RFC: Statistics in Subsurface
Willem Ferguson
willemferguson at zoology.up.ac.za
Sat May 16 07:13:52 PDT 2020
This is just an attempt to enumerate how many types of graphs one is
likely to need, given the discussion until now. As a basis I use Dirk's
Proposal for selecting a appropriate graph.
In the above diagram, the different types of variables have different
colours.
1) The yellow ones are just totals (Total # dives, Total no.
minutes/hours) that are unlikely to have any associated minimum or maximum.
2) The blue ones are variables defined in terms of categories. Date :
day, week, month, etc; Trip : trip locality; suit: type of dive suit;
tags : tag text. There is no dive suite value inbetween wetsuit and
semidry suit because they are two distinct categories.
3) The white ones are continuous numeric variables. Duration can
potentially have any arbitrary number of minutes or hours. The same goes
for Max_depth, Min_temp, SAC, and all the other white ones. Inbetween
any two arbitrary depths there are innumerable intermediate depths and
depth only becomes a value along a continuous scale.
The type of graph that best depicts a relationship between two types of
variables depends on the colour that each of the variables above has. I
need to emphasize that the graphs below are totally open to discussion.
The purpose here is to assess how many types of graphical elements one
would need for a basic statistics tab in Subsurface.
Plotting a yellow variable against a blue variable is probably best
represented by a simplistic bar graph like:
There are no min and max values to indicate. The different suit
categories are indicated along the horizontal axis. There is no need to
specify a degree of "granularity" or increment along the horizontal axis
and no min or max values are involved.
If one plots a yellow variable against a white (continuous) variable,
then a granularity/increment needs to be specified. In the image below,
an increment of 20m was used.
Basically the same type of graph as the one used above. No need for
min/max values. Of course, as was well argued previously, the bar graph
can be horizontal in the case of long names on the horizontal axis, e.g.
dive site names:
While I personally have no qualms with horizontal diagrams where needed,
I would argue it is a regression to default to horizontal orientations
for all bar graphs.
The above graphs deal with yellow variables in Dirk's proposal. Now
about the other categories. Plotting a White variable against a Blue
variable has several options, including box and whisker plots that are
not popular in this discussion. My proposal two days ago was something
like this and there was some discussion around it:
Here SAC is a white (continuous) variable and Suit is a blue
(catagorical) variable. A graphical element that is likely to differ
sharply from the bar graphs used above. Here again, because the
horizontal axis comprises categories, there is no need to specify a
granularity/increment. For lack of a better name (there is actually a
esoteric statistical name for this graph) I call this a dot graph.
What about plotting a Blue (categorical) variable against a White
(continuous) variable? For our case the order in which the blue and
white variables are selected probably does not matter and the dot graph
shown above (or some derivative of it) should suffice.
What if a white (continuous) variable is plotted against another white
variable (e.g. dive duration against dive depth). The most appropriate
type of graph is probably as scatter diagram:
The raw data are indicated on the graph. There is no need for specifying
a granularity value because there in no grouping of values along the
horizontal or vertical axes. If a clear relationship between the two
variables exists, it is clearly visible on the graph as in this case.
We have now dealt with
Yellow/white
Yellow/Blue
White/Blue and Blue/White
White/White
What about Blue/Blue?
There is another type of graph that is potentially extremely useful :
introduce a *third* variable to the graph. For instance, in the case of
the second blue bargraph towards the start of this message (No.dives vs
depth) one could ask what the distribution of a third category is. For
instance, how long did I use various dive suits at different depths? Or
how many dives did I use different dive suits at different depths? This
is the above barchart, divided into the values for different dive suits.
This is also useful to analyse variables used as tags, e.g. the use of
air/nitrox/trimix during dives, the number of boat/shore dives, the
number of training dives compared to fun dives, the number of dives
using different dive modes as a function of depth, dive duration,
temperature, or whatever white variable has been selected.
Since the horizontal axis corresponds to a white (continuous) variable,
one would need to specify a granularity/increment. The UI cost for this
would be an additional dropdown list/comboox to select the appropriate
categorical variable to appropriately subdivide each bar of the graph
(Dirk's Granularity??). This diagram handles cases of graphs with a
blue(categorical) variable plotted against another blue (categorical)
variable, although a third variable needs to be specified to form the
unit of measurement (e.g. dive duration in the above graph). This can
probably be selected using Dirk's Granularity Combobox in his proposal.
This handles basically all the possibilities of the different
combinations of Yellow, White and Blue variables in Dirk's proposal.
There are fundamentally FOUR types of graphs that would be required,
forming the basis of visual presentation of the Statistics tab.
I hope this appears somewhat useful in the present discussion.
Kind regards,
willem
--
This message and attachments are subject to a disclaimer.
Please refer to
http://upnet.up.ac.za/services/it/documentation/docs/004167.pdf
<http://upnet.up.ac.za/services/it/documentation/docs/004167.pdf> for
full
details.
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