and Standard Error related?

Editor's Note:
Because of difficulties in displaying a square root
symbol on the web, we have used exponential notation.
Whenever you see X^{0.5} we are expressing
the square root of X. |

In the
previous parts of this series we have talked about what Standard
Deviation (SD) and Standard Error (SE) really mean. The formulas
for actually calculating them are not really important in
this day and age. How to use them and what they
mean becomes more important all the time.A brief review: __SD__is how spread out THINGS in the population are, and this is calculated (somehow) from the data in your sample. It is useful in describing the population itself.__SE__is how spread out the SAMPLE MEAN will be around the true population mean. It is useful in describing how close your cruise will be to the right answer.
SE = SD /n Now this is really quite a simple and beautiful little
formula. - It starts out with the way the world IS (that's SD
- how spread out the data are, and there is virtually
__NOTHING you can do__about it). - It then talks about how hard you WORK (that's the
sample size "n"), and you
__ARE in control__of that. Please note that is how hard you work, not how smart). - It then tells you HOW GOOD your average is likely to be with that amount of effort (the Standard Error).
All this happens with a simple little formula that anybody can understand and remember. It only gets ugly and complicated looking when you have multiple layers of sampling or lots of strata mixed together. The IDEA is simple and easy to grasp.
Luckily, some nice person has figured this out, and
published another table called the " The t-table value depends on the sample size you have
used to estimate the standard deviation. These tables sometimes
use a . |
We now know that 95% of the things in the population are within ±2.086 standard deviations of the sample mean. What is that in pounds? 2.086 * 25 pounds = 52.15 pounds each way. The "confidence interval" is therefore 200 pounds ±52 pounds (between 148 and 252 pounds if you prefer to state the end points). And how close is our SAMPLE MEAN to the true
population mean? Well, even if the population was not normally
distributed we can still use its SD to estimate how
widely spread the sample means will be. We know that sample
means are If you can follow the logic of this example you will
be able to do the most practical parts of statistical analysis.
It may take practice to do it quickly, but these are the main From now on it gets easier. Remember -- this
statistics business has to do with |