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.
2 comments:
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.
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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