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<divid="fig-paralympic-cat-1" class="quarto-float quarto-figure quarto-figure-center anchored" alt="Two separate bar plots. The left panel shows a bar plot counting the number of gold medal athletes from each country. Great Britain has had 8 top finishers, Kenya has had 7 top finishers, and Tunisia and Algeria have both had 5. The right panel shows a bar plot counting the number of Games which have happened in each country. The USA has hosted 4 Games, the UK has hosted 3 Games, and each of Japan, Greece, Germany, France, and Australia have hosted the Games twice. ">
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<divid="fig-paralympic-cat-1" class="quarto-float quarto-figure quarto-figure-center anchored" alt="Two separate bar plots. The left panel shows a bar plot counting the number of gold medal athletes from each country. Great Britain has had 8 top finishers, Kenya has had 7 top finishers, and Tunisia and Algeria have both had 5. The right panel shows a bar plot counting the number of Games which have happened in each country. The USA has hosted 4 Games, the UK has hosted 3 Games, and each of Japan, Greece, Germany, France, and Australia have hosted the Games twice. ">
<ahref="data-applications_files/figure-html/fig-paralympic-cat-1.png" class="lightbox" data-gallery="fig-paralympic-cat" title="Figure 3.1 (a): Country of origin of the athlete"><imgsrc="data-applications_files/figure-html/fig-paralympic-cat-1.png" class="img-fluid figure-img" style="width:90.0%" data-ref-parent="fig-paralympic-cat" alt="Two separate bar plots. The left panel shows a bar plot counting the number of gold medal athletes from each country. Great Britain has had 8 top finishers, Kenya has had 7 top finishers, and Tunisia and Algeria have both had 5. The right panel shows a bar plot counting the number of Games which have happened in each country. The USA has hosted 4 Games, the UK has hosted 3 Games, and each of Japan, Greece, Germany, France, and Australia have hosted the Games twice. "></a>
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<ahref="data-applications_files/figure-html/fig-paralympic-cat-1.png" class="lightbox" data-gallery="fig-paralympic-cat" title="Figure 3.1 (a): Country in which the Games took place"><imgsrc="data-applications_files/figure-html/fig-paralympic-cat-1.png" class="img-fluid figure-img" style="width:90.0%" data-ref-parent="fig-paralympic-cat" alt="Two separate bar plots. The left panel shows a bar plot counting the number of gold medal athletes from each country. Great Britain has had 8 top finishers, Kenya has had 7 top finishers, and Tunisia and Algeria have both had 5. The right panel shows a bar plot counting the number of Games which have happened in each country. The USA has hosted 4 Games, the UK has hosted 3 Games, and each of Japan, Greece, Germany, France, and Australia have hosted the Games twice. "></a>
<divid="fig-paralympic-cat-2" class="quarto-float quarto-figure quarto-figure-center anchored" alt="Two separate bar plots. The left panel shows a bar plot counting the number of gold medal athletes from each country. Great Britain has had 8 top finishers, Kenya has had 7 top finishers, and Tunisia and Algeria have both had 5. The right panel shows a bar plot counting the number of Games which have happened in each country. The USA has hosted 4 Games, the UK has hosted 3 Games, and each of Japan, Greece, Germany, France, and Australia have hosted the Games twice. ">
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<divid="fig-paralympic-cat-2" class="quarto-float quarto-figure quarto-figure-center anchored" alt="Two separate bar plots. The left panel shows a bar plot counting the number of gold medal athletes from each country. Great Britain has had 8 top finishers, Kenya has had 7 top finishers, and Tunisia and Algeria have both had 5. The right panel shows a bar plot counting the number of Games which have happened in each country. The USA has hosted 4 Games, the UK has hosted 3 Games, and each of Japan, Greece, Germany, France, and Australia have hosted the Games twice. ">
<ahref="data-applications_files/figure-html/fig-paralympic-cat-2.png" class="lightbox" data-gallery="fig-paralympic-cat" title="Figure 3.1 (b): Country in which the Games gook place"><imgsrc="data-applications_files/figure-html/fig-paralympic-cat-2.png" class="img-fluid figure-img" style="width:90.0%" data-ref-parent="fig-paralympic-cat" alt="Two separate bar plots. The left panel shows a bar plot counting the number of gold medal athletes from each country. Great Britain has had 8 top finishers, Kenya has had 7 top finishers, and Tunisia and Algeria have both had 5. The right panel shows a bar plot counting the number of Games which have happened in each country. The USA has hosted 4 Games, the UK has hosted 3 Games, and each of Japan, Greece, Germany, France, and Australia have hosted the Games twice. "></a>
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<ahref="data-applications_files/figure-html/fig-paralympic-cat-2.png" class="lightbox" data-gallery="fig-paralympic-cat" title="Figure 3.1 (b): Country of origin of the athlete"><imgsrc="data-applications_files/figure-html/fig-paralympic-cat-2.png" class="img-fluid figure-img" style="width:90.0%" data-ref-parent="fig-paralympic-cat" alt="Two separate bar plots. The left panel shows a bar plot counting the number of gold medal athletes from each country. Great Britain has had 8 top finishers, Kenya has had 7 top finishers, and Tunisia and Algeria have both had 5. The right panel shows a bar plot counting the number of Games which have happened in each country. The USA has hosted 4 Games, the UK has hosted 3 Games, and each of Japan, Greece, Germany, France, and Australia have hosted the Games twice. "></a>
<p>Let’s start by considering how the 1500m gold medal race times have changed over year. <ahref="#fig-paralympic-ungrouped" class="quarto-xref">Figure <span>3.3</span></a> shows a scatterplot describing 1500m race times and year for Men’s Olympic and Paralympic (T11) athletes with a line of best fit (to the entire dataset) superimposed (see <ahref="model-slr.html" class="quarto-xref"><span>Chapter 7</span></a> where we will present fitting a line to a scatterplot). Notice that the line of best fit shows a <em>positive</em> relationship between race time and year. That is, for later years, the predicted gold medal time is higher than in earlier years.</p>
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<divid="fig-paralympic-ungrouped" class="quarto-float quarto-figure quarto-figure-center anchored" alt="A scatterplot with year on the x-axis and gold medal 1500m time on the y-axis. A line of best fit is drawn over the points. ">
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<divid="fig-paralympic-ungrouped" class="quarto-float quarto-figure quarto-figure-center anchored" alt="A scatterplot with year on the x-axis and gold medal 1500m time on the y-axis. A line of best fit is drawn over the points. ">
<ahref="data-applications_files/figure-html/fig-paralympic-ungrouped-1.png" class="lightbox" data-gallery="quarto-lightbox-gallery-4" title="Figure 3.3: 1500m race time for Men’s Olympic and Paralympic (T11) athletes. The line represents a line of best fit to the entire dataset."><imgsrc="data-applications_files/figure-html/fig-paralympic-ungrouped-1.png" class="img-fluid figure-img" style="width:90.0%" alt="A scatterplot with year on the x-axis and gold medal 1500m time on the y-axis. A line of best fit is drawn over the points. "></a>
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<ahref="data-applications_files/figure-html/fig-paralympic-ungrouped-1.png" class="lightbox" data-gallery="quarto-lightbox-gallery-4" title="Figure 3.3: 1500m race time for Men’s Olympic and Paralympic (T11) athletes. The line represents a line of best fit to the entire dataset."><imgsrc="data-applications_files/figure-html/fig-paralympic-ungrouped-1.png" class="img-fluid figure-img" style="width:90.0%" alt="A scatterplot with year on the x-axis and gold medal 1500m time on the y-axis. A line of best fit is drawn over the points. "></a>
<p>A proficient analyst will have a good sense of the types of data they are working with and how to visualize the data in order to gain a complete understanding of the variables. Equally important, however, is the data source. In this chapter, we have discussed randomized experiments and taking good, random, representative samples from a population. When we discuss inferential methods (starting in <ahref="foundations-randomization.html" class="quarto-xref"><span>Chapter 11</span></a>), the conclusions that can be drawn will be dependent on how the data were collected. <ahref="#fig-randsampValloc" class="quarto-xref">Figure <span>2.8</span></a> summarizes how sampling and assignment methods relate to the scope of inference.<ahref="#fn10" class="footnote-ref" id="fnref10" role="doc-noteref"><sup>10</sup></a> Regularly revisiting <ahref="#fig-randsampValloc" class="quarto-xref">Figure <span>2.8</span></a> will be important when making conclusions from a given data analysis.</p>
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<divid="fig-randsampValloc" class="quarto-float quarto-figure quarto-figure-center anchored" data-fig-pos="H" alt="A two by two table describing the scenarios of random sample or not and random allocation or not. Selecting randomly from a population allows for generalization back to the population. Randomly allocating in an experiment allows for establishing causation. ">
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<divid="fig-randsampValloc" class="quarto-float quarto-figure quarto-figure-center anchored" alt="A two by two table describing the scenarios of random sample or not and random allocation or not. Selecting randomly from a population allows for generalization back to the population. Randomly allocating in an experiment allows for establishing causation. " data-fig-pos="H">
<ahref="images/randsampValloc.png" class="lightbox" data-gallery="quarto-lightbox-gallery-8" title="Figure 2.8: Analysis conclusions should be made carefully according to how the data were collected. Very few datasets come from the top left box because usually ethics require that random assignment of treatments can only be given to volunteers. Both representative (ideally random) sampling and experiments (random assignment of treatments) are important for how statistical conclusions can be made on populations."><imgsrc="images/randsampValloc.png" class="img-fluid figure-img" style="width:96.0%" data-fig-pos="H" alt="A two by two table describing the scenarios of random sample or not and random allocation or not. Selecting randomly from a population allows for generalization back to the population. Randomly allocating in an experiment allows for establishing causation. "></a>
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