Ch 1 Quantitative Analysis

precision

reproducibility

Accuracy

nearness to the “truth”

uncertainty

variability in measurements

error

difference between measured and “true value”

Percent Error

• absolute value of the error makes it a positive numbers

False

A standard deviation close to zero means that the data points are highly accurate

True

A standard deviaiton close to zero means that the data points are close to the mean of the set

False

The population mean is the same as the sample mean

Population Mean

average of every individual in the entire population

used when you have data for everyone (RARE IN PRACTICE)

Sample Mean

• average of a subset (sample) taken from the population

• it is statistic ( varies from sample to sample)

• used to estimate population mean

  • what we use

For a larger number of measurements,

sample mean approaches population mean.

Relative Standard Deviation (RSD)

ppt (part per thousand)

Sometimes reported as ppt

Variance

the square of the standard deviation

Coefficient of variation (CV)

is the relative standard deviation (RSD) expressed as percent

• standard deviation (S)

• RSD

• Variance (s²)

• Coefficient of variation (CV)

How is precision expressed by

the true value may never be known

What is the problem with accuracy

deviation

for comparision, precision analysis often uses

Types of Error

1. random

2. systematic error

3. gross

Random error (indeterminate error)

• arises from the effect of uncontrolled (or uncontrollable) variables in the measurements

• has equal chance of being positive or negative

  • always present and cannot be corrected

Systematic Error (determinate error)

• Arises from a flaw in equipment or the design of the experiment

• can be discovered and corrected

• examples: incorrectly standardized pH meter, uncalibrated burette or flask, or a metod with wrong reaction (incomplete or too slow)

Systematic error Sources A

Instrument Errors

• imperfections or instability

• calibrate glassware

• contamination in the inner wall of the flask

• Instrument issues: power supplies are unstable, and dirty contacts are causing an increase in resistance

Systematic error Sources B

Method Errors

• non-ideal chemical or physical behavior of the system

• instability of the chemicals

• slow or incomplete reactions

• non-specificity of the reagents

COMMON and DIFFICULT TO DETECT

Recommendations for Method Error

• analyze standard reference samples. Concetrations of analytes are known

• use a second method to verify

• perform blank analysis

Systematic error Sources C

Personal errors

• careless or personal limitations

• levels of liquid in burette

• prejudice- have a natural tendency to underestimate the reading

Gross Error (blunder)

• neither random or systematic

  • no known distribution or modeling and can be of any magnitiude

• human mistakes

• leads to outliers

• identify outliers (Q-test or Grubb test)

Grubbs test

• test to decide whether to discard one datapoint that appears discreptant (outlier)

• If Gcalculated > Gtable, then reject the data point

• there is a <5% chance that the sus data point is a member of the same population as the other measurements

• difference is considered significant

Grubbs Test

In the absence of a recorded blunder, use the …..