Counting And all That WALTA Meeting Toby Burnett, UW.

Slides:

Advertisements

Similar presentations

Lesson 74: Measuring Speed

Advertisements

Probability models- the Normal especially.

3/2003 Rev 1 I.2.13 – slide 1 of 48 Part IReview of Fundamentals Module 2Basic Physics and Mathematics Used in Radiation Protection Session 13Statistics.

G. Cowan Lectures on Statistical Data Analysis 1 Statistical Data Analysis: Lecture 7 1Probability, Bayes’ theorem, random variables, pdfs 2Functions of.

The Poisson Distribution (Not in Reif’s book)

4-1 Continuous Random Variables 4-2 Probability Distributions and Probability Density Functions Figure 4-1 Density function of a loading on a long,

ANALYTICAL CHEMISTRY CHEM 3811

Standard error of estimate & Confidence interval.

Statistics Introduction 1.)All measurements contain random error  results always have some uncertainty 2.)Uncertainty are used to determine if two or.

Statistical Analysis of Systematic Errors and Small Signals Reinhard Schwienhorst University of Minnesota 10/26/99.

Physics 114: Lecture 15 Probability Tests & Linear Fitting Dale E. Gary NJIT Physics Department.

STA Lecture 161 STA 291 Lecture 16 Normal distributions: ( mean and SD ) use table or web page. The sampling distribution of and are both (approximately)

Noise & Uncertainty ASTR 3010 Lecture 7 Chapter 2.

Measurement Uncertainties Physics 161 University Physics Lab I Fall 2007.

Every measurement must have a unit. Three targets with three arrows each to shoot. Can you hit the bull's-eye? Both accurate and precise Precise.

R. Kass/W03P416/Lecture 7 1 Lecture 7 Some Advanced Topics using Propagation of Errors and Least Squares Fitting Error on the mean (review from Lecture.

Physics 270 – Experimental Physics. Standard Deviation of the Mean (Standard Error) When we report the average value of n measurements, the uncertainty.

LECTURER PROF.Dr. DEMIR BAYKA AUTOMOTIVE ENGINEERING LABORATORY I.

I Introductory Material A. Mathematical Concepts Scientific Notation and Significant Figures.

LECTURER PROF.Dr. DEMIR BAYKA AUTOMOTIVE ENGINEERING LABORATORY I.

Uncertainties for AH Phys. Accuracy and Precision The accuracy of a measurement tells you how close the measurement is to the “true” or accepted value.

A taste of statistics Normal error (Gaussian) distribution  most important in statistical analysis of data, describes the distribution of random observations.

Analysis of Residuals ©2005 Dr. B. C. Paul. Examining Residuals of Regression (From our Previous Example) Set up your linear regression in the Usual manner.

+ “Statisticians use a confidence interval to describe the amount of uncertainty associated with a sample estimate of a population parameter.”confidence.

Lecture 2d: Performance Comparison. Quality of Measurement Characteristics of a measurement tool (timer) Accuracy: Absolute difference of a measured value.

Radiation Detection and Measurement, JU, First Semester, (Saed Dababneh). 1 Counting Statistics and Error Prediction Poisson Distribution ( p.

Inferences from sample data Confidence Intervals Hypothesis Testing Regression Model.

1 Methods of Experimental Particle Physics Alexei Safonov Lecture #25.

Significant Figures Mr. Nelson – Uncertainty The pin is ½ way between the smallest lines on the ruler – what do we do? We have to IMAGINE that there.

4.3 More Discrete Probability Distributions NOTES Coach Bridges.

One Sample Mean Inference (Chapter 5)

G. Cowan Lectures on Statistical Data Analysis Lecture 8 page 1 Statistical Data Analysis: Lecture 8 1Probability, Bayes’ theorem 2Random variables and.

Analysis of Experimental Data; Introduction

Statistics Review ChE 475 Fall 2015 Dr. Harding. 1. Repeated Data Points Use t-test based on measured st dev (s) true mean measured mean In Excel, =T.INV(

Measurements 1. A very concrete methods of dealing with the description and understanding of nature 2.

Statistics: Unlocking the Power of Data Lock 5 Section 6.4 Distribution of a Sample Mean.

1 Probability and Statistics Confidence Intervals.

10.1 – Estimating with Confidence. Recall: The Law of Large Numbers says the sample mean from a large SRS will be close to the unknown population mean.

Uncertainty2 Types of Uncertainties Random Uncertainties: result from the randomness of measuring instruments. They can be dealt with by making repeated.

Lecture 8: Measurement Errors 1. Objectives List some sources of measurement errors. Classify measurement errors into systematic and random errors. Study.

THE SCIENTIFIC METHOD: It’s the method you use to study a question scientifically.

Statistical Analysis and Expression of Data Reading: Lab Manual Today: Some basics that will help you the entire year The mean or average =  true.

CHAPTER- 3.1 ERROR ANALYSIS.  Now we shall further consider  how to estimate uncertainties in our measurements,  the sources of the uncertainties,

Political Science 30: Political Inquiry. The Magic of the Normal Curve Normal Curves (Essentials, pp ) The family of normal curves The rule of.

Uncertainty in Measurement How would you measure 9 ml most precisely? What is the volume being measured here? What is the uncertainty measurement? For.

 Normal Curves  The family of normal curves  The rule of  The Central Limit Theorem  Confidence Intervals  Around a Mean  Around a Proportion.

AP Statistics From Randomness to Probability Chapter 14.

. Chapter 14 From Randomness to Probability. Slide Dealing with Random Phenomena A is a situation in which we know what outcomes could happen, but.

GS/PPAL Research Methods and Information Systems

Physics 114: Lecture 11-a Error Analysis, Part III

4-1 Continuous Random Variables 4-2 Probability Distributions and Probability Density Functions Figure 4-1 Density function of a loading on a long,

Physics 114: Lecture 13 Probability Tests & Linear Fitting

The Poisson probability distribution

Confidence intervals for µ

Probability and Statistics for Particle Physics

Target for Today Know what can go wrong with a survey and simulation

Ex1: Event Generation (Binomial Distribution)

Discrete Probability Distributions

Basic Error Analysis Considerations

Sources of Variation and Error in Wafer Fab Processing

Comparing Theory and Measurement

Lecture 2d1: Quality of Measurements

1200 Hz = 1200/sec would mean in 5 minutes we

Counting Statistics and Error Prediction

Problems: Q&A chapter 6, problems Chapter 6:

Today (1/21/15) Learning objectives:

Discrete Event Simulation - 4

Counting Statistics and Error Prediction

CHAPTER- 3.1 ERROR ANALYSIS.

Precision & Uncertainties

Presentation transcript:

Counting And all That WALTA Meeting Toby Burnett, UW

How do we measure a rate? Measure number of “events” or counts: N Measure time interval T. Rate is the ratio N/T, usually expressed in Hz, or counts per second.

Basic rule for presenting experimental data: Determine the uncertainty: –Statistical (easy) –Systematic (very hard, especially if you don’t know what might be wrong! Best way to tell: repeat, repeat

Statistical uncertainty for counting

Apply to a rate Rate is counts/time:

What does the  x  mean? The “true” measurement is: –within the interval x-  to x+  68% of the time –within the interval x-2  to x+2  95% of the time If N is greater than 10 or so, the distribution is approximately that of a gaussian: –example with mean 0 and sigma 1.

But wait: what about Mr. Poisson?

Example: Measure 49 counts in 10 minutes Rate is 49/10 = 4.9 counts/min Statistical uncertainty is: Statistical error in the rate is 7/10 = 0.7 counts/min Rate should be quoted as: