Visualized Data

Today's post is going to look at graphical representations of my data.  First though, let's get a reminder of my missions:

Mission	Description	Variables	Hypothesis
1	Determine if there's an association between the number of layers visible and the latitude of the crater.	NUMBER_LAYERS and LATITUDE_CIRCLE_IMAGE	Weak association
2	Determine if there's an association between the number of layers visible and the morphology of the ejecta	NUMBER_LAYERS and MORPHOLOGY_EJECTA_1	Association
Bonus	Determine if there's an association between the ejecta morphology and the latitude	MORPHOLOGY_EJECTA_1 and LATITUDE_CIRCLE_IMAGE	Known correlation for certain morphologies and known lack of association for other morphologies
New Bonus	Determine if there's an association between the number of visible layers and crater depth.	NUMBER_LAYERS and DEPTH_RIMFLOOR_TOPOG	Association

Before I can make graphs, I have to refine my mission descriptions so that there's a clear causal relationship between the two variables.  (Note that this doesn't mean that one variable actually causes a change in another - it's just a way to format the data and the research question to help us make sense of things).

Here are my new descriptions:

1. Does the number of layers visible in a crater (response variable) depend on the latitude of the crater (explanatory variable)?
2. Does the number of layers depend (response variable) on the morphology of the ejecta (explanatory variable)?
3. Bonus: Does the depth of craters (response variable) change with the number of layers visible (explanatory variable)?

But let's back up for a second.  Before we start comparing variables, let's look at each one individually and see what we can find out.

Univariate Graphs

Latitude Ranges 

Number of craters, sorted by latitude

I made a vertical bar graph of the latitude ranges but, as you can see, it's really difficult to read the horizontal axis labels.  Thus, the horizontal bar graph was born:

Number of craters by latitude, now with some extra statistics!

From these two graphs (and the statistics table generated by SAS), we can see that the center is around -7.199 with a standard deviation of 33.609.  It also looks like a unimodal distribution but there's some skew, with most of the craters being located slightly below the equator and a tail reaching out towards the north pole.

And, just for fun, I wanted to see what the bar graph would look like for the un-binned latitudes so I made this (notice that the vertical axis has the latitudes going from -90 at the top to 90 at the bottom, which is the opposite of the graphs above):

Where all the craters would be if Mars was upside-down

 It's got more resolution than the earlier graphs but it's got the same basic shape.  It's unimodal (or maybe a little bit bimodal, with the second mode being around 20 degrees), with most of the crates being below the equator.

Number of Layers

Number of visible layers in the craters

 This graph shows a hugely skewed right set of data.  Almost all (95%) of the craters have no visible layers with it steadily decreasing from there until we get an almost invisibly short bar for 5 layers.  The mean number of layers is close to 0 (obviously) and the standard deviation is only 0.3, not even a full 1 layer.


Morphology

Craters, by type.  Here's a refresher on what those types mean

 Since morphology is categorical, it's not really useful to talk about the shape of the graph.  It's obvious that most (60%) of the craters fall into the Rd (radial) category, followed by about 30% in the SLE (single layer ejecta) category.

Depth

Depth had the same display problems as Latitude so it also gets to be a horizontal graph.

The depth of craters is unimodal and skewed right, with almost 95% of craters having a depth between 0 and 5 km.  (And, if you're curious, it's because 80% of the craters have a depth of 0km.)  The mean depth is 0.076 km with a standard deviation of 0.222.



Bivariate Graphs

Now it's time to move on to the Mars Missions to see what sort of relationships exist.


Mission 1: Layers vs Latitude

 Because the numbers of layers is discrete, I decided to go with a bar graph for this one.

It looks like there's probably a relationship between latitude and number of layers but it's not incredibly strong.  The relationship seems to be that there are slightly more layers visible in the far north (around 70-80 degrees) and fewer visible closer to the equator and as we get close to the south pole, the number of layers starts to drop even more.  However, it's important to note that the scale on the vertical axis is pretty small.  Some craters have up to 5 layers visible but our average number of layers is hovering between 0.07 and 0.20.

Just for fun, I made a scatter plot of number of layers vs latitude (not the 10 degree latitude bins I made earlier, but the actual continuous range of latitudes).  This is what it looked like:

As you can see, this is a super useful graph.

The scatter plot doesn't really show a whole lot of useful information.  Maybe there are some clumps of 3- and 4-layered craters around certain latitudes but it's hard to tell from this graph if those clumps are significant or just expected within a randomly scattering of craters.

Mission 2: Numbers of Layers vs Ejecta Morphology

Shocking results

Remember the joke about the guy in the hot air balloon?  His balloon had drifted and he didn't know where he was but he'd flown close enough to a skyscraper to ask the people inside.  In response, the people in the building told him, "you're in a hot air balloon."  This graph is kinda like that joke.

The first type, DLE (or dual-layer ejecta) has ..drumroll.. two visible layers.  MLE (multiple-layer ejecta) has slightly more than 3.  SLE (single-layer ejecta) has one.  The other two types are actually interesting though.  Pd (pedestal) has about 0 layers and and Rd (radial) has slightly more than that.

Bonus Mission: Depth vs Layers

There's a clear relationship between depth and number of visible layers.  The greater the number of observed layers, the greater the depth of the crater.  That's not really surprising but it's nice to have confirmation of it.

Summary

It looks like there are associations between layers and depth, layers and morphology, and possibly between layers and latitude.

And, finally, here's the program that made it all possible:

Thank you and good night.