T'ai Chi : Some math/stat questions for you

[BillHoyt]

As our resident math/stat expert, I was hoping you could answer a few questions in those areas:

1. Let f(x) be differentiable on [a,b]. At x=0, the function's concavity changes. Is it a relative minimum or an inflection point? What test do we apply here?

2. How many gaussian statistics must we collect together before we reach the binomial distribution?

3. In universities, students are frequently taught the student's t-test. Why? What do the professionals actually use?

4. What does the standard deviation have to do with efficiency?

Cheerfully awaiting your responses,

 

[UKBoy1977]

Question 1 does not seem answerable.

Question 2. The bigger the value of np(1-p) is (where n and p are the binomial parameters) the better the approximation is. One textbook I referred to suggested it should be at least 10, but the choice is arbitrary.

Is question 3 a joke?

Question 4. Nope, the concept of efficiency has left my head

Oh well, let's see how T'ai Chi does!

 

[BillHoyt]

Question 1 does not seem answerable.

Question 2. The bigger the value of np(1-p) is (where n and p are the binomial parameters) the better the approximation is. One textbook I referred to suggested it should be at least 10, but the choice is arbitrary.

Is question 3 a joke?

Question 4. Nope, the concept of efficiency has left my head

Oh well, let's see how T'ai Chi does!

I assure you, they are all answerable. Let's see how T'ai fares.

 

[TruthSeeker]

While I think I know what you are after in Question 3 (we'll see if I'm correct), it did make me laugh.

I'd like to add one question: How big a nerd do you have to be to laugh at stats questions on a Sunday morning?

 

[Iconoclast]

3. In universities, students are frequently taught the student's t-test. Why? What do the professionals actually use?

While I'll let T'ai Chi answer the other questions -- I guess he and Billy are having some sort of intellectual p*ssing contest at the moment -- I remember back in first year engineering one of the students in my maths class asked the very same question, even worded it the same way. It turns out that Student was the name of the guy who came up with the Student-T distribution.

Maybe T'ai Chi was the dude that invented the Chi Squared distribution, so surely he can explain how it relates to the Normal distribution, and they ARE related in a very interesting way.

 

[TruthSeeker]

Icon,

Shhhhhhhhhhh....I think you gave away the answer.

I had been pronouncing the two Chi's differently but good catch.

So, yes, let's ask for an explanation of how the Chi Squared and Normal (Named after the distinguished Dr. Abraham Normal) distribution are related. Or the t and F test. It's easy, but I'll add that.

And maybe later, we can get into multivariates.

But I'll need more coffee first.

 

[Iconoclast]

...Named after the distinguished Dr. Abraham Normal...

I thought it was a woman, first name Abby.

 

[TruthSeeker]

I thought it was a woman, first name Abby.

Same joke but your name choice is much much better. You have my congrats.

 

[BillHoyt]

While I think I know what you are after in Question 3 (we'll see if I'm correct), it did make me laugh.

I'd like to add one question: How big a nerd do you have to be to laugh at stats questions on a Sunday morning?

I'm glad you got the joke. The bigger joke, however, is T'ai's railing on about his degrees and playing the authority card. In light of some of the comments he has made and questions he has asked, the degrees are suspect. He also is beginning to smell like someone whom we've seen before.

The first tip-off for me was his post about his degrees in math and stat. The second tip-off was his post chiding someone for saying nobody had super powers. T'ai's reason? That other poster hadn't tested everyone! This from someone supposedly versed in statistical methods? I recommended he burn his degrees and spank his professors.

 

[BillHoyt]

Same joke but your name choice is much much better. You have my congrats.

I like Click & Clack's fictitious statistician, Marge Innavera.

 

[JamesM]

Re: Re: T'ai Chi : Some math/stat questions for you

It turns out that Student was the name of the guy who came up with the Student-T distribution.

It was the pen-name of a chap who worked for a brewery, wasn't it?

 

[TruthSeeker]

Re: Re: T'ai Chi : Some math/stat questions for you

No one asked, but I'll answer 3 anyway

Students t is just for the case where you have a single independent variable with two levels (e.g., male versus female).

If that's the kind of data you have, then that's the stat to use. With a few exceptions statistician's don't pick their tests; the data themselves dictacte which tests are appropriate.

However, some researchers frown on t-tests as unsophisticated, so some will instead to do an F-test / anova on data like these, to make it "look better" (it's the same test in the two group case, and t squared = F).

My first comment would be that it is the hypothesis and study design rather than the data which dictate the analysis. Except of course, when the data require transformation. Then clearly, the data dictate the analysis.

The other comment would be that the major objection to the t-test is the high likelihood of making a type I error when repeated tests are used. That is, the more t-tests you run on a given data base the higher the chances some will be significant by chance. I think of it as running across a busy highway. The more often you do it, the greater your chances of being hit by a car.

There are a couple of ways around it. The simplest is to apply a correction (a Bonferroni for instance) which leads you to adopt a more conservative p-level for significance or to use a multivariate test (depending on the research design).

La la la....

I'm still laughing at Marge. I may steal that one.

 

[TruthSeeker]

I'm glad you got the joke. The bigger joke, however, is T'ai's railing on about his degrees and playing the authority card. In light of some of the comments he has made and questions he has asked, the degrees are suspect. He also is beginning to smell like someone whom we've seen before.

The first tip-off for me was his post about his degrees in math and stat. The second tip-off was his post chiding someone for saying nobody had super powers. T'ai's reason? That other poster hadn't tested everyone! This from someone supposedly versed in statistical methods? I recommended he burn his degrees and spank his professors.

I agree that the authority card is a tricky one to play except for in very specialized circumstances. Given his comment about not testing everybody, I would like to ask him how he would determine the prevalence of a low base-rate event? Clearly, epidemiologists (and others) do it regularly. It should not be difficult for him to describe the methods and statistical tests.

I am too new here to comment on your comment about him seeming like someone you've seen before. I shall defer to your experience, but only if you can back it up with a PhD.

 

[UKBoy1977]

With regards to this superpower questions, obviously given that no-one has yet demonstrated any superpowers satisfactorily, the assigned probability that someone has them is approaching zero.

However it is true to say that until you have tested everyone you cannot be 100% certain that no-one has them.

Or am I missing something?

 

[Diamond]

Looks like the fish slipped away, Bill.

 

[T'ai Chi]

Looks like the fish slipped away, Bill.

Good God, it hasn't even been a full day yet, sheesh!

I just woke up, took a shower, and see a thread with easy math/stat questions.

I'll answer them all.

 

[T'ai Chi]

With regards to this superpower questions, obviously given that no-one has yet demonstrated any superpowers satisfactorily, the assigned probability that someone has them is approaching zero.

However it is true to say that until you have tested everyone you cannot be 100% certain that no-one has them.

Or am I missing something?

I am saying that logically, one cannot conclude that no one has had, has, or will have, "superpowers" (whatever "superpowers" means), just by saying that the people tested lacked them during the tests.

I personally don't believe "superpowers" exist, for what it is worth.

 

[T'ai Chi]

Re: Re: T'ai Chi : Some math/stat questions for you

While I'll let T'ai Chi answer the other questions -- I guess he and Billy are having some sort of intellectual p*ssing contest at the moment --

Yeah, it is fairly one-sided so far. Bill apparently thinks that by asking me questions, he can avoid answering my questions about his degrees and expertise...

It turns out that Student was the name of the guy who came up with the Student-T distribution.

That's almost correct. Student was the pseudonym of a William Sealy Gosset, a statistician who worked analyzing samples at the Guiness brewing factory. He did his work with the t-distribution to allow for analyzing small samples- something to do with yeast if I am remembering correctly. Guiness didn't want their competitors to know that they had a huge advantage by having a statistician working for them, hence the pseudonym.

Maybe T'ai Chi was the dude that invented the Chi Squared distribution, so surely he can explain how it relates to the Normal distribution, and they ARE related in a very interesting way.

Chi in Chinese (note, this is not the same word as "ch'i") and chi in Greek, are, of course, pronounced differently.

In any case, if Z is a standard normal random variable, then Z^2 is a chi-square random variable with 1 degree of freedom.

 

[T'ai Chi]

As our resident math/stat expert, I was hoping you could answer a few questions in those areas:

Hey, I never made that claim. I simply said that I have a mathematics degree, and a higher statistics degree.

1. 1st derivative test

2. It is the opposite. We approximate the binomial distribution with a normal distribution.

3. The t-tools are used in many situations. -Mostly when a measure of variance is unknown/estimated, or the sample sizes are small. They are used all the time by professionals and by students, especially in comparing the means of two groups, and in testing regression coefficients. Also, knowledge of the t-distribution is important because the t-distribution is related to or makes up other distributions that are used.

4. Ratios of the standard deviations (their squares, the variances anyway) are used to determine the relative efficiency of experiments.

Do I pass???

 

[T'ai Chi]

Given his comment about not testing everybody, I would like to ask him how he would determine the prevalence of a low base-rate event? Clearly, epidemiologists (and others) do it regularly. It should not be difficult for him to describe the methods and statistical tests.

In my opinion, I think this question is a little more vague than the rest. I can give you some general guidelines here, if you'd like. (even though biostatistics is not really my area)

I shall defer to your experience, but only if you can back it up with a PhD.

Hey, if someone calls me stupid, I will stick up for myself, and then call them on it.