Hypothesis testing

OK, I give up. I've tried for 60 minutes to make two edits to the post.

There should be a space following the word "Edition" and readers are asked to respond, not response.

For future reference, how does one edit a posting (within 60 minutes) or is that no longer an option? Just curious.

If you remain logged in after posting, you should see an Edit option in the lower right of the post. That is valid for 60 minutes or until someone posts a reply under your post, whichever comes first.

Of course it moved.

The typical contractor tie out is feet-inches to a paint dot.

Speaking of aluminum...we have a coastal forest with hundreds of concrete monuments with brass caps. They range from a few miles inland to 20 miles inland. I have never seen one with environmental damage. They were mostly set during the 1960s. We have been setting aluminum caps for the past 6 years since I have worked for the department. I didn't purchase them, we inherited boxes of aluminum monuments. We visited some of the older ones last week. It's disappointing to see them pitted with corrosion. I imagine they will be in pretty poor shape in 50 years. Funny how we can spend thousands on a survey but an extra 40 bucks for a decent monument is somehow impossible.

>It's disappointing to see them pitted with corrosion. I imagine they will be in pretty poor shape in 50 years. Funny how we can spend thousands on a survey but an extra 40 bucks for a decent monument is somehow impossible.

Sometimes a well marked stone with an excellent location and durable references is they way to go!

Would a stainless steel monument hold up better?

Maybe a precast concrete pillar with encapsulated magnets would fit the bill?

For Star*Net users, here is Earl's problem set in a more familiar form (if I haven't slipped a number converting his ECEF coordinates and variance-covariance values into a more usable format):

[pre]

.GPS WEIGHT COVARIANCE
.GPS FACTOR 1.0 VERT 1.0
.UNITS METERS

PH Bromilow1 32-16-52.334080 106-45-15.772734 1165.523 ! ! !
G0 'V1
G1 Bromilow1-BromilowBefore 0 0 0
G2 0.000002189667 0.000005644996 0.000004765234
G3 0.000002352389 -0.000001759475 -0.000003591109

PH Bromilow2 32-16-52.334414 106-45-15.772540 1165.529 ! ! !
G0 'V2
G1 Bromilow2-BromilowAfter 0 0 0
G2 0.000001688855 0.000004450108 0.000002123308
G3 0.000000000011 0.000000329961 -0.000000000131

.rel BromilowBefore-BromilowAfter

[/pre]

The punchline is that the two different positions are not identical because the 95%-confidence error ellipses around the Before and After positions don't overlap.

The error ellipses in the sketch below are drawn to scale.

I should add these project settings will work:

[pre]
Type of Adjustment : 3D
Project Units : Meters; DMS
Coordinate System : Mercator NAD83; NM Central 3002
Geoid Height : 0.0000 (Default, Meters)
[/pre]

The inversed bearing and distance from BromilowAfter to BromilowBefore is:

S26-32W, 0.012m with an uncertainty of 0.005m at 95% confidence.

In other words there is far less than a 5% chance that the computed distance between the After and Before positions is smaller than the uncertainty in that distance.

Stated more formally: if the distance inversed between two points is less than the uncertainty in the computed distance at 95% confidence, then the hypothesis that the two points are in fact in the same position is not disproven at the 95% confidence level.

Thanks, I believe my mistake was logging off right away, then attempting to edit after logging back in. I've edited postings before but it was frustrating this time that I could not.

And, you are quite correct - I edited this posting as you described.

If I need a disclaimer, the aluminum tablet was in place long before I arrived on campus.

Anyway, we get very little rain here which might delay corrosion. And, the tablet is in an area of high foot traffic - quite close to the front door of Goddard Hall and the Office of the Dean of Engineering.

I had access to Star*Net in the computer lab at NMSU and really liked using it. However I am more of a novice than an expert with it.

I sincerely appreciate your kind help - the graphics are rather convincing.

I am also attempting to get my arms around Chapter 5 on Statistical Testing in Ghilani's Adjustment book - which brings me to another question. Should I devote more effort to proving I'm right (that the location is different) or proving that he is wrong when he says, "it is in the same place"? How should I formulate the Null Hypothesis?

>How should I formulate the Null Hypothesis?

The Null Hypothesis would be that the two positions are not significantly different at the 95% confidence level. That would lead to the test proposition that D<U, where D is the computed distance between the two positions and U is the uncertainty in that computed distance at 5% uncertainty (95% confidence).

> >How should I formulate the Null Hypothesis?
>
> The Null Hypothesis would be that the two positions are not significantly different at the 95% confidence level. That would lead to the test proposition that D<U, where D is the computed distance between the two positions and U is the uncertainty in that computed distance at 5% uncertainty (95% confidence).

Or, taking one more stab at this:

The Null Hypothesis would be that the distance inversed between the two difference positions cannot be shown to be different from 0 at 95% confidence level. That is

D-U < 0 < D+U,

where D is inversed distance and U is the uncertainty in the distance at the 95% confidence level.

I really appreciate the insights and assistance. On an intuitive level I feel somewhat comfortable but when it comes to those specific mathematical formulations, I'm uneasy. I'll probably be back for more help before submitting the final manuscript.

[sarcasm]Before breaking out the calculators I noticed the difference of about 0.04' in the elevation. [/sarcasm]

> [sarcasm]Before breaking out the calculators I noticed the difference of about 0.04' in the elevation. [/sarcasm]

But, did you later realize that the height difference was actually 0.006m?

On a side note, the title has a grammatical typo. It should read ".. Is it in the same position?"