Analytical Chemistry - Section 3-1 PDF

University of Mines and Technology Analytical Chemistry (CH & RP 174) Section 3 – Data Handling & Statistics Dr Benjamin Edem Meteku Department of Chemical & Petrochemical Engineering [email protected] July 2024  DAT...

University of Mines and Technology Analytical Chemistry (CH & RP 174) Section 3 – Data Handling & Statistics Dr Benjamin Edem Meteku Department of Chemical & Petrochemical Engineering [email protected] July 2024  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Error In the analytical methodology, measurements are taken by; - Total Analysis technique (Classical analysis / wet chemical analysis) techniques in which the signal respond to the absolute amount of analyte. Mass and volume being the common signals. - Concentration techniques - A technique in which the signal is proportional to the analyte’s concentration; also called “instrumental” technique or analysis BEM 2  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Error - Measurement of the concentration of analyte is done in several aliquots (portions/parts). - The purpose of replicate measurements (repeated measurements) is to assess the variability (uncertainty) in the analysis and to guard against a gross error in the analysis of a single aliquot. What then is error? BEM 3  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Error BEM 4  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Error - Example BEM 5  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Important Terms BEM 6  DATA HANDLING AND STATISTICAL ANALYSIS ❖ 1) Replicates BEM 7  DATA HANDLING AND STATISTICAL ANALYSIS ❖ 2) Mean, x̅ BEM 8  DATA HANDLING AND STATISTICAL ANALYSIS ❖ 3) Median ✓The middle result when replicate data are arranged according to increasing or decreasing value. ✓For an odd number results, the median can be evaluated directly. ✓For an even number, the mean of the middle pair is used. (1. You add them up 2. Divide the result by two) BEM 9  DATA HANDLING AND STATISTICS ❖ Example 1 BEM 10  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Answer BEM 11  DATA HANDLING AND STATISTICS ❖ Example 2 BEM 12  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Answer BEM 13  DATA HANDLING AND STATISTICAL ANALYSIS ❖ 4) Precision ✓ The reproducibility of measurements ✓ The closeness of results that have been obtained in exactly the same way ✓ Three terms are widely used to describe the precision of a set of replica data - standard deviation - variance - coefficient of variation BEM 14  DATA HANDLING AND STATISTICAL ANALYSIS ❖ 5) Accuracy BEM 15  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Accuracy and Precision BEM 16  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Accuracy and Precision BEM 17  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Example 3 BEM 18  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Answer BEM 19  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Example 4 BEM 20  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Answer BEM 21  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Types of Error in Experimental Data BEM 22  DATA HANDLING AND STATISTICAL ANALYSIS ❖ 1) Systematic / Determinate Error BEM 23  DATA HANDLING AND STATISTICAL ANALYSIS ❖ i) Instrumental Error BEM 24  DATA HANDLING AND STATISTICAL ANALYSIS ❖ ii) Method Error BEM 25  DATA HANDLING AND STATISTICAL ANALYSIS ❖ iii) Personal Error BEM 26  DATA HANDLING AND STATISTICAL ANALYSIS ❖ 2) Gross Error BEM 27  DATA HANDLING AND STATISTICAL ANALYSIS ❖ 3) Random/ Indeterminate Error BEM 28  DATA HANDLING AND STATISTICAL ANALYSIS ❖ 3) Random/ Indeterminate Error 29 BEM  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Statistical Treatment of Random Error 30 BEM  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Samples and Population 31 BEM  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Example of Normal Distribution of a Set of Data 32 BEM  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Frequency Distribution from Table on Previous Page 33 BEM  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Normal / Gaussian Curve 34 BEM  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Properties of the Gaussian Curve 35 BEM  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Properties of the Gaussian Curve 36 BEM  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Properties of the Gaussian Curve 37 BEM  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Properties of the Gaussian Curve 38 BEM  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Example 5 BEM 39  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Answer BEM 40  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Answer BEM 41  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Variance and Other Measurements 42 BEM  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Other Measurements 43 BEM  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Other Measurements 44 BEM  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Example 6 BEM 45  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Answer BEM 46  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Answer BEM 47  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Answer BEM 48  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Example 7 BEM 49  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Answer BEM 50  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Example 8 The masses of seven different same denominated coins (penny) is provided in the table. Find a) Mean b) Median c) Range or spread d) Standard deviation e) Variance BEM 51  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Answer BEM 52  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Answer BEM 53  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Answer BEM 54  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Answer BEM 55  DATA HANDLING AND STATISTICAL ANALYSIS ❖ Trial Question BEM 56  ACKNOWLEDGEMENT Materials for the lecture presentations were adapted from the works of the following; 1. Dr Cornelius B. Bavoh 2. Dr Gideon Abaidoo Ocran 3. Dr Hayyiratul Fatimah Zaid 4. Dr Johannes Ami BEM 57