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<!DOCTYPE html>
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<title>Chapter 2 Overview | Statistical Techniques for Biological and Environmental Sciences</title>
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<meta name="twitter:title" content="Chapter 2 Overview | 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="2022-08-24" />
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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#jamovi-statistical-software"><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="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>
<li class="chapter" data-level="1.3" data-path="background_mathematics.html"><a href="background_mathematics.html#tidy-data"><i class="fa fa-check"></i><b>1.3</b> Tidy data</a></li>
<li class="chapter" data-level="1.4" data-path="background_mathematics.html"><a href="background_mathematics.html#data-files"><i class="fa fa-check"></i><b>1.4</b> Data files</a></li>
<li class="chapter" data-level="1.5" data-path="background_mathematics.html"><a href="background_mathematics.html#libreoffice-calc"><i class="fa fa-check"></i><b>1.5</b> LibreOffice Calc</a></li>
<li class="chapter" data-level="1.6" data-path="background_mathematics.html"><a href="background_mathematics.html#exercise-organising-data-1"><i class="fa fa-check"></i><b>1.6</b> Exercise Organising data 1</a></li>
<li class="chapter" data-level="1.7" data-path="background_mathematics.html"><a href="background_mathematics.html#exercise-organising-data-2"><i class="fa fa-check"></i><b>1.7</b> Exercise Organising data 2</a></li>
<li class="chapter" data-level="1.8" data-path="background_mathematics.html"><a href="background_mathematics.html#exercise-organising-data-3"><i class="fa fa-check"></i><b>1.8</b> Exercise Organising data 3</a></li>
<li class="chapter" data-level="1.9" data-path="background_mathematics.html"><a href="background_mathematics.html#summary-of-exercises-and-why-they-are-useful."><i class="fa fa-check"></i><b>1.9</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="2" data-path="overview.html"><a href="overview.html"><i class="fa fa-check"></i><b>2</b> Overview</a></li>
<li class="chapter" data-level="3" data-path="populations-and-samples.html"><a href="populations-and-samples.html"><i class="fa fa-check"></i><b>3</b> Populations and samples</a></li>
<li class="chapter" data-level="4" data-path="types-of-variables.html"><a href="types-of-variables.html"><i class="fa fa-check"></i><b>4</b> Types of variables</a></li>
<li class="chapter" data-level="5" data-path="units-precision-and-accuracy.html"><a href="units-precision-and-accuracy.html"><i class="fa fa-check"></i><b>5</b> Units, precision, and accuracy</a></li>
<li class="chapter" data-level="6" data-path="uncertainty-propogation.html"><a href="uncertainty-propogation.html"><i class="fa fa-check"></i><b>6</b> Uncertainty propogation</a></li>
<li class="chapter" data-level="7" data-path="practical.-introduction-to-jamovi.html"><a href="practical.-introduction-to-jamovi.html"><i class="fa fa-check"></i><b>7</b> <em>Practical</em>. Introduction to Jamovi</a>
<ul>
<li class="chapter" data-level="7.1" data-path="practical.-introduction-to-jamovi.html"><a href="practical.-introduction-to-jamovi.html#exercise-for-summary-statistics"><i class="fa fa-check"></i><b>7.1</b> Exercise for summary statistics</a></li>
<li class="chapter" data-level="7.2" data-path="practical.-introduction-to-jamovi.html"><a href="practical.-introduction-to-jamovi.html#exercise-to-compute-variable"><i class="fa fa-check"></i><b>7.2</b> Exercise to compute variable</a></li>
<li class="chapter" data-level="7.3" data-path="practical.-introduction-to-jamovi.html"><a href="practical.-introduction-to-jamovi.html#exercise-on-transforming-variables"><i class="fa fa-check"></i><b>7.3</b> Exercise on transforming variables</a></li>
</ul></li>
<li class="part"><span><b>III Summary statistics</b></span></li>
<li class="chapter" data-level="8" data-path="decimal-places-and-significant-figures.html"><a href="decimal-places-and-significant-figures.html"><i class="fa fa-check"></i><b>8</b> Decimal places and significant figures</a>
<ul>
<li class="chapter" data-level="8.1" data-path="decimal-places-and-significant-figures.html"><a href="decimal-places-and-significant-figures.html#general-principles"><i class="fa fa-check"></i><b>8.1</b> General principles</a></li>
<li class="chapter" data-level="8.2" data-path="decimal-places-and-significant-figures.html"><a href="decimal-places-and-significant-figures.html#histograms"><i class="fa fa-check"></i><b>8.2</b> Histograms</a></li>
<li class="chapter" data-level="8.3" data-path="decimal-places-and-significant-figures.html"><a href="decimal-places-and-significant-figures.html#box-whisker-plots"><i class="fa fa-check"></i><b>8.3</b> Box-whisker plots</a></li>
<li class="chapter" data-level="8.4" data-path="decimal-places-and-significant-figures.html"><a href="decimal-places-and-significant-figures.html#some-biological-example"><i class="fa fa-check"></i><b>8.4</b> Some biological example</a></li>
<li class="chapter" data-level="8.5" data-path="decimal-places-and-significant-figures.html"><a href="decimal-places-and-significant-figures.html#some-environmental-example"><i class="fa fa-check"></i><b>8.5</b> Some environmental example</a></li>
<li class="chapter" data-level="8.6" data-path="decimal-places-and-significant-figures.html"><a href="decimal-places-and-significant-figures.html#summary-of-exercises-and-why-they-are-useful.-1"><i class="fa fa-check"></i><b>8.6</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="9" data-path="introduction-to-probability-models.html"><a href="introduction-to-probability-models.html"><i class="fa fa-check"></i><b>9</b> Introduction to probability models</a>
<ul>
<li class="chapter" data-level="9.1" data-path="introduction-to-probability-models.html"><a href="introduction-to-probability-models.html#a-practical-example"><i class="fa fa-check"></i><b>9.1</b> A practical example</a></li>
<li class="chapter" data-level="9.2" data-path="introduction-to-probability-models.html"><a href="introduction-to-probability-models.html#probability-distributions"><i class="fa fa-check"></i><b>9.2</b> Probability distributions</a>
<ul>
<li class="chapter" data-level="9.2.1" data-path="introduction-to-probability-models.html"><a href="introduction-to-probability-models.html#binomial-distribution"><i class="fa fa-check"></i><b>9.2.1</b> Binomial distribution</a></li>
<li class="chapter" data-level="9.2.2" data-path="introduction-to-probability-models.html"><a href="introduction-to-probability-models.html#poisson-distribution"><i class="fa fa-check"></i><b>9.2.2</b> Poisson distribution</a></li>
<li class="chapter" data-level="9.2.3" data-path="introduction-to-probability-models.html"><a href="introduction-to-probability-models.html#normal-distribution"><i class="fa fa-check"></i><b>9.2.3</b> Normal distribution</a></li>
</ul></li>
<li class="chapter" data-level="9.3" data-path="introduction-to-probability-models.html"><a href="introduction-to-probability-models.html#examples-of-the-clt-in-action"><i class="fa fa-check"></i><b>9.3</b> Examples of the CLT in action</a></li>
<li class="chapter" data-level="9.4" data-path="introduction-to-probability-models.html"><a href="introduction-to-probability-models.html#the-standard-normal-distribution"><i class="fa fa-check"></i><b>9.4</b> The standard normal distribution</a></li>
<li class="chapter" data-level="9.5" data-path="introduction-to-probability-models.html"><a href="introduction-to-probability-models.html#what-are-z-scores"><i class="fa fa-check"></i><b>9.5</b> What are z-scores?</a></li>
<li class="chapter" data-level="9.6" data-path="introduction-to-probability-models.html"><a href="introduction-to-probability-models.html#calculating-probability-exercise-1"><i class="fa fa-check"></i><b>9.6</b> Calculating probability exercise 1</a></li>
<li class="chapter" data-level="9.7" data-path="introduction-to-probability-models.html"><a href="introduction-to-probability-models.html#calculating-probability-exercise-2"><i class="fa fa-check"></i><b>9.7</b> Calculating probability exercise 2</a></li>
<li class="chapter" data-level="9.8" data-path="introduction-to-probability-models.html"><a href="introduction-to-probability-models.html#calculating-probability-from-normal-distribution"><i class="fa fa-check"></i><b>9.8</b> Calculating probability from normal distribution</a></li>
<li class="chapter" data-level="9.9" data-path="introduction-to-probability-models.html"><a href="introduction-to-probability-models.html#normal-distribution-and-sample-size"><i class="fa fa-check"></i><b>9.9</b> Normal distribution and sample size</a></li>
<li class="chapter" data-level="9.10" data-path="introduction-to-probability-models.html"><a href="introduction-to-probability-models.html#simulating-the-central-limit-theorem"><i class="fa fa-check"></i><b>9.10</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="10" data-path="sample-statistics-and-population-parameters.html"><a href="sample-statistics-and-population-parameters.html"><i class="fa fa-check"></i><b>10</b> Sample statistics and population parameters</a>
<ul>
<li class="chapter" data-level="10.1" data-path="sample-statistics-and-population-parameters.html"><a href="sample-statistics-and-population-parameters.html#example-constructing-confidence-intervals"><i class="fa fa-check"></i><b>10.1</b> Example constructing confidence intervals</a></li>
<li class="chapter" data-level="10.2" data-path="sample-statistics-and-population-parameters.html"><a href="sample-statistics-and-population-parameters.html#confidence-interval-for-different-levels-t--and-z-"><i class="fa fa-check"></i><b>10.2</b> Confidence interval for different levels (t- and z-)</a></li>
<li class="chapter" data-level="10.3" data-path="sample-statistics-and-population-parameters.html"><a href="sample-statistics-and-population-parameters.html#proportion-confidence-intervals"><i class="fa fa-check"></i><b>10.3</b> Proportion confidence intervals</a></li>
<li class="chapter" data-level="10.4" data-path="sample-statistics-and-population-parameters.html"><a href="sample-statistics-and-population-parameters.html#another-confidence-interval-example"><i class="fa fa-check"></i><b>10.4</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="part"><span><b>VII Hypothesis testing</b></span></li>
<li class="chapter" data-level="11" data-path="what-is-hypothesis-testing.html"><a href="what-is-hypothesis-testing.html"><i class="fa fa-check"></i><b>11</b> What is hypothesis testing?</a>
<ul>
<li class="chapter" data-level="11.1" data-path="what-is-hypothesis-testing.html"><a href="what-is-hypothesis-testing.html#exercise-on-a-simple-one-sample-t-test"><i class="fa fa-check"></i><b>11.1</b> Exercise on a simple one sample t-test</a></li>
<li class="chapter" data-level="11.2" data-path="what-is-hypothesis-testing.html"><a href="what-is-hypothesis-testing.html#exercise-on-an-independent-sample-t-test"><i class="fa fa-check"></i><b>11.2</b> Exercise on an independent sample t-test</a></li>
<li class="chapter" data-level="11.3" data-path="what-is-hypothesis-testing.html"><a href="what-is-hypothesis-testing.html#exercise-involving-multiple-comparisons"><i class="fa fa-check"></i><b>11.3</b> Exercise involving multiple comparisons</a></li>
<li class="chapter" data-level="11.4" data-path="what-is-hypothesis-testing.html"><a href="what-is-hypothesis-testing.html#exercise-with-non-parametric"><i class="fa fa-check"></i><b>11.4</b> Exercise with non-parametric</a></li>
<li class="chapter" data-level="11.5" data-path="what-is-hypothesis-testing.html"><a href="what-is-hypothesis-testing.html#another-exercise-with-non-parametric"><i class="fa fa-check"></i><b>11.5</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="12" data-path="what-is-anova.html"><a href="what-is-anova.html"><i class="fa fa-check"></i><b>12</b> What is ANOVA?</a>
<ul>
<li class="chapter" data-level="12.1" data-path="what-is-anova.html"><a href="what-is-anova.html#anova-exercise-1"><i class="fa fa-check"></i><b>12.1</b> ANOVA Exercise 1</a></li>
<li class="chapter" data-level="12.2" data-path="what-is-anova.html"><a href="what-is-anova.html#anova-exercise-2"><i class="fa fa-check"></i><b>12.2</b> ANOVA Exercise 2</a></li>
<li class="chapter" data-level="12.3" data-path="what-is-anova.html"><a href="what-is-anova.html#anova-exercise-3"><i class="fa fa-check"></i><b>12.3</b> ANOVA Exercise 3</a></li>
<li class="chapter" data-level="12.4" data-path="what-is-anova.html"><a href="what-is-anova.html#anova-exercise-4"><i class="fa fa-check"></i><b>12.4</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="13" data-path="frequency-and-count-data.html"><a href="frequency-and-count-data.html"><i class="fa fa-check"></i><b>13</b> Frequency and count data</a>
<ul>
<li class="chapter" data-level="13.1" data-path="frequency-and-count-data.html"><a href="frequency-and-count-data.html#chi-square-exercise-1"><i class="fa fa-check"></i><b>13.1</b> Chi-Square Exercise 1</a></li>
<li class="chapter" data-level="13.2" data-path="frequency-and-count-data.html"><a href="frequency-and-count-data.html#chi-square-association-exercise-2"><i class="fa fa-check"></i><b>13.2</b> Chi-Square association Exercise 2</a></li>
<li class="chapter" data-level="13.3" data-path="frequency-and-count-data.html"><a href="frequency-and-count-data.html#correlation-exercise-3"><i class="fa fa-check"></i><b>13.3</b> Correlation Exercise 3</a></li>
<li class="chapter" data-level="13.4" data-path="frequency-and-count-data.html"><a href="frequency-and-count-data.html#correlation-exercise-4"><i class="fa fa-check"></i><b>13.4</b> Correlation Exercise 4</a></li>
</ul></li>
<li class="part"><span><b>X Linear Regression</b></span></li>
<li class="chapter" data-level="14" data-path="regression-key-concepts.html"><a href="regression-key-concepts.html"><i class="fa fa-check"></i><b>14</b> Regression key concepts</a>
<ul>
<li class="chapter" data-level="14.1" data-path="regression-key-concepts.html"><a href="regression-key-concepts.html#regression-exercise-1"><i class="fa fa-check"></i><b>14.1</b> Regression Exercise 1</a></li>
<li class="chapter" data-level="14.2" data-path="regression-key-concepts.html"><a href="regression-key-concepts.html#regression-exercise-2"><i class="fa fa-check"></i><b>14.2</b> Regression Exercise 2</a></li>
<li class="chapter" data-level="14.3" data-path="regression-key-concepts.html"><a href="regression-key-concepts.html#regression-exercise-3"><i class="fa fa-check"></i><b>14.3</b> Regression Exercise 3</a></li>
<li class="chapter" data-level="14.4" data-path="regression-key-concepts.html"><a href="regression-key-concepts.html#regression-exercise-4"><i class="fa fa-check"></i><b>14.4</b> Regression Exercise 4</a></li>
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<li class="part"><span><b>XI Randomisation approaches</b></span></li>
<li class="chapter" data-level="15" data-path="introduction-to-randomisation.html"><a href="introduction-to-randomisation.html"><i class="fa fa-check"></i><b>15</b> Introduction to randomisation</a>
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<li class="chapter" data-level="15.1" data-path="introduction-to-randomisation.html"><a href="introduction-to-randomisation.html#r-exercise-1"><i class="fa fa-check"></i><b>15.1</b> R Exercise 1</a></li>
<li class="chapter" data-level="15.2" data-path="introduction-to-randomisation.html"><a href="introduction-to-randomisation.html#r-exercise-2"><i class="fa fa-check"></i><b>15.2</b> R Exercise 2</a></li>
<li class="chapter" data-level="15.3" data-path="introduction-to-randomisation.html"><a href="introduction-to-randomisation.html#r-exercise-3"><i class="fa fa-check"></i><b>15.3</b> R Exercise 3</a></li>
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<li class="part"><span><b>XII Statistical Reporting</b></span></li>
<li class="chapter" data-level="16" data-path="reporting-statistics.html"><a href="reporting-statistics.html"><i class="fa fa-check"></i><b>16</b> Reporting statistics</a>
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<li class="chapter" data-level="16.1" data-path="reporting-statistics.html"><a href="reporting-statistics.html#r-exercise-1-1"><i class="fa fa-check"></i><b>16.1</b> R Exercise 1</a></li>
<li class="chapter" data-level="16.2" data-path="reporting-statistics.html"><a href="reporting-statistics.html#r-exercise-2-1"><i class="fa fa-check"></i><b>16.2</b> R Exercise 2</a></li>
<li class="chapter" data-level="16.3" data-path="reporting-statistics.html"><a href="reporting-statistics.html#r-exercise-3-1"><i class="fa fa-check"></i><b>16.3</b> R Exercise 3</a></li>
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<li class="part"><span><b>XIII Review of parts (VII-XII)</b></span></li>
<li class="chapter" data-level="" data-path="references.html"><a href="references.html"><i class="fa fa-check"></i>References</a></li>
<li class="appendix"><span><b>Appendix</b></span></li>
<li class="chapter" data-level="A" data-path="statistical-tables.html"><a href="statistical-tables.html"><i class="fa fa-check"></i><b>A</b> Statistical tables</a></li>
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<div class="line-block"><strong>Week:</strong> | 2 |<br />
<strong>Dates</strong> | 3 |<br />
<strong>Reading</strong> | Recommended: |<br />
<strong>Assessments</strong> | Practice quiz |</div>
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<p>In week 2, we focus on concepts that will be used throughout this module.
In particular, it is important to understand the difference between a <strong>population</strong> and a <strong>sample</strong>, and to recognise that there are many types of variables in statistics.
Different types of variables have different characteristics, which will affect how these variables are visualised in figures and analysed with statistical techniques.</p>
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