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Minitab v13 - Correlation

The Minitab Project is available. It contains the following data:

Column
N
Comments
Math 5 scores on a 20 point quiz.
Science 5 scores on a 20 point quiz.
Beauty 5 ranks on beauty (1=most)
Sociability 5 ranks on beauty (1=most)
Beautyrk 5 ranks on beauty (5=most)
SciRank 5 ranks on science quiz (5=most/best)

Pearson R

First have Minitab creat the scatterplot. Use the "Scatter Plot..." command off of the "Graph, Character Graphs" menu. That is:

That will take you to the following dialog box:

Type in (or double click them from the left hand menu) Math and Science for the "Y and X variables". We won't bother with annotating or altering the scale. The output will look like:

Plot

     -
     -                                                  x
 17.5+
     -
Math -
     -                                 x
     -
 15.0+
     -
     -
     -
     -      x
 12.5+
     -                          x
     -
     -             x
     -
       --------+---------+---------+---------+---------+-
            10.5      12.0      13.5      15.0      16.5
                                             
Science

Then compute the correlation. Use the "Correlation..." command off of the "Stat, Basic Statistics" menu. That is:

That will take you to the following dialog box:

Type in (or double click them from the left hand menu) Math and Science. Also, make sure that "Display p-values" and "Store matrix" are unchecked for now. The output will look like this:

Correlations: Math, Science

Pearson correlation of Math and Science = 0.845

Spearman's Rho - Example 1

First have Minitab creat the scatterplot. Use the "Scatter Plot..." command off of the "Graph, Character Graphs" menu. That is:

That will take you to the following dialog box:

Type in (or double click them from the left hand menu) Beauty and Sociab for the "Y and X variables". We won't bother with annotating or altering the scale. The resulting graph will look like:

Plot

Beauty
   -
   -                                        x
   -
4.5+
   -
   -                                                    x
   -
   -
3.0+                            x
   -
   -
   -    x
   -
1.5+
   -
   -                 x
   -
     +---------+---------+---------+---------+---------+-
  0.80      1.60      2.40      3.20      4.00      4.80
                                                 Sociab

Since when Pearson's r is computed on ranked data it gives the same value as Spearman's Rho, we compute the correlation in the same way that we did for Pearson's r. That is, use the "Correlation..." command off of the "Stat, Basic Statistics" menu. That is:

That will take you to the following dialog box:

Type in (or double click them from the left hand menu) Beauty and Sociab. Also, make sure that "Display p-values" and "Store matrix" are unchecked for now. The output will look like this:

Correlations: Beauty, Sociab

Pearson correlation of Beauty and Sociab = 0.800

Spearman's Rho - Example 2

First we need to have Minitab rank the Science data. We will use the calculator in Minitab to generate that variable. Use the "Calculator..." command off of the "Calc" menu. That is:

That will take you to the following dialog box:

Type in (or double click on) SciRank for the "Store result in variable:" box. For the "Expression:", you can type or click on the necessary values. Minitab has lots of useful "Functions:". We can also rerank Beauty (so the numbers go from low to high) using the transformation indicated below. It simply flips the ranking.

Now that both variables are ranked, we can compute the scatterplot. Use the "Scatter Plot..." command off of the "Graph, Character Graphs" menu. That is:

That will take you to the following dialog box:

Type in (or double click them from the left hand menu) the values for the "Y and X variables". We won't bother with annotating or altering the scale. The resulting graph will look like:

Plot

BeautyRk
   -
   -    x
   -
4.5+
   -
   -                                                    x
   -
   -
3.0+                x
   -
   -
   -                                         x
   -
1.5+
   -
   -                            x
   -
     +---------+---------+---------+---------+---------+-
  0.80      1.60      2.40      3.20      4.00       4.80
                                             SciRank

Then compute the correlation. Use the "Correlation..." command off of the "Stat, Basic Statistics" menu. That is:

That will take you to the following dialog box:

Type in (or double click them from the left hand menu) the appropriate values. Also, make sure that "Display p-values" and "Store matrix" are unchecked for now. The output will look like this:

Correlations: BeautyRk, SciRank

Pearson correlation of BeautyRk and SciRank = -0.300


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