Supplementary Exercise 2.7 of IPS7e
-----------------------------------

A study on trapping of cereal leaf beetles in an oat field on boards of
different colours. Four board colours (lemon yellow, white, green, blue)
were used, and there were six boards per colour.


(a) We use Minitab to display the counts in an Individual Value Plot,
and to compute descriptive statistics. In Minitab 17, the means can
be added directly to the Individual Value Plot by selecting Means as the
Label in the Labels-Data Labels submenu. It is also possible to edit the
the plot after it has been displayed (right-click on values, choose 
Add - Data Labels, select the Means tab and use y-values to display the 
means). It is not obvious why one would want to connect the means across 
the different categories (colours); such connecting lines could be viewed 
as misleading because the order of the categories has no real meaning. 

Another option to display the data points is a dotplot. A boxplot
will instead display the 5-number summary (which is quite noisy here 
with only 6 observations per group), and in a similar fashion as
described above the group means (or medians) can be inserted onto the
graph.

MTB > WOpen "R:\Chapter 2\ex02_007.mtw".
Retrieving worksheet from file: ‘R:\Chapter 2\ex02_007.mtw’
Worksheet was saved on 06/09/2014

MTB > Indplot ( 'beetles' ) * 'color';
SUBC>   MeaLabel;
SUBC>     YValue;
SUBC>   Individual.
Individual Value Plot of beetles 

MTB > Dotplot ( 'beetles' ) * 'color'.
Dotplot of beetles 

MTB > Boxplot ( 'beetles' ) * 'color';
SUBC>   MeaLabel;
SUBC>     YValue;
SUBC>   IQRBox;
SUBC>   Outlier.
Boxplot of beetles 

MTB > Describe 'beetles';
SUBC>   By 'color'.
Descriptive Statistics: beetles 

Variable  color  N  N*   Mean  SE Mean  StDev  Minimum     Q1  Median     Q3  Maximum
beetles   Blue   6   0  14.83     2.18   5.34     7.00  10.00   15.00  20.25    21.00
          Green  6   0  31.50     4.05   9.91    15.00  22.50   34.50  39.50    41.00
          Lemon  6   0  47.17     2.77   6.79    38.00  43.25   46.50  50.75    59.00
          White  6   0  15.67     1.36   3.33    12.00  12.75   15.50  18.00    21.00


(b) Although the data set is small, it seems that the lemon yellow
boards attract most beetles, followed by the green boards. There is a
little overlap in the distributions for these two colours. The white and
blue boards seem to attract substantially less beetles than the lemon
yellow board because the beetle counts for those two colours are all
less than those for the lemon yellow board; in other words, the
distributions appear completely separated. The largest spread in the
beetle counts is observed for the green boards, with the lowest count as 
low as for the blue and white boards and with the highest counts as high
as for the lemon yellow board. Without a proper statistical analysis it
is impossible to say whether the differences observed could have
happened by chance alone (that is, whether they are statistically
significant), but intuitively one would expect at least the differences
between the lemon yellow and the two boards with lowest counts (blue and
white) to be significant.


(c) No. The board colour is a categorical variable, and we can only speak
about positive or negative associations between quantitative variables.