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<!DOCTYPE html>
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<title>Chapter 9 Decimal places and significant figures | Statistical Techniques for Biological and Environmental Sciences</title>
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<meta property="og:title" content="Chapter 9 Decimal places and significant figures | Statistical Techniques for Biological and Environmental Sciences" />
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<meta name="twitter:title" content="Chapter 9 Decimal places and significant figures | Statistical Techniques for Biological and Environmental Sciences" />
<meta name="twitter:description" content="This is a minimal example of using the bookdown package to write a book. The output format for this example is bookdown::gitbook." />
<meta name="author" content="Brad Duthie" />
<meta name="date" content="2022-08-29" />
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<ul class="summary">
<li><a href="./">A Minimal Book Example</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="0.1" data-path="index.html"><a href="index.html#what-is-statistics"><i class="fa fa-check"></i><b>0.1</b> What is statistics?</a></li>
<li class="chapter" data-level="0.2" data-path="index.html"><a href="index.html#why-this-module-is-important"><i class="fa fa-check"></i><b>0.2</b> Why this module is important</a></li>
<li class="chapter" data-level="0.3" data-path="index.html"><a href="index.html#teaching-overview"><i class="fa fa-check"></i><b>0.3</b> Teaching overview</a></li>
<li class="chapter" data-level="0.4" data-path="index.html"><a href="index.html#assessment-overview"><i class="fa fa-check"></i><b>0.4</b> Assessment overview</a>
<ul>
<li class="chapter" data-level="0.4.1" data-path="index.html"><a href="index.html#test-1f"><i class="fa fa-check"></i><b>0.4.1</b> Test 1F</a></li>
<li class="chapter" data-level="0.4.2" data-path="index.html"><a href="index.html#test-1s"><i class="fa fa-check"></i><b>0.4.2</b> Test 1S</a></li>
<li class="chapter" data-level="0.4.3" data-path="index.html"><a href="index.html#test-2s"><i class="fa fa-check"></i><b>0.4.3</b> Test 2S</a></li>
<li class="chapter" data-level="0.4.4" data-path="index.html"><a href="index.html#mock-exam"><i class="fa fa-check"></i><b>0.4.4</b> Mock Exam</a></li>
<li class="chapter" data-level="0.4.5" data-path="index.html"><a href="index.html#exam"><i class="fa fa-check"></i><b>0.4.5</b> Exam</a></li>
</ul></li>
<li class="chapter" data-level="0.5" data-path="index.html"><a href="index.html#intro_jamovi"><i class="fa fa-check"></i><b>0.5</b> Jamovi statistical software</a></li>
<li class="chapter" data-level="0.6" data-path="index.html"><a href="index.html#textbooks"><i class="fa fa-check"></i><b>0.6</b> Textbooks</a></li>
<li class="chapter" data-level="0.7" data-path="index.html"><a href="index.html#canvas"><i class="fa fa-check"></i><b>0.7</b> Canvas</a></li>
<li class="chapter" data-level="0.8" data-path="index.html"><a href="index.html#timetable"><i class="fa fa-check"></i><b>0.8</b> Timetable</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="week-1-overview.html"><a href="week-1-overview.html"><i class="fa fa-check"></i>Week 1 Overview</a></li>
<li class="chapter" data-level="1" data-path="background_mathematics.html"><a href="background_mathematics.html"><i class="fa fa-check"></i><b>1</b> Background mathematics</a>
<ul>
<li class="chapter" data-level="1.1" data-path="background_mathematics.html"><a href="background_mathematics.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="background_mathematics.html"><a href="background_mathematics.html#order-of-operations"><i class="fa fa-check"></i><b>1.2</b> Order of operations</a></li>
</ul></li>
<li class="chapter" data-level="2" data-path="data_organisation.html"><a href="data_organisation.html"><i class="fa fa-check"></i><b>2</b> Data organisation</a>
<ul>
<li class="chapter" data-level="2.1" data-path="data_organisation.html"><a href="data_organisation.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="data_organisation.html"><a href="data_organisation.html#data-files"><i class="fa fa-check"></i><b>2.2</b> Data files</a></li>
</ul></li>
<li class="chapter" data-level="3" data-path="practical-preparing-real-datasets.html"><a href="practical-preparing-real-datasets.html"><i class="fa fa-check"></i><b>3</b> <em>Practical</em>: Preparing real datasets</a>
<ul>
<li class="chapter" data-level="3.1" data-path="practical-preparing-real-datasets.html"><a href="practical-preparing-real-datasets.html#libreoffice-calc"><i class="fa fa-check"></i><b>3.1</b> LibreOffice Calc</a></li>
<li class="chapter" data-level="3.2" data-path="practical-preparing-real-datasets.html"><a href="practical-preparing-real-datasets.html#exercise-organising-data-1"><i class="fa fa-check"></i><b>3.2</b> Exercise Organising data 1</a></li>
<li class="chapter" data-level="3.3" data-path="practical-preparing-real-datasets.html"><a href="practical-preparing-real-datasets.html#exercise-organising-data-2"><i class="fa fa-check"></i><b>3.3</b> Exercise Organising data 2</a></li>
<li class="chapter" data-level="3.4" data-path="practical-preparing-real-datasets.html"><a href="practical-preparing-real-datasets.html#exercise-organising-data-3"><i class="fa fa-check"></i><b>3.4</b> Exercise Organising data 3</a></li>
<li class="chapter" data-level="3.5" data-path="practical-preparing-real-datasets.html"><a href="practical-preparing-real-datasets.html#summary-of-exercises-and-why-they-are-useful."><i class="fa fa-check"></i><b>3.5</b> Summary of exercises and why they are useful.</a></li>
</ul></li>
<li class="part"><span><b>II Statistical concepts</b></span></li>
<li class="chapter" data-level="" data-path="week-2-overview.html"><a href="week-2-overview.html"><i class="fa fa-check"></i>Week 2 Overview</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 propogation</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> <em>Practical</em>. 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>
</ul></li>
<li class="part"><span><b>III Summary statistics</b></span></li>
<li class="chapter" data-level="" data-path="week-3-overview.html"><a href="week-3-overview.html"><i class="fa fa-check"></i>Week 3 Overview</a></li>
<li class="chapter" data-level="9" data-path="decimal-places-and-significant-figures.html"><a href="decimal-places-and-significant-figures.html"><i class="fa fa-check"></i><b>9</b> Decimal places and significant figures</a></li>
<li class="chapter" data-level="10" data-path="the-mean.html"><a href="the-mean.html"><i class="fa fa-check"></i><b>10</b> The mean</a></li>
<li class="chapter" data-level="11" data-path="the-mode.html"><a href="the-mode.html"><i class="fa fa-check"></i><b>11</b> The mode</a></li>
<li class="chapter" data-level="12" data-path="the-median-and-quantiles.html"><a href="the-median-and-quantiles.html"><i class="fa fa-check"></i><b>12</b> The median and quantiles</a></li>
<li class="chapter" data-level="13" data-path="mean-mode-median-and-resistance.html"><a href="mean-mode-median-and-resistance.html"><i class="fa fa-check"></i><b>13</b> Mean, mode, median, and resistance</a></li>
<li class="chapter" data-level="14" data-path="plots.html"><a href="plots.html"><i class="fa fa-check"></i><b>14</b> Plots</a>
<ul>
<li class="chapter" data-level="14.1" data-path="plots.html"><a href="plots.html#general-principles"><i class="fa fa-check"></i><b>14.1</b> General principles</a></li>
<li class="chapter" data-level="14.2" data-path="plots.html"><a href="plots.html#histograms"><i class="fa fa-check"></i><b>14.2</b> Histograms</a></li>
<li class="chapter" data-level="14.3" data-path="plots.html"><a href="plots.html#box-whisker-plots"><i class="fa fa-check"></i><b>14.3</b> Box-whisker plots</a></li>
</ul></li>
<li class="chapter" data-level="15" data-path="practical.-real-data-with-jamovi.html"><a href="practical.-real-data-with-jamovi.html"><i class="fa fa-check"></i><b>15</b> <em>Practical</em>. Real data with Jamovi</a>
<ul>
<li class="chapter" data-level="15.1" data-path="practical.-real-data-with-jamovi.html"><a href="practical.-real-data-with-jamovi.html#some-biological-example"><i class="fa fa-check"></i><b>15.1</b> Some biological example</a></li>
<li class="chapter" data-level="15.2" data-path="practical.-real-data-with-jamovi.html"><a href="practical.-real-data-with-jamovi.html#some-environmental-example"><i class="fa fa-check"></i><b>15.2</b> Some environmental example</a></li>
<li class="chapter" data-level="15.3" data-path="practical.-real-data-with-jamovi.html"><a href="practical.-real-data-with-jamovi.html#summary-of-exercises-and-why-they-are-useful.-1"><i class="fa fa-check"></i><b>15.3</b> Summary of exercises and why they are useful.</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="week-4-overview.html"><a href="week-4-overview.html"><i class="fa fa-check"></i>Week 4 Overview</a></li>
<li class="chapter" data-level="16" data-path="introduction-to-probability-models.html"><a href="introduction-to-probability-models.html"><i class="fa fa-check"></i><b>16</b> Introduction to probability models</a>
<ul>
<li class="chapter" data-level="16.1" data-path="introduction-to-probability-models.html"><a href="introduction-to-probability-models.html#a-practical-example"><i class="fa fa-check"></i><b>16.1</b> A practical example</a></li>
<li class="chapter" data-level="16.2" data-path="introduction-to-probability-models.html"><a href="introduction-to-probability-models.html#probability-distributions"><i class="fa fa-check"></i><b>16.2</b> Probability distributions</a>
<ul>
<li class="chapter" data-level="16.2.1" data-path="introduction-to-probability-models.html"><a href="introduction-to-probability-models.html#binomial-distribution"><i class="fa fa-check"></i><b>16.2.1</b> Binomial distribution</a></li>
<li class="chapter" data-level="16.2.2" data-path="introduction-to-probability-models.html"><a href="introduction-to-probability-models.html#poisson-distribution"><i class="fa fa-check"></i><b>16.2.2</b> Poisson distribution</a></li>
<li class="chapter" data-level="16.2.3" data-path="introduction-to-probability-models.html"><a href="introduction-to-probability-models.html#normal-distribution"><i class="fa fa-check"></i><b>16.2.3</b> Normal distribution</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="17" data-path="the-central-limit-theorem-clt.html"><a href="the-central-limit-theorem-clt.html"><i class="fa fa-check"></i><b>17</b> The Central Limit Theorem (CLT)</a>
<ul>
<li class="chapter" data-level="17.1" data-path="the-central-limit-theorem-clt.html"><a href="the-central-limit-theorem-clt.html#examples-of-the-clt-in-action"><i class="fa fa-check"></i><b>17.1</b> Examples of the CLT in action</a></li>
<li class="chapter" data-level="17.2" data-path="the-central-limit-theorem-clt.html"><a href="the-central-limit-theorem-clt.html#the-standard-normal-distribution"><i class="fa fa-check"></i><b>17.2</b> The standard normal distribution</a></li>
<li class="chapter" data-level="17.3" data-path="the-central-limit-theorem-clt.html"><a href="the-central-limit-theorem-clt.html#what-are-z-scores"><i class="fa fa-check"></i><b>17.3</b> What are z-scores?</a></li>
</ul></li>
<li class="chapter" data-level="18" data-path="practical.-probability-and-simulation.html"><a href="practical.-probability-and-simulation.html"><i class="fa fa-check"></i><b>18</b> <em>Practical</em>. Probability and simulation</a>
<ul>
<li class="chapter" data-level="18.1" data-path="practical.-probability-and-simulation.html"><a href="practical.-probability-and-simulation.html#calculating-probability-exercise-1"><i class="fa fa-check"></i><b>18.1</b> Calculating probability exercise 1</a></li>
<li class="chapter" data-level="18.2" data-path="practical.-probability-and-simulation.html"><a href="practical.-probability-and-simulation.html#calculating-probability-exercise-2"><i class="fa fa-check"></i><b>18.2</b> Calculating probability exercise 2</a></li>
<li class="chapter" data-level="18.3" data-path="practical.-probability-and-simulation.html"><a href="practical.-probability-and-simulation.html#calculating-probability-from-normal-distribution"><i class="fa fa-check"></i><b>18.3</b> Calculating probability from normal distribution</a></li>
<li class="chapter" data-level="18.4" data-path="practical.-probability-and-simulation.html"><a href="practical.-probability-and-simulation.html#normal-distribution-and-sample-size"><i class="fa fa-check"></i><b>18.4</b> Normal distribution and sample size</a></li>
<li class="chapter" data-level="18.5" data-path="practical.-probability-and-simulation.html"><a href="practical.-probability-and-simulation.html#simulating-the-central-limit-theorem"><i class="fa fa-check"></i><b>18.5</b> Simulating the 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="week-5-overview.html"><a href="week-5-overview.html"><i class="fa fa-check"></i>Week 5 Overview</a></li>
<li class="chapter" data-level="19" data-path="sample-statistics-and-population-parameters.html"><a href="sample-statistics-and-population-parameters.html"><i class="fa fa-check"></i><b>19</b> Sample statistics and population parameters</a></li>
<li class="chapter" data-level="20" data-path="standard-normal-distribution.html"><a href="standard-normal-distribution.html"><i class="fa fa-check"></i><b>20</b> Standard Normal Distribution</a></li>
<li class="chapter" data-level="21" data-path="confidence-intervals.html"><a href="confidence-intervals.html"><i class="fa fa-check"></i><b>21</b> Confidence intervals</a></li>
<li class="chapter" data-level="22" data-path="the-t-interval.html"><a href="the-t-interval.html"><i class="fa fa-check"></i><b>22</b> The t-interval</a></li>
<li class="chapter" data-level="23" data-path="practical.-z--and-t--intervals.html"><a href="practical.-z--and-t--intervals.html"><i class="fa fa-check"></i><b>23</b> <em>Practical</em>. z- and t- intervals</a>
<ul>
<li class="chapter" data-level="23.1" data-path="practical.-z--and-t--intervals.html"><a href="practical.-z--and-t--intervals.html#example-constructing-confidence-intervals"><i class="fa fa-check"></i><b>23.1</b> Example constructing confidence intervals</a></li>
<li class="chapter" data-level="23.2" data-path="practical.-z--and-t--intervals.html"><a href="practical.-z--and-t--intervals.html#confidence-interval-for-different-levels-t--and-z-"><i class="fa fa-check"></i><b>23.2</b> Confidence interval for different levels (t- and z-)</a></li>
<li class="chapter" data-level="23.3" data-path="practical.-z--and-t--intervals.html"><a href="practical.-z--and-t--intervals.html#proportion-confidence-intervals"><i class="fa fa-check"></i><b>23.3</b> Proportion confidence intervals</a></li>
<li class="chapter" data-level="23.4" data-path="practical.-z--and-t--intervals.html"><a href="practical.-z--and-t--intervals.html#another-confidence-interval-example"><i class="fa fa-check"></i><b>23.4</b> Another confidence interval example?</a></li>
</ul></li>
<li class="part"><span><b>VI Review of parts I-V</b></span></li>
<li class="chapter" data-level="" data-path="week-6-overview-reading-week.html"><a href="week-6-overview-reading-week.html"><i class="fa fa-check"></i>Week 6 Overview (Reading week)</a></li>
<li class="part"><span><b>VII Hypothesis testing</b></span></li>
<li class="chapter" data-level="" data-path="week-7-overview.html"><a href="week-7-overview.html"><i class="fa fa-check"></i>Week 7 Overview</a></li>
<li class="chapter" data-level="24" data-path="what-is-hypothesis-testing.html"><a href="what-is-hypothesis-testing.html"><i class="fa fa-check"></i><b>24</b> What is hypothesis testing?</a></li>
<li class="chapter" data-level="25" data-path="making-and-using-hypotheses-and-types-of-tests.html"><a href="making-and-using-hypotheses-and-types-of-tests.html"><i class="fa fa-check"></i><b>25</b> Making and using hypotheses and types of tests</a></li>
<li class="chapter" data-level="26" data-path="an-example-of-hypothesis-testing.html"><a href="an-example-of-hypothesis-testing.html"><i class="fa fa-check"></i><b>26</b> An example of hypothesis testing</a></li>
<li class="chapter" data-level="27" data-path="hypothesis-testing-and-confidence-intervals.html"><a href="hypothesis-testing-and-confidence-intervals.html"><i class="fa fa-check"></i><b>27</b> Hypothesis testing and confidence intervals</a></li>
<li class="chapter" data-level="28" data-path="student-t-distribution-and-one-sample-t-test.html"><a href="student-t-distribution-and-one-sample-t-test.html"><i class="fa fa-check"></i><b>28</b> Student t-distribution and one sample t-test</a></li>
<li class="chapter" data-level="29" data-path="another-example-of-a-one-sample-t-test.html"><a href="another-example-of-a-one-sample-t-test.html"><i class="fa fa-check"></i><b>29</b> Another example of a one sample t-test</a></li>
<li class="chapter" data-level="30" data-path="independent-t-test.html"><a href="independent-t-test.html"><i class="fa fa-check"></i><b>30</b> Independent t-test</a></li>
<li class="chapter" data-level="31" data-path="paired-sample-t-test.html"><a href="paired-sample-t-test.html"><i class="fa fa-check"></i><b>31</b> Paired sample t-test</a></li>
<li class="chapter" data-level="32" data-path="violations-of-assumptions.html"><a href="violations-of-assumptions.html"><i class="fa fa-check"></i><b>32</b> Violations of assumptions</a></li>
<li class="chapter" data-level="33" data-path="non-parametric-tests-and-what-these-are..html"><a href="non-parametric-tests-and-what-these-are..html"><i class="fa fa-check"></i><b>33</b> Non-parametric tests, and what these are.</a></li>
<li class="chapter" data-level="34" data-path="practical.-hypothesis-testing-and-t-tests.html"><a href="practical.-hypothesis-testing-and-t-tests.html"><i class="fa fa-check"></i><b>34</b> <em>Practical</em>. Hypothesis testing and t-tests</a>
<ul>
<li class="chapter" data-level="34.1" data-path="practical.-hypothesis-testing-and-t-tests.html"><a href="practical.-hypothesis-testing-and-t-tests.html#exercise-on-a-simple-one-sample-t-test"><i class="fa fa-check"></i><b>34.1</b> Exercise on a simple one sample t-test</a></li>
<li class="chapter" data-level="34.2" data-path="practical.-hypothesis-testing-and-t-tests.html"><a href="practical.-hypothesis-testing-and-t-tests.html#exercise-on-an-independent-sample-t-test"><i class="fa fa-check"></i><b>34.2</b> Exercise on an independent sample t-test</a></li>
<li class="chapter" data-level="34.3" data-path="practical.-hypothesis-testing-and-t-tests.html"><a href="practical.-hypothesis-testing-and-t-tests.html#exercise-involving-multiple-comparisons"><i class="fa fa-check"></i><b>34.3</b> Exercise involving multiple comparisons</a></li>
<li class="chapter" data-level="34.4" data-path="practical.-hypothesis-testing-and-t-tests.html"><a href="practical.-hypothesis-testing-and-t-tests.html#exercise-with-non-parametric"><i class="fa fa-check"></i><b>34.4</b> Exercise with non-parametric</a></li>
<li class="chapter" data-level="34.5" data-path="practical.-hypothesis-testing-and-t-tests.html"><a href="practical.-hypothesis-testing-and-t-tests.html#another-exercise-with-non-parametric"><i class="fa fa-check"></i><b>34.5</b> Another exercise with non-parametric</a></li>
</ul></li>
<li class="part"><span><b>VIII Analysis of Variance (ANOVA)</b></span></li>
<li class="chapter" data-level="" data-path="week-8-overview.html"><a href="week-8-overview.html"><i class="fa fa-check"></i>Week 8 Overview</a></li>
<li class="chapter" data-level="35" data-path="what-is-anova.html"><a href="what-is-anova.html"><i class="fa fa-check"></i><b>35</b> What is ANOVA?</a></li>
<li class="chapter" data-level="36" data-path="one-way-anova.html"><a href="one-way-anova.html"><i class="fa fa-check"></i><b>36</b> One-way ANOVA</a></li>
<li class="chapter" data-level="37" data-path="two-way-anova.html"><a href="two-way-anova.html"><i class="fa fa-check"></i><b>37</b> Two-way ANOVA</a></li>
<li class="chapter" data-level="38" data-path="kruskall-wallis-h-test.html"><a href="kruskall-wallis-h-test.html"><i class="fa fa-check"></i><b>38</b> Kruskall-Wallis H test</a></li>
<li class="chapter" data-level="39" data-path="practical.-anova-and-associated-tests.html"><a href="practical.-anova-and-associated-tests.html"><i class="fa fa-check"></i><b>39</b> <em>Practical</em>. ANOVA and associated tests</a>
<ul>
<li class="chapter" data-level="39.1" data-path="practical.-anova-and-associated-tests.html"><a href="practical.-anova-and-associated-tests.html#anova-exercise-1"><i class="fa fa-check"></i><b>39.1</b> ANOVA Exercise 1</a></li>
<li class="chapter" data-level="39.2" data-path="practical.-anova-and-associated-tests.html"><a href="practical.-anova-and-associated-tests.html#anova-exercise-2"><i class="fa fa-check"></i><b>39.2</b> ANOVA Exercise 2</a></li>
<li class="chapter" data-level="39.3" data-path="practical.-anova-and-associated-tests.html"><a href="practical.-anova-and-associated-tests.html#anova-exercise-3"><i class="fa fa-check"></i><b>39.3</b> ANOVA Exercise 3</a></li>
<li class="chapter" data-level="39.4" data-path="practical.-anova-and-associated-tests.html"><a href="practical.-anova-and-associated-tests.html#anova-exercise-4"><i class="fa fa-check"></i><b>39.4</b> ANOVA Exercise 4</a></li>
</ul></li>
<li class="part"><span><b>IX Counts and Correlation</b></span></li>
<li class="chapter" data-level="" data-path="week-9-overview.html"><a href="week-9-overview.html"><i class="fa fa-check"></i>Week 9 Overview</a></li>
<li class="chapter" data-level="40" data-path="frequency-and-count-data.html"><a href="frequency-and-count-data.html"><i class="fa fa-check"></i><b>40</b> Frequency and count data</a></li>
<li class="chapter" data-level="41" data-path="chi-squared-goodness-of-fit.html"><a href="chi-squared-goodness-of-fit.html"><i class="fa fa-check"></i><b>41</b> Chi-squared goodness of fit</a></li>
<li class="chapter" data-level="42" data-path="chi-squared-test-of-association.html"><a href="chi-squared-test-of-association.html"><i class="fa fa-check"></i><b>42</b> Chi-squared test of association</a></li>
<li class="chapter" data-level="43" data-path="correlation-key-concepts.html"><a href="correlation-key-concepts.html"><i class="fa fa-check"></i><b>43</b> Correlation key concepts</a></li>
<li class="chapter" data-level="44" data-path="correlation-mathematics.html"><a href="correlation-mathematics.html"><i class="fa fa-check"></i><b>44</b> Correlation mathematics</a></li>
<li class="chapter" data-level="45" data-path="correlation-hypothesis-testing.html"><a href="correlation-hypothesis-testing.html"><i class="fa fa-check"></i><b>45</b> Correlation hypothesis testing</a></li>
<li class="chapter" data-level="46" data-path="practical.-analysis-of-count-data-correlation-and-regression.html"><a href="practical.-analysis-of-count-data-correlation-and-regression.html"><i class="fa fa-check"></i><b>46</b> <em>Practical</em>. Analysis of count data, correlation, and regression</a>
<ul>
<li class="chapter" data-level="46.1" data-path="practical.-analysis-of-count-data-correlation-and-regression.html"><a href="practical.-analysis-of-count-data-correlation-and-regression.html#chi-square-exercise-1"><i class="fa fa-check"></i><b>46.1</b> Chi-Square Exercise 1</a></li>
<li class="chapter" data-level="46.2" data-path="practical.-analysis-of-count-data-correlation-and-regression.html"><a href="practical.-analysis-of-count-data-correlation-and-regression.html#chi-square-association-exercise-2"><i class="fa fa-check"></i><b>46.2</b> Chi-Square association Exercise 2</a></li>
<li class="chapter" data-level="46.3" data-path="practical.-analysis-of-count-data-correlation-and-regression.html"><a href="practical.-analysis-of-count-data-correlation-and-regression.html#correlation-exercise-3"><i class="fa fa-check"></i><b>46.3</b> Correlation Exercise 3</a></li>
<li class="chapter" data-level="46.4" data-path="practical.-analysis-of-count-data-correlation-and-regression.html"><a href="practical.-analysis-of-count-data-correlation-and-regression.html#correlation-exercise-4"><i class="fa fa-check"></i><b>46.4</b> Correlation Exercise 4</a></li>
</ul></li>
<li class="part"><span><b>X Linear Regression</b></span></li>
<li class="chapter" data-level="" data-path="week-10-overview.html"><a href="week-10-overview.html"><i class="fa fa-check"></i>Week 10 Overview</a></li>
<li class="chapter" data-level="47" data-path="regression-key-concepts.html"><a href="regression-key-concepts.html"><i class="fa fa-check"></i><b>47</b> Regression key concepts</a></li>
<li class="chapter" data-level="48" data-path="regression-validity.html"><a href="regression-validity.html"><i class="fa fa-check"></i><b>48</b> Regression validity</a></li>
<li class="chapter" data-level="49" data-path="introduction-to-multiple-regression.html"><a href="introduction-to-multiple-regression.html"><i class="fa fa-check"></i><b>49</b> Introduction to multiple regression</a></li>
<li class="chapter" data-level="50" data-path="model-selection-maybe-remove-this.html"><a href="model-selection-maybe-remove-this.html"><i class="fa fa-check"></i><b>50</b> Model selection (maybe remove this?)</a></li>
<li class="chapter" data-level="51" data-path="practical.-using-regression.html"><a href="practical.-using-regression.html"><i class="fa fa-check"></i><b>51</b> <em>Practical</em>. Using regression</a>
<ul>
<li class="chapter" data-level="51.1" data-path="practical.-using-regression.html"><a href="practical.-using-regression.html#regression-exercise-1"><i class="fa fa-check"></i><b>51.1</b> Regression Exercise 1</a></li>
<li class="chapter" data-level="51.2" data-path="practical.-using-regression.html"><a href="practical.-using-regression.html#regression-exercise-2"><i class="fa fa-check"></i><b>51.2</b> Regression Exercise 2</a></li>
<li class="chapter" data-level="51.3" data-path="practical.-using-regression.html"><a href="practical.-using-regression.html#regression-exercise-3"><i class="fa fa-check"></i><b>51.3</b> Regression Exercise 3</a></li>
<li class="chapter" data-level="51.4" data-path="practical.-using-regression.html"><a href="practical.-using-regression.html#regression-exercise-4"><i class="fa fa-check"></i><b>51.4</b> Regression Exercise 4</a></li>
</ul></li>
<li class="part"><span><b>XI Randomisation approaches</b></span></li>
<li class="chapter" data-level="" data-path="week-11-overview.html"><a href="week-11-overview.html"><i class="fa fa-check"></i>Week 11 Overview</a></li>
<li class="chapter" data-level="52" data-path="introduction-to-randomisation.html"><a href="introduction-to-randomisation.html"><i class="fa fa-check"></i><b>52</b> Introduction to randomisation</a></li>
<li class="chapter" data-level="53" data-path="assumptions-of-randomisation.html"><a href="assumptions-of-randomisation.html"><i class="fa fa-check"></i><b>53</b> Assumptions of randomisation</a></li>
<li class="chapter" data-level="54" data-path="bootstrapping.html"><a href="bootstrapping.html"><i class="fa fa-check"></i><b>54</b> Bootstrapping</a></li>
<li class="chapter" data-level="55" data-path="monte-carlo.html"><a href="monte-carlo.html"><i class="fa fa-check"></i><b>55</b> Monte Carlo</a></li>
<li class="chapter" data-level="56" data-path="practical.-using-r.html"><a href="practical.-using-r.html"><i class="fa fa-check"></i><b>56</b> <em>Practical</em>. Using R</a>
<ul>
<li class="chapter" data-level="56.1" data-path="practical.-using-r.html"><a href="practical.-using-r.html#r-exercise-1"><i class="fa fa-check"></i><b>56.1</b> R Exercise 1</a></li>
<li class="chapter" data-level="56.2" data-path="practical.-using-r.html"><a href="practical.-using-r.html#r-exercise-2"><i class="fa fa-check"></i><b>56.2</b> R Exercise 2</a></li>
<li class="chapter" data-level="56.3" data-path="practical.-using-r.html"><a href="practical.-using-r.html#r-exercise-3"><i class="fa fa-check"></i><b>56.3</b> R Exercise 3</a></li>
</ul></li>
<li class="part"><span><b>XII Statistical Reporting</b></span></li>
<li class="chapter" data-level="" data-path="week-12-overview.html"><a href="week-12-overview.html"><i class="fa fa-check"></i>Week 12 Overview</a></li>
<li class="chapter" data-level="57" data-path="reporting-statistics.html"><a href="reporting-statistics.html"><i class="fa fa-check"></i><b>57</b> Reporting statistics</a></li>
<li class="chapter" data-level="58" data-path="more-introduction-to-r.html"><a href="more-introduction-to-r.html"><i class="fa fa-check"></i><b>58</b> More introduction to R</a></li>
<li class="chapter" data-level="59" data-path="more-getting-started-with-r.html"><a href="more-getting-started-with-r.html"><i class="fa fa-check"></i><b>59</b> More getting started with R</a></li>
<li class="chapter" data-level="60" data-path="practical.-using-r-1.html"><a href="practical.-using-r-1.html"><i class="fa fa-check"></i><b>60</b> <em>Practical</em>. Using R</a>
<ul>
<li class="chapter" data-level="60.1" data-path="practical.-using-r-1.html"><a href="practical.-using-r-1.html#r-exercise-1-1"><i class="fa fa-check"></i><b>60.1</b> R Exercise 1</a></li>
<li class="chapter" data-level="60.2" data-path="practical.-using-r-1.html"><a href="practical.-using-r-1.html#r-exercise-2-1"><i class="fa fa-check"></i><b>60.2</b> R Exercise 2</a></li>
<li class="chapter" data-level="60.3" data-path="practical.-using-r-1.html"><a href="practical.-using-r-1.html#r-exercise-3-1"><i class="fa fa-check"></i><b>60.3</b> R Exercise 3</a></li>
</ul></li>
<li class="part"><span><b>XIII Review of parts (VII-XII)</b></span></li>
<li class="chapter" data-level="" data-path="module-summary.html"><a href="module-summary.html"><i class="fa fa-check"></i>Module summary</a></li>
<li class="appendix"><span><b>Appendix</b></span></li>
<li class="chapter" data-level="A" data-path="appendixA_units.html"><a href="appendixA_units.html"><i class="fa fa-check"></i><b>A</b> Statistical units</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></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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<h1><span class="header-section-number">Chapter 9</span> Decimal places and significant figures<a href="decimal-places-and-significant-figures.html#decimal-places-and-significant-figures" class="anchor-section" aria-label="Anchor link to header"></a></h1>
<p>It is important to know how to write a number you have calculated to the appropriate number of digits, typically either defined as a number of decimal places or as a number of ‘significant figures’. This is especially important in any module (for example, this one) where you are required to put numeric answers into a test or exam, as the computer will only recognise the answer as being correct if it is expressed in the way stated in the question. If you are unfamiliar with how to work out the right number of decimal places or significant figures, then these guides should be useful, although there are many other web-sources that would explain the concepts too.</p>
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