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Areas of Statistics

Trying to visualize the areas of statistics, and how they are related. For teaching undergraduates.
by

Morten Fenger

on 21 May 2011

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Transcript of Areas of Statistics

Areas of Statistics Sampling Theory Descriptive Statistics Inferential Statistics Using Statistics to Predict the Future! [This is the (often) "ignored" part of statistics,
where the whole fundamental of the analysis
is made...] The data gathering process! Must be random! ... you could also select a sample
according to a selection system,
that warants non-random sampling, if you
have information available to support
that decision. (We'll not focus more on
this situation here, however.) ... or you should sample the full
population Keywords here are:

RANDOMNESS and
INDEPENDENCE

between observations sampled Selection method and theory... Random Sampling Cluster Sampling Stratified Sampling So for now just remember:

Statistics is based on probability calculus, and most statistical techniques assumes
that our observations are independent.

If this requirement is not met, then we
cannot trust conclusions based on
techniques that requires independence
(... obviously) ... describes your data! In other words, you try to summarize the information
that you gathered in the previous step the mean % graphs... you do this by using some descriptive meassurements (know as statistical parameters) together with graphic representation of your data.

You are already familiar with much of this, e.g... [Which might be both impractical, expensive and impossible!] (would you like your doctor to sample all your blood, or are you happy she just takes a bit??!) Therefore... This is the very interesting area of Statistics... (Which very few people refer to, when they say 'Statistics'!) Most people only knows about... However, Inferential Statistics is the area that really can be used for strategic management ... a bit like gambling, but with controlled risk,
so that you can expect to win in the long run! Inferential statistics is where statistics gets interesting,
and this area is (unfortunately?) reserved for those* who
spend time studying... Mathematical Statistics Thanks to Fischer, Bonferroni, Pearson, Wald, Levine, White and many
others who devoted their career to develop techniques on which the rest of us
benefit. We'll use their techniques (=applied statistics), without worrying too
much about how they came up with the formulas (=theoretical statistics) The major techniques of Inferential Statistics are
Confidence Intervals, and
Hypothesis Tests
... and that's pretty much it! If you understand these concepts, then the "only" thing left to learn, is:
which Test Statistics should be used in which situation?
which assumptions are the Test Statistics you use based on?
How to calculate the Test Statistic and other relevant parameters?
How to interpret your findings? *: Including you, since you read this! Techniques includes...
- Testing one and two means
- Testing more than two means (ANOVA-designs)
- Testing proportions of categorical variables (Tests on Contingency Tables)
- Testing how some variables might be able to explain another variable (Regression Analysis ≈ Econometrics)
- Testing underlying structures of large datasets (Factoranalysis)
- ... and many other techniques, enough to keep you occupied for some time ;) Benefit: we can make informed decisions based on our data
in an uncertain business environment! If you want more certain decisions, well then just decrease alpha! Disadvantage: loss of statistical power* *: ability to detect a significant relationship [Significant: something that's very unlikely to happen by chance alone] Even though these techniques
might be challenging to learn,
the biggest challenge is almost invisible... ... it's the quality of your data! Thats why the sampling process is soooooo important! It's not about advanced statistics here, just about gathering a representative sample! If your data is from different time periods, you can also try to predict the future from your data. As such, the Statistician is the new "magician of deviation", who people (read: scientists, businesses, government and ngo's) turn to, when they want to know something about tomorrow or next year, or even 100 or billions of years out in the future. The name applied here is stolen from metheorology, and called "Forecasting" Here, statistics will give you "the business forecast" (e.g. "... Sunny sales for the rest of the week, with a possible 'thunderstorm' of many staffs calling sick Saturday and Sunday morning...") But really - can statistics tell us something we couldn't figure out with our common sence? Yes. if you situation is just slightly more complicated than what you can visualize in a screen-sized Excel spreadsheet Forecasting is an area of it self, and a prerequisite is good understanding of basic statistics [now you know which way to go...] [End of presentation.] Further, it's nice to know that you'll
be right 19 out of 20 situations,
if you go for alpha=0.05! And actually, Statistics IS commonsence, just mixed with probability calculus in a funky cocktail Further, you can use statistics to argue for your case (in case people want more than just your 'oppinion' on something) “In God we trust; all others must bring data.”
W. Edwards Deming
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