Yay! While the science mission is not a national priority, having a backup transmitter for the rovers is. Whatever the logic, glad it’s moving forward.

Government shutdown stops MAVEN work; threatens Mars launchThe upcoming Nov. 18 blastoff of NASA’s next mission to Mars – the “breathtaking beautiful” MAVEN orbiter – is threatened by today’s (Oct. 1) shutdown of the US Federal Government. And the team is very “concerned”, although not yet “panicked.”

MAVEN’s on time launch is endangered by the endless political infighting in Washington DC. And the bitter gridlock could cost taxpayers tens of millions of dollars or more on this mission alone!

Why? Because launch preparations at NASA’s Kennedy Space Center (KSC) have ceased today when workers were ordered to stay home, said the missions top scientist in an exclusive to Universe Today.

The nominal interplanetary launch window for NASA’s $650 Million MAVEN (Mars Atmosphere and Volatile EvolutioN Mission) mission to study the Red Planet’s upper atmosphere only extends about three weeks until Dec. 7.

If MAVEN misses the window of opportunity this year, liftoff atop the Atlas V rocket would have to be postponed until early 2016 because the Earth and Mars only align favorably for launches every 26 months.

Any launch delay could potentially add upwards of tens to hundreds of millions of dollars in unbudgeted costs to maintain the spacecraft and rocket – and that’s money that NASA absolutely does not have in these fiscally austere times.

MAVEN and much of NASA are not considered “essential” – despite having responsibility for hundreds of ongoing mission operations costing tens of billions of dollars that benefit society here on Earth. So about 97% of NASA employees were furloughed today.

Image credit: Ken Kremer/kenkremer.com

Pedestal Crater - We call this a “pedestal crater” because the ejecta surrounding the crater seems elevated above the rest of the surface. While the ejecta of other impact craters is usually darker than the surroundings, you can see here that it looks like accumulated material that is distinct.

A bit of formatting and checking to do, but it’s almost all there now!

### R code for Pearson correlation

We were ready for an easy one!

vars <- data.frame(has_layers$number_layers, has_layers$diam_circle_image)

print(cor(vars, use="complete.obs", method="pearson"))

test_output <- cor.test(has_layers$number_layers, has_layers$diam_circle_image,

method="pearson")

print(test_output)

print(paste("square of correlation coefficient is ",

test_output$estimate * test_output$estimate))

plot(has_layers$diam_circle_image, has_layers$number_layer

### Pearson tests - part 2

Among craters with layered ejecta (our sample), the correlation between latitude of crater (quantitative explanatory variable) and number of layers (quantitative response variable) was 0.099 (p<.0001), suggesting that barely one percent (i.e .099 squared is 0.0099) of the variance in number of ejecta layers can be explained by crater diameter.

This plot shows that the spread of latitude values versus layer values is very uniform, especially for the most common values of one or two layers. (Zero layers is the most common of all, representing about 95% of the Robbins Crater Database.)

### Pearson tests

Among craters with layered ejecta (our sample), the correlation between diameter of crater (quantitative explanatory variable) and number of layers (quantitative response variable) was 0.448 (p<.0001), suggesting that about 20% (i.e. 0.448 squared) of the variance in number of ejecta layers can be explained by crater diameter.

The plot looks really weird…

### Practicing Chi Squares

To understand what the chi square statistic is telling us, we’re doing a quick test to see if pedestal craters are associated with the number of ejecta layers. Here is part of the R output:

|-------------------------| | N | | Expected N | |-------------------------| ==================================== pedestal layer_bin 0 1 Total ------------------------------------ (0,1] 15263 204 15467 15271.0 196.0 ------------------------------------ (1,2] 3390 45 3435 3391.5 43.5 ------------------------------------ (2,6] 828 1 829 818.5 10.5 ==================================== Statistics for All Table Factors Pearson's Chi-squared test ------------------------------------------------------------ Chi^2 = 9.09308 d.f. = 2 p = 0.01060383 [1] "need to pairwise test" [1] "nlev is 3" [1] "num_tests is 3" [1] "p-adj for bonferroni test is 0.0166666666666667" [1] "(0,1] and (1,2]" "0.96701385588958" "FALSE" [1] "(0,1] and (2,6]" "0.00256191030878133" "TRUE" [1] "(1,2] and (2,6]" "0.00292570157715207" "TRUE"

Since the p < 0.05, something in the data is significantly different from at least one other category. The Bonferroni test tells which that is.

"p-adj for bonferroni test is 0.0166666666666667"

The test says that Multiple Layer Ejecta (2, 6) is significantly different from Single Layer Ejecta (0, 1) and Double Layer Ejecta (1, 2). The bar chart shows that is has less Pd craters.

### Chi-square test (or in how many ways can your pairs vary?)

A chi-square test of the prevalence of rampart ejecta craters within the subset of craters containing layered ejecta by location was performed. The measure of location used so far has been USGS region_id. Unfortunately, with 30 different regions, a chi-square pairwise test for independence would require 435 separate pairwise tests.

Instead, the data was first broken into 5 latitude bands following USGS region lines. The lowest band was at -65, then -30, then 0, then 30, then 65 degrees north. Within the middle 4 latitude bands, the variation within USGS region was also examined. (The north and south polar regions are only one USGS region each so there are no subsets in those bands.)

This test does not analyze whether regions that are adjacent in the north-south direction (for example, regions 5, 12, 13, 21, 22, and 27) have rampart ejecta frequencies which are associated or independent. Maybe later. :-)

For latitude bands 1-6, the presence of rampart ejecta is associated with latitude band with a p-factor of zero.

rampart lat_band 0 1 1 325 708 2 2455 1759 3 1481 2940 4 2030 3250 5 3000 1235 6 354 194 Number of cases in table: 19731 Number of factors: 2 Test for independence of all factors: Chisq = 1793.7, df = 5, p-value = 0

The cross table plot looks like this:

(The width of the bars represents the number of craters with any layered ejecta in the region, and the height of the bars represents the presence or absence of the rampart layered ejecta morphology.)

Pairwise chi-q tests with bonferroni adjustment of p=.003 shows that almost all of the difference in rampart prevalence by latitude band are statistically significant. The exceptions are latitude pairs (1 and 3) and (2 and 6).

Within latitude band 2 (USGS region ids 2 - 7), the results show that rampart prevalence is associated with region id with a p-value of less than .0001.

rampart region_id 0 1 2 250 270 3 378 337 4 440 367 5 445 297 6 545 245 7 397 243 Number of cases in table: 4214 Number of factors: 2 Test for independence of all factors: Chisq = 77.38, df = 5, p-value = 2.961e-15

The cross-table plot looks like this:

The pairwise tests show that 7 of 15 of the pairwise tests are statistically significant, and 8 are not. The best way to analyze these (which I will not be able to reproduce in tumblr’s editior) seems to be to draw a “clock” with the numbers 1 through 7 (because as you go around the latitude line, bins 1 and 7 are adjacent), then draw lines between numbers that are statistically independent. Doing so reveals that most of the independent pairs (2 and 5; 2 and 6; 2 and 7; 3 and 6; 3 and 7) are basically on opposite ends of the globe from each other. The exceptions are pairs (5 and 6) and (4 and 6) which are also statistically independent.

Within latitude band 3 (USGS region ids 8-15), the results again show that rampart prevalence is associated with region id with a p-value of less than .0001.

rampart region_id 0 1 8 95 185 9 36 96 10 145 465 11 282 573 12 364 609 13 226 375 14 203 382 15 130 255 Number of cases in table: 4421 Number of factors: 2 Test for independence of all factors: Chisq = 39.96, df = 7, p-value = 1.283e-06

The cross table plot looks like:

Pairwise tests in this band show that region 10 is statistically different from regions 8, 11, 12, 13, 14, and 15. No other pairs are statistically independent.

Within latitude band 4 (USGS region ids 16-23), the results again show that rampart prevalence is associated with region id with a p-value of less than .0001.

rampart region_id 0 1 16 236 494 17 84 188 18 236 549 19 293 336 20 343 368 21 289 349 22 247 536 23 302 430 Number of cases in table: 5280 Number of factors: 2 Test for independence of all factors: Chisq = 118.7, df = 7, p-value = 1.425e-22

The cross table plot looks like this:

The pairwise tests show that the “dip” at regions 19-21 is real, as is the dip at 23. All the pairs of statistically significant differences include exactly one of these four regions.

Within latitude band 5 (USGS region ids 24-29), the results again show that rampart prevalence is associated with region id with a p-value of less than .0001.

rampart region_id 0 1 24 638 330 25 463 230 26 373 143 27 521 123 28 399 141 29 606 268 Number of cases in table: 4235 Number of factors: 2 Test for independence of all factors: Chisq = 52.3, df = 5, p-value = 4.677e-10

The cross-table plot looks like this:

The pairwise tests are somewhat similar to the ones in the latitude bin above, showing that the dip in the bars is statistically significant. However, in this case the dip is statistically “steeper” — bins 26, 27,and 28 are statistically independent of each other, not just with their taller neighbors.

If you read this far, you can see that even though for each latitude band I found similar top-level chi-square test results, the graphs and pairwise tests revealed different underlying patterns.