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03/20/08

Permalink 01:19:00 pm, by millercommamatt, 82 words   English (US)
Categories: General, US News

NCAA Backetball Tournament Fun Fact

I case anyone was curious, there are 264 (two to the sixty fourth power) ways to fill out an NCAA basket including the play-in game.

One play-in game, 32 first round games, 16 second round games, 8 sweet sixteen games, 4 elite eight game, 2 final four games, and the final gives you:

21 x 232 x 216 x 28 x 24 x 22 x 21 = 264
(18,446,744,073,709,551,616)

You have better odds of winning the lottery several times than you do filling out a NCAA tournament bracket randomly and correctly picking the winner of all the games.

03/09/08

Permalink 10:11:47 pm, by millercommamatt, 130 words   English (US)
Categories: General

A tip for laying out captioned figures in Microsoft Word

Anyone who has tried to work with images in Microsoft Word knows that the images rarely behave like you want them to and are prone to jumping across pages and leading to gaping holes in text due to spacing issues they generate. The addition of captions only seems to complicate matters.

I suggest creating figure captions in a textbox before placing the associated image. Then you can place the image inside the text box so that the image and its caption can be moved as one entity. Make sure you use the layout options to set the proper text wrapping (I frequently use top and bottom) and that you specify your location relative to the page margins so that your images doesn't try to jump around if your text shifts.

02/19/08

Permalink 03:10:53 pm, by millercommamatt, 845 words   English (US)
Categories: General, Meteorology

Correlation, Confidence Interval, and Sample Size

I haven't made a post to this journal in a very long time and I'm about to end that drought with something very nerdy. [WARNING - MATH AHEAD]

Lately in my research, I've been looking at correlations between data. For those of you who aren't familiar with the concept, correlation ranges between -1 and 1 and is an expression of the linear relationship between two sets of data. In English, it is an expression of how well one variable relates to another variable.

To give an example, temperature and the number of people at the beach are well correlated. When the temperatures are warm, there are typically a lot of people at the beach. When the temperatures are cold, there are typically not a lot of people at the beach. Thus, you can use temperature to predict the number of people at the beach and you can use the number of people at the beach to predict the temperature. When two things are not well correlated is basically means that knowing something about one thing doesn't give you any predictive information about the second thing. It's important to note that correlation doesn't provide any information about causation. Just because two things are correlated, does mean they affect each other in any way. To play off our earlier example, the number of people at the beach has no effect on the air temperature. For a more well written written explanation of correlation with some visual illustrations, I suggest reading the following linked Wikipedia article: Wikipeida - Correlation

Anyway, correlation statistics are based on samples of data taken from a larger set. Since the entire dataset isn't being sampled (at least for any real-world dataset) there is some uncertainty about the calculated correlation value. The confidence interval for a given correlation value is calculated as follows:

1) The correlation (r) is transformed using a Fisher's Z transformation. This is the same as: hyperbolic arctangent - arctanh(r) = Z'

2) Calculate the upper and lower bounds using the following formula:
,
where Z' is a product of the transformation described in step 1, N is the number of samples, and Z is a value taken from a statistical Z table depending on the confidence interval you want to use. For a 95% confidence interval (i.e. the correlation of the true dataset has a 95% chance of being within the calculated upper and lower bounds) we use a value of 1.96.

3) You take the two values calculated from step 2 and turn them back into correlation values using an inverse Fisher's Z transform. This is the same as taking the hyperbolic tangent of the values from step 2.

For the statistical reasoning behind this process, I suggest reading the following link: Confidence Interval on Pearson's Correlation

The resulting values are the upper and lower bounds for the correlation values. The true correlation for the dataset you sampled should be somewhere within those bounds. If you examine the formula you can see that the more samples you have, the more narrow your bounds are and the more certain you can be of the true correlation.

In my research, I've been working a lot recently with correlations and their confidence intervals. I started wondering exactly how the confidence interval changed for different sample sizes for a given correlation. I also wondered about the symmetry of the confidence intervals. Often in published research, you see a correlation with its confidence interval expressed as follows: 0.6±0.1. This states that the correlation is 0.6 with an upper bound of 0.7 and a lower bound of 0.5. This states that the upper and lower bounds are symmetric (different by the same amount) about the correlation value. The problem is that when you actually look how confidence intervals are calculated, you'll see that they are never truly symmetric. To illustrate this, I created the following graph for a correlation of 0.6 with 95% confidence intervals:

Correlation Statistics Graph

If you take a look at the graph, you can see how the upper and lower correlation bounds narrow with increasing sample size. As the number of samples increases, you become more certain about what the true correlation, but never 100%. The confidence only become really narrow (0.01 or less above or below the correlation value) for obscenely large sample sizes (~100,000+).

The curve in blue is an expression of the symmetry of the correlation bounds. It's basically a plot of the difference between the upper bound and the correlation and the lower bound and the correlation. If the value is zero, the bounds are perfectly symmetric. As you can see from the graph, the symmetry is large for small sample sizes and decreases asymptotically towards zero. It's worth noting that the correlation bounds are never truly symmetric.

The question I'm currently grappling with is how symmetric is symmetric enough to where I can just write the correlation values as being such and when can I not do this?

For the education of the curious, I have versions of the above graphs for two other correlation values.

Correlation Statistics Graph

Correlation Statistics Graph

It's also worth noting that the correlation bounds are wider for correlation values closer to zero for any given number of samples.

12/17/07

Permalink 12:36:40 pm, by millercommamatt, 95 words   English (US)
Categories: News, World News

Global Warming - Not Funny Anymore

That's it! Global Warming isn't fun anymore!

According to some Scottish researchers, many coastal Scotch Whisky distilleries - most notably some of my favorites on the Isle of Islay - may become flooded if the sea level rises to levels forecasted by recent reports on global warming including the recently released ICPP report. I adore the whisky from many of those distilleries. I can't have anything bad happen to them. The distilleries threatened include, but are not limited to: Bowmore, Laphroaig, Talisker, Lagavulin, Bunnahabhain, and Glenmorangie.

Link to the article:
Dramageddon - Too much water

12/12/07

Permalink 05:03:56 pm, by millercommamatt, 77 words   English (US)
Categories: Fiji

Christams List 2007 Part II

I know I'm a little late with a follow up list, but I figured better late than never.

A Dresser/Chest
I would like a new dresser for my bedroom. The one I have is too small for my needs. The drawers are too shallow and no longer slide very well. I would like a new dresser with deeper drawers (20" - 24+"). Four or more drawers would be nice. I don't need anything real fancy, just something functional.

11/12/07

Permalink 03:31:23 am, by millercommamatt, 159 words   English (US)
Categories: Gift Lists

Christmas List 2007 Part I

Christmas isn't too far off and it's the time of year when family starts asking me what I want. Therefore, I thought I would post a few of the things that have come to mind already.

Canon XTi SLR Digital Camera
Just the body can be found online for ~$600.

Network Harddrive
One of these will allow me to backup and store data for all the computers on my home network. This will be nice to have considering that the harddrive in Christina's laptop is near death.

$260 at newegg.com

A Black Blazer
I figured that this one was self-explanatory. A black single-breasted two or three button coat can be worn with just about anything. I don't want anything too fancy. I just want something light and simple.

Tennis Shoes
My current tennis shoes need to be replaced. The hard part about getting shoes these days is that most of the ones available are either really expensive or look ridiculous.

11/05/07

Permalink 02:55:16 pm, by millercommamatt, 165 words   English (US)
Categories: General

Unconditional Pass

w00t! Today, I successfully defended my master's thesis. I received an unconditional pass. I still have to have my thesis reviewed for formatting by the NCSU library and there is some departmental paperwork to do, but for all intents and purposes I am now the proud holder of a Master of Science degree in Marine, Earth, and Atmospheric Sciences.

Today is the 5th of November so that means it's Guy Fawkes Day! 502 years ago today, terrorism was avoided and no one blew up Parliament. You know... remember remember the fifth of November gunpowder treason and plot. If you're in the UK, you're probably getting drunk and getting ready to watch some fireworks. Sounds like fun.

Speaking of memorable days, today is my parent's 30th wedding anniversary. After 30 years, not only have they not killed each other, but they actually love each other. They are people I truly love and admire. I dearly hope my own marriage has the same success. Congratulations Mom and Dad!

10/29/07

Permalink 06:28:31 pm, by millercommamatt, 109 words   English (US)
Categories: General

One week until defense

My master's defense is a week from today. I gave the initial version of my presentation to my adviser today. I need to clarify some things, cut out about 15 minuets worth of material to meet my time constraints, emphasize some key points better, and work on my usual poor public speaking habits. Nevertheless, things are moving along and I expect to be ready for my defense next week. Getting my defense over and done with will take an enormous weight off my shoulders. I'm on the home stretch, but I'm having to avoid getting complacent. Everyone has heard of senior-itis, but I'm not sure that masters-itis is as common.

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