Spearman Rank Correlation Coefficient

<p class="MsoNormal" style="text-align:justify;line-height:200%"> <span style="font-family:Arial">The table shows the recorded grades of the 10 students on the midterm test as well as the final examination for the subject of probability. Determine the correlation using the Spearman Rank Correlation. </span></p><br /><p class="MsoNormal" align="center" style="text-align:center"> <span style="font-size:10.0pt;font-family:Arial">Student</span></p><br /><p class="MsoNormal" align="center" style="text-align:center"> <span style="font-size:10.0pt;font-family:Arial">Midterm Test</span></p><br /><p class="MsoNormal" align="center" style="text-align:center"> <span style="font-size:10.0pt;font-family:Arial">Final Exam</span></p><br /><p class="MsoNormal" align="center" style="text-align:center"> <span style="font-size:10.0pt;font-family:Arial">1</span></p><br /><p class="MsoNormal" align="center" style="text-align:center"> <span style="font-size:10.0pt;font-family:Arial">87</span></p><br /><p class="MsoNormal" align="center" style="text-align:center"> <span style="font-size:10.0pt;font-family:Arial">77</span></p><br /><p class="MsoNormal" align="center" style="text-align:center"> <span style="font-size:10.0pt;font-family:Arial">2</span></p><br /><p class="MsoNormal" align="center" style="text-align:center"> <span style="font-size:10.0pt;font-family:Arial">92</span></p><br /><p class="MsoNormal" align="center" style="text-align:center"> <span style="font-size:10.0pt;font-family:Arial">88</span></p><br /><p class="MsoNormal" align="center" style="text-align:center"> <span style="font-size:10.0pt;font-family:Arial">3</span></p><br /><p class="MsoNormal" align="center" style="text-align:center"> <span style="font-size:10.0pt;font-family:Arial">78</span></p><br /><p class="MsoNormal" align="center" style="text-align:center"> <span style="font-size:10.0pt;font-family:Arial">80</span></p><br /><p class="MsoNormal" align="center" style="text-align:center"> <span style="font-size:10.0pt;font-family:Arial">4</span></p><br /><p class="MsoNormal" align="center" style="text-align:center"> <span style="font-size:10.0pt;font-family:Arial">80</span></p><br /><p class="MsoNormal" align="center" style="text-align:center"> <span style="font-size:10.0pt;font-family:Arial">91</span></p><br /><p class="MsoNormal" align="center" style="text-align:center"> <span style="font-size:10.0pt;font-family:Arial">5</span></p><br /><p class="MsoNormal" align="center" style="text-align:center"> <span style="font-size:10.0pt;font-family:Arial">93</span></p><br /><p class="MsoNormal" align="center" style="text-align:center"> <span style="font-size:10.0pt;font-family:Arial">78</span></p><br /><p class="MsoNormal" align="center" style="text-align:center"> <span style="font-size:10.0pt;font-family:Arial">6</span></p><br /><p class="MsoNormal" align="center" style="text-align:center"> <span style="font-size:10.0pt;font-family:Arial">86</span></p><br /><p class="MsoNormal" align="center" style="text-align:center"> <span style="font-size:10.0pt;font-family:Arial">78</span></p><br /><p class="MsoNormal" align="center" style="text-align:center"> <span style="font-size:10.0pt;font-family:Arial">7</span></p><br /><p class="MsoNormal" align="center" style="text-align:center"> <span style="font-size:10.0pt;font-family:Arial">72</span></p><br /><p class="MsoNormal" align="center" style="text-align:center"> <span style="font-size:10.0pt;font-family:Arial">66</span></p><br /><p class="MsoNormal" align="center" style="text-align:center"> <span style="font-size:10.0pt;font-family:Arial">8</span></p><br /><p class="MsoNormal" align="center" style="text-align:center"> <span style="font-size:10.0pt;font-family:Arial">91</span></p><br /><p class="MsoNormal" align="center" style="text-align:center"> <span style="font-size:10.0pt;font-family:Arial">87</span></p><br /><p class="MsoNormal" align="center" style="text-align:center"> <span style="font-size:10.0pt;font-family:Arial">9</span></p><br /><p class="MsoNormal" align="center" style="text-align:center"> <span style="font-size:10.0pt;font-family:Arial">98</span></p><br /><p class="MsoNormal" align="center" style="text-align:center"> <span style="font-size:10.0pt;font-family:Arial">63</span></p><br /><p class="MsoNormal" align="center" style="text-align:center"> <span style="font-size:10.0pt;font-family:Arial">10</span></p><br /><p class="MsoNormal" align="center" style="text-align:center"> <span style="font-size:10.0pt;font-family:Arial">84</span></p><br /><p class="MsoNormal" align="center" style="text-align:center"> <span style="font-size:10.0pt;font-family:Arial">73</span></p><br /><p class="MsoNormal" style="text-align:justify;line-height:200%"> <span style="font-family:Arial"> </span></p><br /><p class="MsoNormal" style="text-align:justify;line-height:200%"> <span style="font-family:Arial">Using the Spearman Rank Correlation Coefficient, the value of r is:</span></p><br /><p class="MsoNormal" style="text-align:justify;line-height:200%"> <span style="font-family:Arial">            r = 1 – 6 ∑ d2/ n (n-1) = 1</span></p><br /><p class="MsoNormal" style="text-align:justify;line-height:200%"> <span style="font-family:Arial">               = 1 – 6 (125.5)/10(102 -1) </span></p><br /><p class="MsoNormal" style="text-align:justify;text-indent:.5in;line-height:200%"> <span style="font-family:Arial">   = 1 – 753/990 </span></p><br /><p class="MsoNormal" style="margin-left:.5in;text-align:justify;line-height:200%"> <span style="font-family:Arial">   = 1 – 0.76</span></p><br /><p><span style="font-size: 12.0pt; font-family: Arial">   = 0.24 or has the low correlation </span></p><br /></p><br /><p><br />Credit:ivythesis.typepad.com</p><br />

Spearman Rank Correlation Coefficient

The table shows the recorded grades of the 10 students on the midterm test as well as the final examination for the subject of probabilit...

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