The Horror of Math... Statistics Edition

[Antisocial_Worker]

Anyone any good at statistics, or can you recommend a good site for help developing my final project for the class? This thing is going off the rails.

Long story short, I have raw data. I'm comparing the population decline of one city to the increase of another, then analyzing the county to county migration between the two cities. Both, surprisingly, show a negative correlation when I run the numbers through Excel. What I'm having trouble with, is just what that means, and also how to develop a mathematical hypothesis from a hearsay supposition. I ran this all by my stats teacher earlier today, and even he seemed confused, and shunted me off to another math teacher. Turns out the whole thing is a lot more complicated than I'd though, and in the end they recommended just making a hypothesis about the nature of one city (ie, City A is in decline, alternate hypothesis being that City A is not in decline -- I think. Null hypothesis mystifies me.)

Anway... I'm freaking out. Who can direct me to some help turning all these raw numbers into a workable project?

[Chromatix]

It may help to understand what a correlation *is*.

If you draw a scatter-plot (which you can do by hand) with each point taking the population of one city on one axis and the population of the other city in the same year on the other axis, then a top-left to bottom-right trend is a negative correlation while a bottom-left to top-right trend is a positive correlation. A horizontal or vertical trend or a disorganised cloud of points would indicate no correlation.

It may also help to normalise the county-to-county migration figures against population. That is, what is the migration *per capita*? That may reveal some more interesting information than the raw numbers.

[Amina516]

I took stats at the beginning of the semester. I used this site ( http://www.dummies.com/Section/Conte...ry=correlation ) when my book didnt quite allow me to understand what was going on. I used another program (minitab) so I am unfamiliar with excels abilities for statistics.

This also looks helpful. https://people.richland.edu/james/le.../ch11-cor.html

If a scatterplot reveals that there might be a relationship, you measure the strength of that correlation by finding the linear corrrelation coefficient, r or the pearson correlation number. You also need the confidence interval for the significance level. We never had to do this by hand, I dont know if you do. If you do, my condolences...

After finding r, compare the P value or critical value ( I prefer P). With that information, if the P value is less than or equal to the significance level (The other half of your confidence interval), there has to be a linear correlation. If the P value is NOT less than or equal to the significance level, you can conclude that there is not sufficient evidence to support the conclusion.

Since the Ho = 0 (claim that there is no linear correlation) and Ha: p not equal to 0 (claim that there is a linear correlation)

If P Value is less than or equal to the significance level, reject Ho(Null) and conclude that is sufficient evidence to support the claim. + Correlation

If p value is greater than the significance level, fail to reject Ho (null) and conclude that there is not sufficient evidence to support the claim. No correlation.

The wording of the hypothesis always caught me up. I would just word it like my book suggested and I did well. I cant honestly tell you I quite understand wtf is going on, but since my class was alsmot 8 weeks ago, I have purged most memories from my system. I hope this makes sense. It is 6am over here...

[Chromatix]

The "null hypothesis" is simply a hypothesis that states that a conclusion cannot be drawn from the data. In other to confirm any other hypothesis, you must be able to "reject the null hypothesis" - to prove (to a reasonable standard of confidence) that some conclusion can be drawn. Amina described a method of doing so above.

There is a lot of bad statistics out there in the real world. Let's be honest - it is a difficult and confusing subject, and there are a lot of people out there who deliberately use that fact to advance their own agenda. It's worth taking the time to make sure you understand the fundamentals intuitively, after which the rest will probably come a lot easier.

[Jay 2K Winger]

The Horror of Math...

Not going to lie, I assumed something completely different when I saw this in the OP title.

The many-angled lands and the maddening fractal spaces of the Deep Maths...

Iä, Iä, Mathlulhu fthagn!

[42_42_42]

sorry. I took statistics twice and I still don't understand it. I feel your pain about those hypotheses, they always confused the hell out of me.

[Antisocial_Worker]

Anybody got any insight into t-scores? I'm required to perform either a z-test or a t-test on the data, and I seem to recall that t-scores are better for smaller sets of data. I run the test, and I get some ridiculous number, like 7.something. I don't even know what o compare that to, and what it means.

I'm kind of stressed out because I'm afraid of making an idiot of myself in front of the entire class.

[mathnerd]

t-scores are a method of testing hypotheses when the sample size is too small to effectively use Z.

In a nutshell, these tests are a way of comparing your results to the mean, taking advantage of the Central Limit Theorem, which states that if you take enough samples, all data will tend to the normal distribution, regardless of the distribution of the original population. If you perform a t or Z test, you will get number that tells you how many standard deviations from the mean your particular data point lies. This is an effective way of figuring out if your results are within expected ranges.

As for good resources, I'm particularly fond of "The Cartoon Guide to Statistics". I also don't like Excel for statistical analysis. I use SPSS or Minitab. I believe both of them offer free trials.

I'd be happy to take a more detailed look at what you have so far. My master's degree is math with a concentration is probability theory and statistics and I taught for years, though it has been a while. Feel free to PM me.

[MistressOfTangents]

I am very mathematically challenged but when I was studying psychology the set text for the statistics part was 'Statistics for the Terrified' which I found very helpful. It lists all the different tests and shows you how to do them.

The Null Hypothesis simply negates whatever you put as your hypothesis.

[El Pollo Guerrera]

The only thing I have to add is a quote from Mark Twain:

"There are lies, damned lies, and statistics."

[LesserSouthernFroglet]

+1 to Mathnerd re SPSS. Excel has some add-in statistical analysis tools, but SPSS walks all over it.

Three books to suggest:

Statistics for the Utterly Confused (Lloyd Jaisingh) (This one also has instructions on using Minitab and the TI-83/84 calculator)

Statistics for People Who (Think They) Hate Statistics (Excel edition) (Neil J Salkind)

The Complete Idiot's Guide to Statistics (Robert A Donnelly Jr)

I have a fourth book which is designed with SPSS in mind, but my colleague tells me it's sitting on his kitchen table right now and I can't recall the title. It came with a freeby Student's version of SPSS. I've threatened him with a whack around the ears for borrowing it without asking...

[Geek King]

I would also recommend The Manga Guide to Statistics. I've picked up several of the Manga guides on a lark, and they're well written, and usually are good about showing how concepts relate to real life.

Plus you get a comic story to read along with it!