Wednesday, April 22, 2009

Statistics Reflection

Well here we are, at the end of another unit.

And as one might expect, the trip here wasn't easy. For example, I'm still not clear on how to create a histogram. I know I have to put the data in List One, I know I use Zoom Stat in the 2nd Trace menu, and I know I have to select the bar-ed graph from the stat plot menu, and put L1 in the top section and L2 in the bottom section. Unfortunately for me, I haven't a clue what goes in L2. Furthermore, it doesn't appear to be in any of the slides. or any of the scribe posts. I checked more than once. Damnit.

Also, I missed the class on Confidence Intervals and Margins of Error. Thankfully, the process by which they are found is simple enough. Confidence Interval is merely 1.96 σ above and below the mean. Easily expressed as (µ-1.96σ, µ+1.96σ). Likewise, Margin of Error is calculate by (1.96σ)÷(# of trials). For instance, if you had 100 trials with a standard deviation of 10 and a mean of 50, you'd have a confidence interval of (50-1.96(10), 50+1.96(10)), or (30.4, 69.6). The margin of error would be 19.6÷100, or 0.196. Also known as 19.6%

the problem I had with these concepts is the meaning of "Confidence" in this context. My assumption was that if the data was within the confidence interval, I could be confident in the probability of that occurrence. Not so. In fact, all it says is that, were I to repeat the experiment, 19 times out of 20 I'd be likely to find 95% of the data lying between the aforementioned interval. To reuse my previous example, 19 times out of twenty, 95% of the data of an experiment which (when previously tested) resulted in the data µ=50, #trials=100, and σ=10 would lie between 30.4 and 69.6.


Darren Kuropatwa said...

You said:

were I to repeat the experiment, 19 times out of 20 I'd be likely to find 95% of the data lying between the aforementioned interval.That's not quite right.

A 95% confidence interval means:

You are 95% (19 times in 20; 19/20=95%) confident that if you did the same experiment over again, you would get a result that lies in the interval.

What you are confident in is the result you would get if you repeated the experiment. It says NOTHING about "where you'll find 95% of the data." You're not confident in the data, you're confident in the result of the experiment lying within a certain range (the confidence interval) 19 times out of 20.

Daniel said...

Well I suppose I'll take another harder look at this information and hopefully find a way to make it stick. Thanks for clearing that up Mr. K

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