis H test</a></li>
<li class="chapter" data-level="27.5" data-path="Chapter_27.html"><a href="Chapter_27.html#two-way-anova"><i class="fa fa-check"></i><b>27.5</b> Two-way ANOVA</a></li>
</ul></li>
<li class="part"><span><b>VIII Counts and Correlation</b></span></li>
<li class="chapter" data-level="" data-path="Week9.html"><a href="Week9.html"><i class="fa fa-check"></i>Part VIII Overview</a></li>
<li class="chapter" data-level="28" data-path="Chapter_28.html"><a href="Chapter_28.html"><i class="fa fa-check"></i><b>28</b> Frequency and count data</a>
<ul>
<li class="chapter" data-level="28.1" data-path="Chapter_28.html"><a href="Chapter_28.html#the-chi-square-distribution"><i class="fa fa-check"></i><b>28.1</b> The Chi-square distribution</a></li>
<li class="chapter" data-level="28.2" data-path="Chapter_28.html"><a href="Chapter_28.html#chi-squared-goodness-of-fit"><i class="fa fa-check"></i><b>28.2</b> Chi-squared goodness of fit</a></li>
<li class="chapter" data-level="28.3" data-path="Chapter_28.html"><a href="Chapter_28.html#chi-squared-test-of-association"><i class="fa fa-check"></i><b>28.3</b> Chi-squared test of association</a></li>
</ul></li>
<li class="chapter" data-level="29" data-path="Chapter_29.html"><a href="Chapter_29.html"><i class="fa fa-check"></i><b>29</b> Correlation</a>
<ul>
<li class="chapter" data-level="29.1" data-path="Chapter_29.html"><a href="Chapter_29.html#scatterplots"><i class="fa fa-check"></i><b>29.1</b> Scatterplots</a></li>
<li class="chapter" data-level="29.2" data-path="Chapter_29.html"><a href="Chapter_29.html#the-correlation-coefficient"><i class="fa fa-check"></i><b>29.2</b> The correlation coefficient</a>
<ul>
<li class="chapter" data-level="29.2.1" data-path="Chapter_29.html"><a href="Chapter_29.html#pearson-product-moment-correlation-coefficient"><i class="fa fa-check"></i><b>29.2.1</b> Pearson product moment correlation coefficient</a></li>
<li class="chapter" data-level="29.2.2" data-path="Chapter_29.html"><a href="Chapter_29.html#spearman-rank-correlation-coefficient"><i class="fa fa-check"></i><b>29.2.2</b> Spearman rank correlation coefficient</a></li>
</ul></li>
<li class="chapter" data-level="29.3" data-path="Chapter_29.html"><a href="Chapter_29.html#correlation-hypothesis-testing"><i class="fa fa-check"></i><b>29.3</b> Correlation hypothesis testing</a></li>
</ul></li>
<li class="chapter" data-level="30" data-path="Chapter_30.html"><a href="Chapter_30.html"><i class="fa fa-check"></i><b>30</b> <em>Practical</em>. Analysis of counts and correlations</a>
<ul>
<li class="chapter" data-level="30.1" data-path="Chapter_30.html"><a href="Chapter_30.html#survival-goodness-of-fit"><i class="fa fa-check"></i><b>30.1</b> Survival goodness of fit</a></li>
<li class="chapter" data-level="30.2" data-path="Chapter_30.html"><a href="Chapter_30.html#colony-goodness-of-fit"><i class="fa fa-check"></i><b>30.2</b> Colony goodness of fit</a></li>
<li class="chapter" data-level="30.3" data-path="Chapter_30.html"><a href="Chapter_30.html#chi-square-test-of-association"><i class="fa fa-check"></i><b>30.3</b> Chi-Square test of association</a></li>
<li class="chapter" data-level="30.4" data-path="Chapter_30.html"><a href="Chapter_30.html#pearson-product-moment-correlation-test"><i class="fa fa-check"></i><b>30.4</b> Pearson product moment correlation test</a></li>
<li class="chapter" data-level="30.5" data-path="Chapter_30.html"><a href="Chapter_30.html#spearman-rank-correlation-test"><i class="fa fa-check"></i><b>30.5</b> Spearman rank correlation test</a></li>
<li class="chapter" data-level="30.6" data-path="Chapter_30.html"><a href="Chapter_30.html#untidy-goodness-of-fit"><i class="fa fa-check"></i><b>30.6</b> Untidy goodness of fit</a></li>
</ul></li>
<li class="part"><span><b>IX Linear Regression</b></span></li>
<li class="chapter" data-level="" data-path="Week10.html"><a href="Week10.html"><i class="fa fa-check"></i>Part IX Overview</a></li>
<li class="chapter" data-level="31" data-path="Chapter_31.html"><a href="Chapter_31.html"><i class="fa fa-check"></i><b>31</b> Simple linear regression</a>
<ul>
<li class="chapter" data-level="31.1" data-path="Chapter_31.html"><a href="Chapter_31.html#visual-interpretation-of-regression"><i class="fa fa-check"></i><b>31.1</b> Visual interpretation of regression</a></li>
<li class="chapter" data-level="31.2" data-path="Chapter_31.html"><a href="Chapter_31.html#intercepts-slopes-and-residuals"><i class="fa fa-check"></i><b>31.2</b> Intercepts, slopes, and residuals</a></li>
<li class="chapter" data-level="31.3" data-path="Chapter_31.html"><a href="Chapter_31.html#regression-coefficients"><i class="fa fa-check"></i><b>31.3</b> Regression coefficients</a></li>
<li class="chapter" data-level="31.4" data-path="Chapter_31.html"><a href="Chapter_31.html#regression-line-calculation"><i class="fa fa-check"></i><b>31.4</b> Regression line calculation</a></li>
<li class="chapter" data-level="31.5" data-path="Chapter_31.html"><a href="Chapter_31.html#coefficient-of-determination"><i class="fa fa-check"></i><b>31.5</b> Coefficient of determination</a></li>
<li class="chapter" data-level="31.6" data-path="Chapter_31.html"><a href="Chapter_31.html#regression-assumptions"><i class="fa fa-check"></i><b>31.6</b> Regression assumptions</a></li>
<li class="chapter" data-level="31.7" data-path="Chapter_31.html"><a href="Chapter_31.html#regression-hypothesis-testing"><i class="fa fa-check"></i><b>31.7</b> Regression hypothesis testing</a>
<ul>
<li class="chapter" data-level="31.7.1" data-path="Chapter_31.html"><a href="Chapter_31.html#overall-model-significance"><i class="fa fa-check"></i><b>31.7.1</b> Overall model significance</a></li>
<li class="chapter" data-level="31.7.2" data-path="Chapter_31.html"><a href="Chapter_31.html#significance-of-the-intercept"><i class="fa fa-check"></i><b>31.7.2</b> Significance of the intercept</a></li>
<li class="chapter" data-level="31.7.3" data-path="Chapter_31.html"><a href="Chapter_31.html#significance-of-the-slope"><i class="fa fa-check"></i><b>31.7.3</b> Significance of the slope</a></li>
<li class="chapter" data-level="31.7.4" data-path="Chapter_31.html"><a href="Chapter_31.html#simple-regression-output"><i class="fa fa-check"></i><b>31.7.4</b> Simple regression output</a></li>
</ul></li>
<li class="chapter" data-level="31.8" data-path="Chapter_31.html"><a href="Chapter_31.html#prediction-with-linear-models"><i class="fa fa-check"></i><b>31.8</b> Prediction with linear models</a></li>
<li class="chapter" data-level="31.9" data-path="Chapter_31.html"><a href="Chapter_31.html#conclusion"><i class="fa fa-check"></i><b>31.9</b> Conclusion</a></li>
</ul></li>
<li class="chapter" data-level="32" data-path="Chapter_32.html"><a href="Chapter_32.html"><i class="fa fa-check"></i><b>32</b> Multiple regression</a>
<ul>
<li class="chapter" data-level="32.1" data-path="Chapter_32.html"><a href="Chapter_32.html#adjusted-coefficient-of-determination"><i class="fa fa-check"></i><b>32.1</b> Adjusted coefficient of determination</a></li>
</ul></li>
<li class="chapter" data-level="33" data-path="Chapter_33.html"><a href="Chapter_33.html"><i class="fa fa-check"></i><b>33</b> <em>Practical</em>. Using regression</a>
<ul>
<li class="chapter" data-level="33.1" data-path="Chapter_33.html"><a href="Chapter_33.html#predicting-pyrogenic-carbon-from-soil-depth"><i class="fa fa-check"></i><b>33.1</b> Predicting pyrogenic carbon from soil depth</a></li>
<li class="chapter" data-level="33.2" data-path="Chapter_33.html"><a href="Chapter_33.html#predicting-pyrogenic-carbon-from-fire-frequency"><i class="fa fa-check"></i><b>33.2</b> Predicting pyrogenic carbon from fire frequency</a></li>
<li class="chapter" data-level="33.3" data-path="Chapter_33.html"><a href="Chapter_33.html#multiple-regression-depth-and-fire-frequency"><i class="fa fa-check"></i><b>33.3</b> Multiple regression depth and fire frequency</a></li>
<li class="chapter" data-level="33.4" data-path="Chapter_33.html"><a href="Chapter_33.html#large-multiple-regression"><i class="fa fa-check"></i><b>33.4</b> Large multiple regression</a></li>
<li class="chapter" data-level="33.5" data-path="Chapter_33.html"><a href="Chapter_33.html#predicting-temperature-from-fire-frequency"><i class="fa fa-check"></i><b>33.5</b> Predicting temperature from fire frequency</a></li>
</ul></li>
<li class="part"><span><b>X Randomisation approaches</b></span></li>
<li class="chapter" data-level="" data-path="Week11.html"><a href="Week11.html"><i class="fa fa-check"></i>Part X Overview</a></li>
<li class="chapter" data-level="34" data-path="Chapter_34.html"><a href="Chapter_34.html"><i class="fa fa-check"></i><b>34</b> Randomisation</a>
<ul>
<li class="chapter" data-level="34.1" data-path="Chapter_34.html"><a href="Chapter_34.html#summary-of-parametric-hypothesis-testing"><i class="fa fa-check"></i><b>34.1</b> Summary of parametric hypothesis testing</a></li>
<li class="chapter" data-level="34.2" data-path="Chapter_34.html"><a href="Chapter_34.html#randomisation-approach"><i class="fa fa-check"></i><b>34.2</b> Randomisation approach</a></li>
<li class="chapter" data-level="34.3" data-path="Chapter_34.html"><a href="Chapter_34.html#randomisation-for-hypothesis-testing"><i class="fa fa-check"></i><b>34.3</b> Randomisation for hypothesis testing</a></li>
<li class="chapter" data-level="34.4" data-path="Chapter_34.html"><a href="Chapter_34.html#randomisation-assumptions"><i class="fa fa-check"></i><b>34.4</b> Randomisation assumptions</a></li>
<li class="chapter" data-level="34.5" data-path="Chapter_34.html"><a href="Chapter_34.html#bootstrapping"><i class="fa fa-check"></i><b>34.5</b> Bootstrapping</a></li>
<li class="chapter" data-level="34.6" data-path="Chapter_34.html"><a href="Chapter_34.html#monte-carlo"><i class="fa fa-check"></i><b>34.6</b> Monte Carlo</a></li>
<li class="chapter" data-level="34.7" data-path="Chapter_34.html"><a href="Chapter_34.html#randomisation-conclusions"><i class="fa fa-check"></i><b>34.7</b> Randomisation conclusions</a></li>
</ul></li>
<li class="chapter" data-level="35" data-path="Chapter_35.html"><a href="Chapter_35.html"><i class="fa fa-check"></i><b>35</b> <em>Practical</em>. Using R</a>
<ul>
<li class="chapter" data-level="35.1" data-path="Chapter_35.html"><a href="Chapter_35.html#getting-used-to-the-r-interface"><i class="fa fa-check"></i><b>35.1</b> Getting used to the R interface</a></li>
<li class="chapter" data-level="35.2" data-path="Chapter_35.html"><a href="Chapter_35.html#assigning-variables-in-the-r-console"><i class="fa fa-check"></i><b>35.2</b> Assigning variables in the R console</a></li>
<li class="chapter" data-level="35.3" data-path="Chapter_35.html"><a href="Chapter_35.html#some-descriptive-statistics"><i class="fa fa-check"></i><b>35.3</b> Some descriptive statistics</a></li>
<li class="chapter" data-level="35.4" data-path="Chapter_35.html"><a href="Chapter_35.html#bootstrapping-confidence-intervals"><i class="fa fa-check"></i><b>35.4</b> Bootstrapping confidence intervals</a></li>
</ul></li>
<li class="part"><span><b>XI Experimental Design and Statistical Reporting</b></span></li>
<li class="chapter" data-level="" data-path="Week12.html"><a href="Week12.html"><i class="fa fa-check"></i>Part XI Overview</a></li>
<li class="chapter" data-level="36" data-path="Chapter_36.html"><a href="Chapter_36.html"><i class="fa fa-check"></i><b>36</b> Experimental design</a></li>
<li class="chapter" data-level="37" data-path="Chapter_37.html"><a href="Chapter_37.html"><i class="fa fa-check"></i><b>37</b> Reporting statistics</a>
<ul>
<li class="chapter" data-level="37.1" data-path="Chapter_37.html"><a href="Chapter_37.html#before-collecting-data"><i class="fa fa-check"></i><b>37.1</b> Before collecting data</a></li>
<li class="chapter" data-level="37.2" data-path="Chapter_37.html"><a href="Chapter_37.html#statistical-reporting"><i class="fa fa-check"></i><b>37.2</b> Statistical reporting</a>
<ul>
<li class="chapter" data-level="37.2.1" data-path="Chapter_37.html"><a href="Chapter_37.html#abstract"><i class="fa fa-check"></i><b>37.2.1</b> Abstract</a></li>
<li class="chapter" data-level="37.2.2" data-path="Chapter_37.html"><a href="Chapter_37.html#introduction"><i class="fa fa-check"></i><b>37.2.2</b> Introduction</a></li>
<li class="chapter" data-level="37.2.3" data-path="Chapter_37.html"><a href="Chapter_37.html#methods"><i class="fa fa-check"></i><b>37.2.3</b> Methods</a></li>
<li class="chapter" data-level="37.2.4" data-path="Chapter_37.html"><a href="Chapter_37.html#results"><i class="fa fa-check"></i><b>37.2.4</b> Results</a></li>
<li class="chapter" data-level="37.2.5" data-path="Chapter_37.html"><a href="Chapter_37.html#discussion"><i class="fa fa-check"></i><b>37.2.5</b> Discussion</a></li>
</ul></li>
<li class="chapter" data-level="37.3" data-path="Chapter_37.html"><a href="Chapter_37.html#figures-and-tables"><i class="fa fa-check"></i><b>37.3</b> Figures and tables</a>
<ul>
<li class="chapter" data-level="37.3.1" data-path="Chapter_37.html"><a href="Chapter_37.html#figures"><i class="fa fa-check"></i><b>37.3.1</b> Figures</a></li>
<li class="chapter" data-level="37.3.2" data-path="Chapter_37.html"><a href="Chapter_37.html#tables"><i class="fa fa-check"></i><b>37.3.2</b> Tables</a></li>
</ul></li>
<li class="chapter" data-level="37.4" data-path="Chapter_37.html"><a href="Chapter_37.html#statistical-tests"><i class="fa fa-check"></i><b>37.4</b> Statistical tests</a>
<ul>
<li class="chapter" data-level="37.4.1" data-path="Chapter_37.html"><a href="Chapter_37.html#reporting-t-tests"><i class="fa fa-check"></i><b>37.4.1</b> Reporting t-tests</a></li>
<li class="chapter" data-level="37.4.2" data-path="Chapter_37.html"><a href="Chapter_37.html#reporting-anova"><i class="fa fa-check"></i><b>37.4.2</b> Reporting ANOVA</a></li>
<li class="chapter" data-level="37.4.3" data-path="Chapter_37.html"><a href="Chapter_37.html#reporting-a-main-whitney-u-test"><i class="fa fa-check"></i><b>37.4.3</b> Reporting a Main-Whitney U test</a></li>
<li class="chapter" data-level="37.4.4" data-path="Chapter_37.html"><a href="Chapter_37.html#reporting-a-wilcoxon-signed-rank-test"><i class="fa fa-check"></i><b>37.4.4</b> Reporting a Wilcoxon signed-rank test</a></li>
<li class="chapter" data-level="37.4.5" data-path="Chapter_37.html"><a href="Chapter_37.html#reporting-chi-square-tests"><i class="fa fa-check"></i><b>37.4.5</b> Reporting Chi-square tests</a></li>
<li class="chapter" data-level="37.4.6" data-path="Chapter_37.html"><a href="Chapter_37.html#reporting-correlation-coefficients"><i class="fa fa-check"></i><b>37.4.6</b> Reporting correlation coefficients</a></li>
<li class="chapter" data-level="37.4.7" data-path="Chapter_37.html"><a href="Chapter_37.html#reporting-regressions"><i class="fa fa-check"></i><b>37.4.7</b> Reporting regressions</a></li>
</ul></li>
<li class="chapter" data-level="37.5" data-path="Chapter_37.html"><a href="Chapter_37.html#conclusions"><i class="fa fa-check"></i><b>37.5</b> Conclusions</a></li>
</ul></li>
<li class="chapter" data-level="38" data-path="Chapter_38.html"><a href="Chapter_38.html"><i class="fa fa-check"></i><b>38</b> <em>Practical</em>. Statistical techniques in R</a>
<ul>
<li class="chapter" data-level="38.1" data-path="Chapter_38.html"><a href="Chapter_38.html#working-with-a-data-set"><i class="fa fa-check"></i><b>38.1</b> Working with a data set</a></li>
<li class="chapter" data-level="38.2" data-path="Chapter_38.html"><a href="Chapter_38.html#familiar-statistical-tests-in-r"><i class="fa fa-check"></i><b>38.2</b> Familiar statistical tests in R</a>
<ul>
<li class="chapter" data-level="38.2.1" data-path="Chapter_38.html"><a href="Chapter_38.html#one-way-anova-in-r"><i class="fa fa-check"></i><b>38.2.1</b> One-way ANOVA in R</a></li>
<li class="chapter" data-level="38.2.2" data-path="Chapter_38.html"><a href="Chapter_38.html#two-way-anova-in-r"><i class="fa fa-check"></i><b>38.2.2</b> Two-way ANOVA in R</a></li>
<li class="chapter" data-level="38.2.3" data-path="Chapter_38.html"><a href="Chapter_38.html#chi-square-test-in-r"><i class="fa fa-check"></i><b>38.2.3</b> Chi-square test in R</a></li>
<li class="chapter" data-level="38.2.4" data-path="Chapter_38.html"><a href="Chapter_38.html#correlation-test-in-r"><i class="fa fa-check"></i><b>38.2.4</b> Correlation test in R</a></li>
<li class="chapter" data-level="38.2.5" data-path="Chapter_38.html"><a href="Chapter_38.html#simple-linear-regression-in-r"><i class="fa fa-check"></i><b>38.2.5</b> Simple linear regression in R</a></li>
<li class="chapter" data-level="38.2.6" data-path="Chapter_38.html"><a href="Chapter_38.html#multiple-regression-in-r"><i class="fa fa-check"></i><b>38.2.6</b> Multiple regression in R</a></li>
</ul></li>
<li class="chapter" data-level="38.3" data-path="Chapter_38.html"><a href="Chapter_38.html#statistical-test-assumptions-in-r"><i class="fa fa-check"></i><b>38.3</b> Statistical test assumptions in R</a></li>
</ul></li>
<li class="appendix"><span><b>Appendix</b></span></li>
<li class="chapter" data-level="A" data-path="appendexA_CMS.html"><a href="appendexA_CMS.html"><i class="fa fa-check"></i><b>A</b> Common Marking Scheme</a></li>
<li class="chapter" data-level="B" data-path="uncertainty_derivation.html"><a href="uncertainty_derivation.html"><i class="fa fa-check"></i><b>B</b> Uncertainty derivation</a></li>
<li class="chapter" data-level="C" data-path="appendixC_tables.html"><a href="appendixC_tables.html"><i class="fa fa-check"></i><b>C</b> Statistical tables</a>
<ul>
<li class="chapter" data-level="C.1" data-path="appendixC_tables.html"><a href="appendixC_tables.html#wilcoxon-signed-rank-critical-values"><i class="fa fa-check"></i><b>C.1</b> Wilcoxon signed rank critical values</a></li>
<li class="chapter" data-level="C.2" data-path="appendixC_tables.html"><a href="appendixC_tables.html#mann-whitney-u-critical-values"><i class="fa fa-check"></i><b>C.2</b> Mann-Whitney U critical values</a></li>
</ul></li>
<li class="chapter" data-level="" data-path="references.html"><a href="references.html"><i class="fa fa-check"></i>References</a></li>
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<div id="appendixC_tables" class="section level1 hasAnchor" number="41">
<h1><span class="header-section-number">C</span> Statistical tables<a href="appendixC_tables.html#appendixC_tables" class="anchor-section" aria-label="Anchor link to header"></a></h1>
<div id="wilcoxon-signed-rank-critical-values" class="section level2 hasAnchor" number="41.1">
<h2><span class="header-section-number">C.1</span> Wilcoxon signed rank critical values<a href="appendixC_tables.html#wilcoxon-signed-rank-critical-values" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<table>
<thead>
<tr class="header">
<th align="right">N</th>
<th align="right">alpha == 0.1</th>
<th align="left">alpha == 0.05</th>
<th align="left">alpha == 0.01</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="right">5</td>
<td align="right">0</td>
<td align="left">–</td>
<td align="left">–</td>
</tr>
<tr class="even">
<td align="right">6</td>
<td align="right">2</td>
<td align="left">0</td>
<td align="left">–</td>
</tr>
<tr class="odd">
<td align="right">7</td>
<td align="right">3</td>
<td align="left">2</td>
<td align="left">–</td>
</tr>
<tr class="even">
<td align="right">8</td>
<td align="right">5</td>
<td align="left">3</td>
<td align="left">0</td>
</tr>
<tr class="odd">
<td align="right">9</td>
<td align="right">8</td>
<td align="left">5</td>
<td align="left">1</td>
</tr>
<tr class="even">
<td align="right">10</td>
<td align="right">10</td>
<td align="left">8</td>
<td align="left">3</td>
</tr>
<tr class="odd">
<td align="right">11</td>
<td align="right">13</td>
<td align="left">10</td>
<td align="left">5</td>
</tr>
<tr class="even">
<td align="right">12</td>
<td align="right">17</td>
<td align="left">13</td>
<td align="left">7</td>
</tr>
<tr class="odd">
<td align="right">13</td>
<td align="right">21</td>
<td align="left">17</td>
<td align="left">9</td>
</tr>
<tr class="even">
<td align="right">14</td>
<td align="right">25</td>
<td align="left">21</td>
<td align="left">12</td>
</tr>
<tr class="odd">
<td align="right">15</td>
<td align="right">30</td>
<td align="left">25</td>
<td align="left">15</td>
</tr>
<tr class="even">
<td align="right">16</td>
<td align="right">35</td>
<td align="left">29</td>
<td align="left">19</td>
</tr>
<tr class="odd">
<td align="right">17</td>
<td align="right">41</td>
<td align="left">34</td>
<td align="left">23</td>
</tr>
<tr class="even">
<td align="right">18</td>
<td align="right">47</td>
<td align="left">40</td>
<td align="left">27</td>
</tr>
<tr class="odd">
<td align="right">19</td>
<td align="right">53</td>
<td align="left">46</td>
<td align="left">32</td>
</tr>
<tr class="even">
<td align="right">20</td>
<td align="right">60</td>
<td align="left">52</td>
<td align="left">37</td>
</tr>
<tr class="odd">
<td align="right">21</td>
<td align="right">67</td>
<td align="left">58</td>
<td align="left">42</td>
</tr>
<tr class="even">
<td align="right">22</td>
<td align="right">75</td>
<td align="left">65</td>
<td align="left">48</td>
</tr>
<tr class="odd">
<td align="right">23</td>
<td align="right">83</td>
<td align="left">73</td>
<td align="left">54</td>
</tr>
<tr class="even">
<td align="right">24</td>
<td align="right">91</td>
<td align="left">81</td>
<td align="left">61</td>
</tr>
<tr class="odd">
<td align="right">25</td>
<td align="right">100</td>
<td align="left">89</td>
<td align="left">68</td>
</tr>
<tr class="even">
<td align="right">26</td>
<td align="right">110</td>
<td align="left">98</td>
<td align="left">75</td>
</tr>
<tr class="odd">
<td align="right">27</td>
<td align="right">119</td>
<td align="left">107</td>
<td align="left">83</td>
</tr>
<tr class="even">
<td align="right">28</td>
<td align="right">130</td>
<td align="left">116</td>
<td align="left">91</td>
</tr>
<tr class="odd">
<td align="right">29</td>
<td align="right">140</td>
<td align="left">126</td>
<td align="left">100</td>
</tr>
<tr class="even">
<td align="right">30</td>
<td align="right">151</td>
<td align="left">137</td>
<td align="left">109</td>
</tr>
<tr class="odd">
<td align="right">31</td>
<td align="right">163</td>
<td align="left">147</td>
<td align="left">118</td>
</tr>
<tr class="even">
<td align="right">32</td>
<td align="right">175</td>
<td align="left">159</td>
<td align="left">128</td>
</tr>
<tr class="odd">
<td align="right">33</td>
<td align="right">187</td>
<td align="left">170</td>
<td align="left">138</td>
</tr>
<tr class="even">
<td align="right">34</td>
<td align="right">200</td>
<td align="left">182</td>
<td align="left">148</td>
</tr>
<tr class="odd">
<td align="right">35</td>
<td align="right">213</td>
<td align="left">195</td>
<td align="left">159</td>
</tr>
<tr class="even">
<td align="right">36</td>
<td align="right">227</td>
<td align="left">208</td>
<td align="left">171</td>
</tr>
<tr class="odd">
<td align="right">37</td>
<td align="right">241</td>
<td align="left">221</td>
<td align="left">182</td>
</tr>
<tr class="even">
<td align="right">38</td>
<td align="right">256</td>
<td align="left">235</td>
<td align="left">194</td>
</tr>
<tr class="odd">
<td align="right">39</td>
<td align="right">271</td>
<td align="left">249</td>
<td align="left">207</td>
</tr>
<tr class="even">
<td align="right">40</td>
<td align="right">286</td>
<td align="left">264</td>
<td align="left">220</td>
</tr>
<tr class="odd">
<td align="right">41</td>
<td align="right">302</td>
<td align="left">279</td>
<td align="left">233</td>
</tr>
<tr class="even">
<td align="right">42</td>
<td align="right">319</td>
<td align="left">294</td>
<td align="left">247</td>
</tr>
<tr class="odd">
<td align="right">43</td>
<td align="right">336</td>
<td align="left">310</td>
<td align="left">261</td>
</tr>
<tr class="even">
<td align="right">44</td>
<td align="right">353</td>
<td align="left">327</td>
<td align="left">276</td>
</tr>
<tr class="odd">
<td align="right">45</td>
<td align="right">371</td>
<td align="left">343</td>
<td align="left">291</td>
</tr>
<tr class="even">
<td align="right">46</td>
<td align="right">389</td>
<td align="left">361</td>
<td align="left">307</td>
</tr>
<tr class="odd">
<td align="right">47</td>
<td align="right">407</td>
<td align="left">378</td>
<td align="left">322</td>
</tr>
<tr class="even">
<td align="right">48</td>
<td align="right">426</td>
<td align="left">396</td>
<td align="left">339</td>
</tr>
<tr class="odd">
<td align="right">49</td>
<td align="right">446</td>
<td align="left">415</td>
<td align="left">355</td>
</tr>
<tr class="even">
<td align="right">50</td>
<td align="right">466</td>
<td align="left">434</td>
<td align="left">373</td>
</tr>
</tbody>
</table>
</div>
<div id="mann-whitney-u-critical-values" class="section level2 hasAnchor" number="41.2">
<h2><span class="header-section-number">C.2</span> Mann-Whitney U critical values<a href="appendixC_tables.html#mann-whitney-u-critical-values" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<table>
<colgroup>
<col width="4%" />
<col width="4%" />
<col width="4%" />
<col width="4%" />
<col width="4%" />
<col width="4%" />
<col width="4%" />
<col width="4%" />
<col width="5%" />
<col width="5%" />
<col width="5%" />
<col width="5%" />
<col width="5%" />
<col width="5%" />
<col width="5%" />
<col width="5%" />
<col width="5%" />
<col width="5%" />
<col width="5%" />
<col width="5%" />
</colgroup>
<thead>
<tr class="header">
<th align="left"></th>
<th align="left">2</th>
<th align="left">3</th>
<th align="left">4</th>
<th align="left">5</th>
<th align="left">6</th>
<th align="left">7</th>
<th align="right">8</th>
<th align="right">9</th>
<th align="right">10</th>
<th align="right">11</th>
<th align="right">12</th>
<th align="right">13</th>
<th align="right">14</th>
<th align="right">15</th>
<th align="right">16</th>
<th align="right">17</th>
<th align="right">18</th>
<th align="right">19</th>
<th align="right">20</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left">2</td>
<td align="left">–</td>
<td align="left">–</td>
<td align="left">–</td>
<td align="left">–</td>
<td align="left">–</td>
<td align="left">–</td>
<td align="right">0</td>
<td align="right">0</td>
<td align="right">0</td>
<td align="right">0</td>
<td align="right">1</td>
<td align="right">1</td>
<td align="right">1</td>
<td align="right">1</td>
<td align="right">1</td>
<td align="right">2</td>
<td align="right">2</td>
<td align="right">2</td>
<td align="right">2</td>
</tr>
<tr class="even">
<td align="left">3</td>
<td align="left">–</td>
<td align="left">–</td>
<td align="left">–</td>
<td align="left">0</td>
<td align="left">1</td>
<td align="left">1</td>
<td align="right">2</td>
<td align="right">2</td>
<td align="right">3</td>
<td align="right">3</td>
<td align="right">4</td>
<td align="right">4</td>
<td align="right">5</td>
<td align="right">5</td>
<td align="right">6</td>
<td align="right">6</td>
<td align="right">7</td>
<td align="right">7</td>
<td align="right">8</td>
</tr>
<tr class="odd">
<td align="left">4</td>
<td align="left">–</td>
<td align="left">–</td>
<td align="left">0</td>
<td align="left">1</td>
<td align="left">2</td>
<td align="left">3</td>
<td align="right">4</td>
<td align="right">4</td>
<td align="right">5</td>
<td align="right">6</td>
<td align="right">7</td>
<td align="right">8</td>
<td align="right">9</td>
<td align="right">10</td>
<td align="right">11</td>
<td align="right">11</td>
<td align="right">12</td>
<td align="right">13</td>
<td align="right">14</td>
</tr>
<tr class="even">
<td align="left">5</td>
<td align="left">–</td>
<td align="left">0</td>
<td align="left">1</td>
<td align="left">2</td>
<td align="left">3</td>
<td align="left">5</td>
<td align="right">6</td>
<td align="right">7</td>
<td align="right">8</td>
<td align="right">9</td>
<td align="right">11</td>
<td align="right">12</td>
<td align="right">13</td>
<td align="right">14</td>
<td align="right">15</td>
<td align="right">17</td>
<td align="right">18</td>
<td align="right">19</td>
<td align="right">20</td>
</tr>
<tr class="odd">
<td align="left">6</td>
<td align="left">–</td>
<td align="left">1</td>
<td align="left">2</td>
<td align="left">3</td>
<td align="left">5</td>
<td align="left">6</td>
<td align="right">7</td>
<td align="right">10</td>
<td align="right">11</td>
<td align="right">13</td>
<td align="right">14</td>
<td align="right">16</td>
<td align="right">17</td>
<td align="right">19</td>
<td align="right">21</td>
<td align="right">22</td>
<td align="right">24</td>
<td align="right">25</td>
<td align="right">27</td>
</tr>
<tr class="even">
<td align="left">7</td>
<td align="left">–</td>
<td align="left">1</td>
<td align="left">3</td>
<td align="left">5</td>
<td align="left">6</td>
<td align="left">8</td>
<td align="right">10</td>
<td align="right">12</td>
<td align="right">14</td>
<td align="right">16</td>
<td align="right">18</td>
<td align="right">20</td>
<td align="right">22</td>
<td align="right">24</td>
<td align="right">26</td>
<td align="right">28</td>
<td align="right">30</td>
<td align="right">32</td>
<td align="right">34</td>
</tr>
<tr class="odd">
<td align="left">8</td>
<td align="left">0</td>
<td align="left">2</td>
<td align="left">4</td>
<td align="left">6</td>
<td align="left">7</td>
<td align="left">10</td>
<td align="right">13</td>
<td align="right">15</td>
<td align="right">17</td>
<td align="right">19</td>
<td align="right">22</td>
<td align="right">24</td>
<td align="right">26</td>
<td align="right">29</td>
<td align="right">31</td>
<td align="right">34</td>
<td align="right">36</td>
<td align="right">38</td>
<td align="right">41</td>
</tr>
<tr class="even">
<td align="left">9</td>
<td align="left">0</td>
<td align="left">2</td>
<td align="left">4</td>
<td align="left">7</td>
<td align="left">10</td>
<td align="left">12</td>
<td align="right">15</td>
<td align="right">17</td>
<td align="right">20</td>
<td align="right">23</td>
<td align="right">26</td>
<td align="right">28</td>