Physics307L:Schedule/Week 5 agenda: Difference between revisions

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[[/Week 5 notes]]
(Moved to week 6, 2011)
==Agenda for Lecture==
# [[/PDF|Probability density function]]
# [[/Histogram|Histogram]]
# [http://en.wikipedia.org/wiki/Normal_distribution Normal Distribution]
# [[/CLT|Central Limit Theorem]]


==Agenda for Labs==
==Faster than light neutrinos?==
# Today you definitely need to talk with Koch about what needs to be included in your lab summary.
* [https://plus.google.com/110146523961072500429/posts/CZJHdb69M5w links on Google plus]
# Must finish taking data this week. Summary can be completed at home.
* Arxiv discussion / open science http://arxiv.org/abs/1109.4897
# Must complete your hands-on "quiz" or interview with Koch.


==Scraps==
==Beginning group activity==
* Form groups of two
* Look at the coin flip data from two weeks ago
* Come up with your best guess for the true mean and an uncertainty.  Report your result as mean +/- uncertainty (we'll poll vocally)
** Assume all the nickels are identical and there is a fixed true mean


===Uncertainty===
==2011 Coin Toss Results==
[https://docs.google.com/spreadsheet/ccc?key=0AhLNnjMk2r_qdDBWQnhwcUNfYmRMMG1fN3h6U25aLXc&hl=en_US Google spreadsheet]


This is copied directly from wikipedia: http://en.wikipedia.org/wiki/Uncertainty
==Google Docs Central Limit Theorem Example==
==== Relation between uncertainty, accuracy, precision, standard deviation, standard error, and confidence interval ====
[https://docs.google.com/spreadsheet/pub?hl=en&hl=en&key=0AhLNnjMk2r_qdDRJNlNSMEJWU21MX3UyQXVMS3VHd2c&output=html Monte Carlo Google Doc CLT Example]


The uncertainty of a measurement is stated by giving a range of values which are likely to enclose the true value. This may be denoted by [[error bar]]s on a graph, or as value ± uncertainty, or as decimal fraction(uncertainty). The latter "concise notation" is used for example by [[IUPAC]] in stating the [[List of elements by atomic mass|atomic mass]] of [[Chemical element|elements]].  There, 1.00794(7) stands for 1.00794 ± 0.00007.
==Binomial Distribution==
[http://en.wikipedia.org/wiki/Binomial_distribution Wikipedia Bionomial Distribution]


Often, the uncertainty of a measurement is found by repeating the measurement enough times to get a good estimate of the [[standard deviation]] of the values.  Then, any single value has an uncertainty equal to the standard deviation.  However, if the values are averaged and the mean is reported, then the averaged measurement has uncertainty equal to the [[standard error (statistics)|standard error]] which is the standard deviation divided by the square root of the number of measurements.
==2009 Agenda for Lecture==
# Discussion about labs; [[/Good lab notebooks]];
# [[/Uncertainty|How to report uncertainty]]
#* Make sure to always include units and uncertainty.
# [[/PDF|Probability density function]]
# [[/Histogram|Histogram]]
# [[/CLT|Central Limit Theorem]]
# [[/Normal|Normal Distribution]]
# Possibly: How to graph results w/ theory
# Possibly: sensitivity for uncertainty propagation


When the uncertainty represents the standard error of the measurement, then about 68.2% of the time, the true value of the measured quantity falls within the stated uncertainty range.  For example, it is likely that for 31.8% of the atomic mass values given on the [[list of elements by atomic mass]], the true value lies outside of the stated range.  If the width of the interval is doubled, then probably only 4.6% of the true values lie outside the doubled interval, and if the width is tripled, probably only 0.3% lie outside.  These values follow from the properties of the [[normal distribution]], and they apply only if the measurement process produces normally distributed errors.  In that case, the quoted [[standard error (statistics)|standard error]]s are easily converted to 68.2% ("one sigma"), 95.4% ("two sigma"), or 99.7% ("three sigma") [[confidence interval]]s.
==Agenda for Labs==
 
# Today you definitely need to talk with Koch about what needs to be included in your lab summary.
===Normal Distribution===
# Must finish taking data this week.  Summary should be completed outside of class.
Copied from: http://en.wikibooks.org/wiki/Probability:Important_Distributions
# <s>Must complete your hands-on "quiz" or interview with Koch.</s> The in-class "quiz" is actually on-going...but you can request one at the end if you think I may have a bad impression of your understanding.
====Normal Distribution====
 
The normal or Gaussian distribution is a thing of beauty, appearing in many places in nature.  This probably is a result of the normal distribution resulting from the law of large numbers, by which a sum of many random variables (with finite variance) becomes a normally distributed random variable according to the central limit theorem.
 
Also known as the bell curve, the normal distribution has been applied to many social situations, but it should be noted that its applicability is generally related to how well or how poorly the situation satisfies the property mentioned above, whereby many finitely varying, random inputs result in a normal output.
 
The formula for the density f of a normal distribution with mean <math>\mu</math> and standard deviation <math>\sigma</math> is
:<math>
f(x)
=
\frac{1}{\sigma\sqrt{2\pi}} \, e^{ -\frac 12 \left( \frac{x- \mu}{\sigma}\right)^2 }</math>.
 
A rather thorough article in Wikipedia could be summarized to extend the usefulness of this book: [[w:en:Normal distribution|Normal distribution from Wikipedia]].

Latest revision as of 11:49, 26 September 2011

(Moved to week 6, 2011)

Faster than light neutrinos?

Beginning group activity

  • Form groups of two
  • Look at the coin flip data from two weeks ago
  • Come up with your best guess for the true mean and an uncertainty. Report your result as mean +/- uncertainty (we'll poll vocally)
    • Assume all the nickels are identical and there is a fixed true mean

2011 Coin Toss Results

Google spreadsheet

Google Docs Central Limit Theorem Example

Monte Carlo Google Doc CLT Example

Binomial Distribution

Wikipedia Bionomial Distribution

2009 Agenda for Lecture

  1. Discussion about labs; /Good lab notebooks;
  2. How to report uncertainty
    • Make sure to always include units and uncertainty.
  3. Probability density function
  4. Histogram
  5. Central Limit Theorem
  6. Normal Distribution
  7. Possibly: How to graph results w/ theory
  8. Possibly: sensitivity for uncertainty propagation

Agenda for Labs

  1. Today you definitely need to talk with Koch about what needs to be included in your lab summary.
  2. Must finish taking data this week. Summary should be completed outside of class.
  3. Must complete your hands-on "quiz" or interview with Koch. The in-class "quiz" is actually on-going...but you can request one at the end if you think I may have a bad impression of your understanding.
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