PH101 lab 1 uncertainty analysis statistics. Sciencing So you have an idea. This idea must be testable... or it is not science So we test it. How good.

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Presentation transcript:

PH101 lab 1 uncertainty analysis statistics

Sciencing So you have an idea. This idea must be testable... or it is not science So we test it. How good is our test? How well did it work? a measure of the result & accuracy does it make any sense? predict something else...

Example Your reaction time is better than mine... Every time? By how much? What is the variability? How good is the measurement anyway?

Today: is the deck loaded? one measurement vs. many how does accuracy improve? how to measure accuracy? statistical measures of uncertainty & dispersion

The experiment: picking cards give each one a number Ace = 1, 2 = 2... Jack = King = 13 what is the average card? - we expect it must be 7... what is the spread? how to define this?

150 trials...

cards have values 1-13 equal number of each average must be 7, if one chooses enough cards takes ~50 before ‘luck’ is irrelevant!

standard deviation is a measure of the variability dispersion in a population or data set low standard deviation: data tends to lie close to the average (mean) high standard deviation: data spread over a large range data set: data clustered about average many trials: follow a distribution ~68% within +/- 1 standard deviation ~95% within +/- 2 standard deviations ~99.7% within +/- 3...

so what? knowing the standard deviation tells you - if subsequent measurements are outliers - what to expect next - accuracy of a set of data - variability in a large batch “six sigma” - quality control - means one out of 500 million!

so what? if the mean of the measurements is too far away from the prediction, then the theory being tested probably needs to be revised! particle physics: 3-sigma standard typical more than that... probably a new effect!

expect 75% of cards within 2 standard deviations of average or, 75% are within about 4 cards from the average after 100 trials or, 75% of cards should be between 3 and Jack (inclusive) It works! flip side: we could estimate the distribution of cards without prior knowledge (e.g., remove all 2’s and 3’s... we could tell!)

what else? standard deviation gives accuracy of average if you do n measurements, average is better for higher n

detailed explanation & examples in lab procedure... so read it first excel example included too