Accuracy, Errors and Data Significance

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?
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