# Tag Info

36

There are many ways to control for variables. The easiest, and one you came up with, is to stratify your data so you have sub-groups with similar characteristics - there are then methods to pool those results together to get a single "answer". This works if you have a very small number of variables you want to control for, but as you've rightly discovered, ...

29

I will answer the first question in detail. With a fair coin, the chances of getting 527 or more heads in 1,000 flips is less than 1 in 20, or 5 percent, the conventional cutoff. For a fair coin the number of heads in 1000 trials follows the binomial distribution with number of trials $n=1000$ and probability $p=1/2$. The probability of getting ...

28

Humorously enough, I just wrote a blog post on this very subject: http://confounding.net/2012/03/12/thats-not-how-the-law-of-large-numbers-works/ Essentially, the Law of Large Numbers is that as the number of trials of a random process increases, the mean of those trials will approach the actual mean (or expectation, for more complex distributions). So ...

24

1. Introduction I like @EpiGrad's answer (+1) but let me take a different perspective. In the following I am referring to this PDF document: "Multiple Regression Analysis: Estimation", which has a section on "A 'Partialling Out' Interpretation of Multiple Regression" (p. 83f.). Unfortunately, I have no idea who is the author of this chapter and I will refer ...

12

Here is the rub: Apple is so big, it’s running up against the law of large numbers. Also known as the golden theorem, with a proof attributed to the 17th-century Swiss mathematician Jacob Bernoulli, the law states that a variable will revert to a mean over a large sample of results. In the case of the largest companies, it suggests that high ...

11

Here's one possibility. Assessing teacher performance has traditionally been difficult. One part of this difficulty is that different students have different levels of interest in a given subject. If a given student gets an A, this doesn't necessarily mean that teaching was excellent -- rather, it may mean that a very gifted and interested student did his ...

11

That sentence does not actually make sense and is clearly in error. Data cannot be statistically significant or insignificant. Only relationships between data, the product of statistical tests, can be spoken about in these terms. If the question is: Can we drop data from our analyses because the inclusion of that data means we cannot reject the null ...

10

"Your teaching score depends on how well your students did compared to a prediction made based on What they knew beforehand, as measured by a pretest, How well we think the students can learn based on what we know about them individually (their "characteristics"), And how well students do on average in your district, school, and classroom (if there are ...

6

In the report cited in whuber's comment, it says on page 104 [pg 114 in the pdf]: The survey succeeded in activating the participation of approximately 8,900 doctoral candidates from more than 30 countries... Then, spanning pages 104-105, it says: While conducting data cleaning procedures, the Eurodoc survey experts' team decided to run a power ...

4

The claim that the margin of error is $4.9$% follows from assuming that the poll was conducted as if a box had been filled with tickets--one for each member of the entire population (of "hardcore Republican voters")--thoroughly mixed, $400$ of those were blindly taken out, and each of the associated $400$ voters had written complete answers to all the poll ...

3

I won't try to deliver my own answer, but I would refer you to the "What Is a Survey?" booklet compiled by the Survey Research Methods Section of the American Statistical Association. (Fritz Scheuren endorsing it on the title page is a former President of ASA from about five years ago. He used to be a high profile statistician in federal agencies such as the ...

2

To answer your question: It is possible to extrapolate from a sample of 400 to the views of all 700,000. This is contingent on the sample being random. Statistical Power is the topic you'd want to look into to confirm this. If I ask 400 of my closest friends, this doesn't work. To get a truly random sample, I'd have to get the list of all 700,000 people, ...

2

There is just nothing to understand here. Well, ok, it is just a standard linear regression model. It assumes that the score of a student can be described as a linear function of several factors, including school and teacher efficiency coefficients -- thus it shares all the standard problems of linear models, mainly the fact that it is a great approximation ...

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