# Accuracy, Errors and Data Significance

LevelBasic
Accuracy, Precision, Errors, Confidence intervals, Significance tests and Significance figures.

## Accuracy, Precision, Errors (Video)

Description of accuracy, precision, types of errors, and significant figures as they pertain to analytical chemistry data.

## Confidence Intervals (Video)

Explains confidence intervals and how they are calculated. Provides calculation examples.

## Propagation of Error (Video)

Provides mathematical approach to propagate errors for addition/subtraction, multiplications/division, and functions. Provides calculation examples.

## Significance tests (Video)

General description of significance testing. Provides calculation examples.

## Significant Figures (Video)

Explains the importance of significant figures within analytical chemistry. Provides examples for rounding to the correct number of significant figures based on mathematical operation.

## Exercises 1

Errors, Error Analysis, and Statistics

1) What different kinds of errors can be observed for data collected in lab? List both the general names and then provide a specific example for each.

2) What are accuracy and precision? Why would we care about these in this class?

3) Examples for Addition/Subtraction: Calculate the mathematical answer and absolute standard deviation for each equation.
a) y = 5.75(±0.03) + 0.833(±0.001) – 8.021(±0.001)
b) y = 18.79(±0.04) + 0.0025(±0.0001) + 2.29(±0.08)

4) Examples for Multiplication/Division: Calculate the mathematical answer and absolute standard deviation for each equation.
a) y = 0.0020(±0.0005) x 20.20(±0.02) x 300(±1)
b) y = (163(±0.03)×〖10〗^(-14))/(1.03(±0.04)×〖10〗^(-16) )

5) Example for Mixed Math: Calculate the mathematical answer and absolute standard deviation for each equation.
a) (157(±6)-59(±3))/(1220(±1)+77(±8))

6) Example of Confidence Interval: Calculate the 95% confidence interval for the data set below assuming the sample standard deviation, 0.015, is a good estimate of the population standard deviation. What does this interval mean?
0.514, 0.503, 0.486, 0.497, 0.472

7) Examples of t-Tests

a) Analysis of control sample: The certified percent nickel in a particular NIST reference steel sample is 1.12%, and the standard deviation associated with this number is 0.03%. A new spectroscopic method for the determination of nickel in steel produced the following percentages: 1.10, 1.08, 1.09, 1.12, 1.09. Perform a t-Test to determine if there is any indication of bias in the method at the 95% level or if instead the method can be considered valid.

b) Analysis of same sample by two different methods: In a comparison of two different methods for the determination of chromium in rye grass, the following results were obtained:
Method 1: mean = 1.48 mg/kg, standard deviation 0.28 mg/kg
Method 2: mean = 2.33 mg/kg, standard deviation 0.31 mg/kg
For each method 5 determinations were made. Do these two methods give results having means with differ significantly at a 95% level?