Download presentation

Presentation is loading. Please wait.

Published byNoah Clark Modified over 3 years ago

1
DATA & STATISTICS 101 Presented by Stu Nagourney NJDEP, OQA

2
Precision, Accuracy and Bias 4 Precision: Degree of agreement between a series of measured values under the same conditions 4 Accuracy: Degree of agreement between the measured and the true value 4 Bias: Error caused by some aspect of the measurement system

3
Precision, Accuracy and Bias

4
Sources of Error 4 Systematic Errors: Bias always in the same direction, and constant no matter how many measurements are made 4 Random Errors: Vary in sign and are unpredictable. Average to 0 if enough measurements are made 4 Blunders: The occasional mistake that produces erroneous results; can be minimized but never eliminated

5
Applying Statistics 4 One cannot sample every entity of an entire system or population. Statistics provides estimates of the behavior of an entire system or population, provided that: –Measurement system is stable –Individual measurements are all independent –Individual measurements are random representatives of the system or population

6
Distributions 4 Data generated by a measurement process generally have the following properties: –Results spread symmetrically around a central value –Small deviations from the central value occur more often than large deviations –The frequency distribution of a large amount of data approximates a bell-shaped curve –The mean of even small sets of data represent the overall better than individual values

7
Normal Distribution

8
Other Distributions

9
Issues with Distributions 4 For large amounts of data, distributions are easy to define. For smaller data sets, it is harder to define a distribution. 4 Deviations from normal distributions: –Outliers that are not representative of the population –Shifts in operational characteristics that skew the distribution –Large point-to-point variations that cause broadening

10
Estimation of Standard Deviation 4 The basic parameters that characterize a population are –Mean ( ) –Standard Deviation ( ) 4 Unless the entire population is examined, and cannot be known. They can only be estimated from a representative sample by –Sample Mean (X) –Estimate of Standard Deviation (s)

11
Measures of Central Tendency & Variability 4 Central Tendency: the value about which the individual results tend to cluster 4 Mean: X = [X 1 + X 2 + X 3 + … X n ] / n 4 Median: Middle value of an odd number of results when listed in order 4 s = [ (X i - X) 2 / n-1] 1/2

12
Measures of Central Tendency & Variability

13
Statistics 4 If you make several sets of measurements from a normal distribution, you will get different means and standard deviations 4 Even the best scientist and/or laboratory will have measurement differences when examining the same sample (system) 4 What needs to be defined is the confidence in measurement data and the significance of any differences

14
Estimation of Standard Deviation

15
Does a Measured Value Differ from an Expected Value? 4 Confidence Interval of the Mean (CI) : The probability where a sample mean lies relative to the population mean 4 CI = X ± (t) (s) / (n) 1/2 : value of t depends upon level of confidence desired & # of degrees of freedom (n-1)

16
Does a Measured Value Differ from an Expected Value?

17
Criteria for Rejecting an Observation 4 One can always reject a data point if there is an assignable cause 4 If not, evaluate using statistical techniques 4 Common Outlier Tests –Dixon (Q) Test –Grubbs Test –Youdon Test –Student t Test

18
Criteria for Rejecting an Observation: Dixon (Q) Test

19
Control Charts

Similar presentations

OK

Errors in Chemical Analyses: Assessing the Quality of Results

Errors in Chemical Analyses: Assessing the Quality of Results

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

By appt only movie free Ppt on phonetic transcription examples Ppt on time division switching Ppt on social media marketing Ppt on negotiation skills Ppt on cost ledger accounting Ppt on meeting skills ppt Safety ppt on working at height Ppt on the land of dense forest Ppt on save our planet earth