#sampling distribution

Explain the factors, skewed coefficient and kurtosis coefficient, from the probability distribution determine the minimal sample size.

Sampling Distribution – Business Statistics and Research Methodoloy

SAMPLING DISTRIBUTION

Suppose that we draw all possible samples of size n from a given population. Suppose further that we compute a statistic (e.g., a mean, proportion, standard deviation) for each sample. The probability distribution of this statistic is called a sampling distribution. And the standard deviation of this statistic is called the standard error.

Variability of a Sampling…

Other probabilities are obtained by experiment and are thus approximations which are typically expressed to three significant digits unless there are compelling reasons for more or less precision.

Who the fuck says this is "typical"? More importantly, there are usually good reasons to use fewer significant figures. As in, most studies cited in the news (Pew, Gallup, etc) have N ≈ 1000. That number was chosen by Gallup to minimize cost, giving a just-barely-reportable number.

http://www.gallup.com/178685/methodology-center.aspx

Just-barely-reportable numbers cannot be added and subtracted like regular numbers.

The distance between 30±5 and 35±10 is not 5. It's anywhere between 15 and −10 the other way (=opposite conclusion)

When I read the the New York Times I mentally add ±half of the first sigfig or more. Even ±1 to the first sigfig.

That wipes out most comparisons I have seen in the NYT.

Also note that ±5 in the statistical sense means ±5, ±10, or ±15. That ±sampling error refers to the stdev of a Gaussian or student distribution. (We use Gaussians because the sampling distribution of the mean might be Gaussian even when the data are not.) Gaussians with stdev=5 have a 85% chance of being inside ±5, 95% of being inside ±10, and 98% chance . (That was from memory but I just checked with R's pnorm and qnorm and I'm not far off. You can also check with pt and qt, but since part of my critique is imperfect sampling I would always be far, far more pessimistic than 98% certainty inside ±3σ.

I think explaining mathematics to an arts student, requires one to label out the definitions in words, so that I can fully understand the complexities of the knowledge.

Such was in this case heh.

Correlation: Degree of relation quantified into a coefficient (r), showing how much one variable tends to change when the other changes.

Linear Regression: finds best fit line that predicts Y from X and vice versa (which is why you can't find the value of Y when it is a graph of Y on X. 

Notes:

1. On graph of Y on X, X should be the independent (experimentally manipulated) factor (time etc.) 2. Correlation coefficient is similar of Y on X and X on Y. 3. Regression calculates cause and effect while Correlation doesn't. 4.  Correlation characterizes magnitude; Linear Regression helps you predict or explain your results with particular values. 5. The usual coefficient used is the Pearson product-moment correlation coefficient. 

Other types:

1. Spearman's correlation coefficient (idk what's this!) 2. To estimate extrapolation, the values must be sampled by the Gaussian Distribution - called bivariate Gaussian distribution. (neither do i know what this is.)

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