Sample vs Population (true mean) (sample mean) (sample variance)

Slides:

Advertisements

Similar presentations

Experimental Measurements and their Uncertainties

Advertisements

Uncertainty in fall time surrogate Prediction variance vs. data sensitivity – Non-uniform noise – Example Uncertainty in fall time data Bootstrapping.

The Standard Deviation of the Means

Sampling: Final and Initial Sample Size Determination

6-1 Introduction To Empirical Models 6-1 Introduction To Empirical Models.

Probability Probability; Sampling Distribution of Mean, Standard Error of the Mean; Representativeness of the Sample Mean.

Errors & Uncertainties Confidence Interval. Random – Statistical Error From:

Chapter 7 Introduction to Sampling Distributions

Sampling Distributions

Physics 310 Errors in Physical Measurements Error definitions Measurement distributions Central measures.

Measurement, Quantification and Analysis Some Basic Principles.

Understanding sample survey data

Basics of Sampling Theory P = { x 1, x 2, ……, x N } where P = population x 1, x 2, ……, x N are real numbers Assuming x is a random variable; Mean/Average.

Standard error of estimate & Confidence interval.

1 Psych 5500/6500 Statistics and Parameters Fall, 2008.

Chapter 6 Random Error The Nature of Random Errors

One Sample  M ean μ, Variance σ 2, Proportion π Two Samples  M eans, Variances, Proportions μ1 vs. μ2 σ12 vs. σ22 π1 vs. π Multiple.

Development of An ERROR ESTIMATE P M V Subbarao Professor Mechanical Engineering Department A Tolerance to Error Generates New Information….

- Interfering factors in the comparison of two sample means using unpaired samples may inflate the pooled estimate of variance of test results. - It is.

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)

Introduction to Statistical Inference Chapter 11 Announcement: Read chapter 12 to page 299.

Introduction to Inferential Statistics. Introduction  Researchers most often have a population that is too large to test, so have to draw a sample from.

Measurement Uncertainties Physics 161 University Physics Lab I Fall 2007.

Scientific Methods Error Analysis Random and Systematic Errors Precision and Accuracy.

Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin Chapter 7 Sampling Distributions.

Lab 3b: Distribution of the mean

Chapter 6: Random Errors in Chemical Analysis CHE 321: Quantitative Chemical Analysis Dr. Jerome Williams, Ph.D. Saint Leo University.

Lecture 2 Forestry 3218 Lecture 2 Statistical Methods Avery and Burkhart, Chapter 2 Forest Mensuration II Avery and Burkhart, Chapter 2.

Inference for Regression Simple Linear Regression IPS Chapter 10.1 © 2009 W.H. Freeman and Company.

Statistics PSY302 Quiz One Spring A _____ places an individual into one of several groups or categories. (p. 4) a. normal curve b. spread c.

McGraw-Hill/IrwinCopyright © 2009 by The McGraw-Hill Companies, Inc. All Rights Reserved. Chapter 7 Sampling Distributions.

Determination of Sample Size: A Review of Statistical Theory

Chapter 7 Sampling and Sampling Distributions ©. Simple Random Sample simple random sample Suppose that we want to select a sample of n objects from a.

1 Chapter 7 Sampling Distributions. 2 Chapter Outline  Selecting A Sample  Point Estimation  Introduction to Sampling Distributions  Sampling Distribution.

Uncertainty in Measurement

Experimental Psychology PSY 433 Appendix B Statistics.

Statistical Inference for the Mean Objectives: (Chapter 9, DeCoursey) -To understand the terms: Null Hypothesis, Rejection Region, and Type I and II errors.

Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall Chapter 6 Hypothesis Tests with Means.

1 URBDP 591 A Lecture 12: Statistical Inference Objectives Sampling Distribution Principles of Hypothesis Testing Statistical Significance.

Review of Statistical Terms Population Sample Parameter Statistic.

Measuring change in sample survey data. Underlying Concept A sample statistic is our best estimate of a population parameter If we took 100 different.

Ch 8 Estimating with Confidence 8.1: Confidence Intervals.

Sampling Distributions Chapter 18. Sampling Distributions If we could take every possible sample of the same size (n) from a population, we would create.

Steps in the Scientific Method 1.Observations - quantitative - qualitative 2.Formulating hypotheses - possible explanation for the observation 3.Performing.

Statistical Inference for the Mean Objectives: (Chapter 8&9, DeCoursey) -To understand the terms variance and standard error of a sample mean, Null Hypothesis,

Chapter 9 Day 2. Warm-up  If students picked numbers completely at random from the numbers 1 to 20, the proportion of times that the number 7 would be.

Indicate the length up to one estimated value…. A. B. C.

Instrumental Analysis Elementary Statistics. I. Significant Figures The digits in a measured quantity that are known exactly plus one uncertain digit.

Uncertainties in Measurement Laboratory investigations involve taking measurements of physical quantities. All measurements will involve some degree of.

Sampling and Sampling Distributions

Goals of Statistics.

Precision of a measurment

Comparing Theory and Measurement

Statistical Inference

Frequency and Distribution

Hypothesis Testing: Hypotheses

Making Statistical Inferences

Quantitative Methods PSY302 Quiz 6 Confidence Intervals

Probability “When you deal in large numbers, probabilities are the same as certainties. I wouldn’t bet my life on the toss of a single coin, but I would,

Simple Probability Problem

Significant Figures The significant figures of a (measured or calculated) quantity are the meaningful digits in it. There are conventions which you should.

Sampling Distribution

Sampling Distribution

CHAPTER 6 Statistical Inference & Hypothesis Testing

Sampling Distributions

Sampling Distribution of the Mean

CHAPTER – 1.2 UNCERTAINTIES IN MEASUREMENTS.

Comparing Theory and Measurement

CHAPTER – 1.2 UNCERTAINTIES IN MEASUREMENTS.

Presentation transcript:

Sample vs Population (true mean) (sample mean) (sample variance) (true variance) (sample mean) (sample variance)

Populations Parameters and Sample Statistics Population parameters include its true mean, variance and standard deviation (square root of the variance): Sample statistics with statistical inference can be used to estimate their corresponding population parameters to within an uncertainty.

Populations Parameters and Sample Statistics A sample is a finite-member representation of an ‘infinite’-member population. Sample statistics include its sample mean, variance and standard deviation (square root of the variance):

Example Problem

Normally Distributed Population using MATLAB’s command randtool

Random Sample of 50

Another Random Sample of 50

Effect of Sample Size

Comparing Theory and Measurement

Comparing Theory and Measurement Agreement between theory and experiment does NOT imply correctness. Counter-examples include: bad theory agreeing with bad data bad theory agreeing with good data by coincidence good theory agreeing with bad data because a variable was not considered or controlled in the experiment Scientific information can be misused selectively. Comparisons must be made within the context of uncertainty.

Proper Graphical Comparison with Uncertainty Figure 9.1

How Sure Are We ? When a physical process is quantified, uncertainties associated with describing the process occur. Uncertainties result from Experiments Modeling

Systematic and Random Uncertainties An error is the difference between the measured and the true value. An uncertainty is an estimate of the error. Uncertainties are categorized as either systematic (bias) or random (precision). An uncertainty is assumed to be systematic if no statistical information is provided.

Systematic and Random Uncertainties Systematic, Bi: arises from comparisons with standards (calibration) involves no statistics; the number is given alone related to the accuracy (‘to within ±Bi units’) Random, Pi: based upon repeated measurements involves statistics ( ) related to the precision (scatter) for one more measurement for multiple measurements

Systematic and Random Uncertainties Figure 9.2

Precision and Accuracy Precision Accuracy good poor good good poor poor