Data Analysis - Pharmaceutical Analytical Chemistry 1 PDF

Basic concepts Pharmaceutical Analytical Chemistry 1 Data Analysis 1 Experimental error is the difference between a measurement and the true value or between two measured values Experimental error is dem...

Basic concepts Pharmaceutical Analytical Chemistry 1 Data Analysis 1 Experimental error is the difference between a measurement and the true value or between two measured values Experimental error is demonstrated by accuracy and precision The accuracy of the measurement refers to how close the measured value is to the true or accepted value. For example, if you used a balance to find the mass of a known standard 100.00 g mass, and you got a reading of 78.55 g, your measurement would not be accurate. One important distinction between accuracy and precision is that accuracy can be determined by only one measurement, while precision can only be determined with multiple measurements. 2 1  Precision refers to how close together a group of measurements actually are to each other. Precision has nothing to do with the true or accepted value of a measurement, so it is quite possible to be very precise and totally inaccurate. Precision is sometimes referred to as repeatability or reproducibility. A measurement which is highly reproducible tends to give values which are very close to each other. 3 Not Accurate Not Accurate Accurate Not Precise Precise Precise 4 2  Types of Experimental Errors Experimental errors are not referring to what are commonly called mistakes, or miscalculations, as measuring a width when the length should have been measured, or misreading the scale on an instrument. Such errors are surely significant, but they can be eliminated by performing the experiment again correctly the next time. There are two types of experimental errors: systematic errors and random errors. 5 Systematic Errors Systematic errors are errors that affect the accuracy of a measurement. Systematic errors are one-sided errors, because repeated measurements yield results that differ from the true or accepted value by the same amount. The accuracy of measurements subject to systematic errors cannot be improved by repeating those measurements. Systematic errors cannot easily be analyzed by statistical analysis. Systematic errors can be difficult to detect, but once detected can be reduced only by refining the measurement method or technique. 6 3  Causes of systematic error 1. Faulty calibration of measuring instruments or poorly maintained instruments. 2. Faulty reading of instruments by the user. This systematic error is called ”parallax error” which results from the user reading an instrument at an angle resulting in a reading which is consistently high or consistently low. 3. “Zero error” in which an instrument gives a reading when the true reading at that time is zero. For example a needle of ammeter failing to return to zero when no current flows through it. To reduce the systematic error To reduce the systematic error of a data set, you must identify the source of the error and remove it either by recalibration of instrument or subtraction or addition of error value to the data. Unfortunately, the systematic error cannot be reduced by taking more measurements. 7 Random Errors Random errors are errors that affect the precision of a measurement. Random errors are two-sided errors, because repeated measurements yield results that fluctuate above and below the true value. Causes of random error 1-Unpredictable fluctuations in the readings of a measurement apparatus 2-The experimenter's interpretation of the instrumental reading To reduce the random error 1. Repeat the measurements several times and take the average 2. Random errors are easily analyzed by statistical analysis. 3. Random errors are reduced by refining the measurement method or technique. 8 4  Calculating Experimental Error When reporting the results of an experiment, the report must describe the accuracy and precision of the experimental measurements. Some common ways to describe accuracy and precision are described below. Significant Figures The precision of a measurement can be estimated by the number of significant digits with which the measurement is reported. The number of significant figures in a result is simply the number of figures that are known with some degree of reliability. The number 13.2 is said to have 3 significant figures. The number 13.20 is said to have 4 significant figures. 9 Rules for Significant Digits The rules for identifying significant digits: 1. All non-zero digits are considered significant. For example, 91 has two significant digits (9 and 1), while 123.45 has five significant digits (1, 2, 3, 4 and 5). 2. Zeros. There are three classes of zeros: Leading zeros are zeros that precede all the nonzero digits. These do not count as significant figures. In the number 0.0034, the three zeros simply indicate the position of the decimal point. This number has only two significant figures. 10 5  Rules for Significant Digits Captive zeros are zeros between nonzero digits. These count as significant figures. 1.007 has 4 significant figures. Trailing zeros are zeros at the right end of the decimal point. They are significant only if the number contains a decimal point. The number 100 has only one significant figure whereas the number 1.00 has three significant figures. Also 100. has three significant figures. 11 Multiplying and Dividing RULE: When multiplying or dividing, your answer may only show as many significant digits as the multiplied or divided measurement showing the least number of significant digits. Example: When multiplying 22.37 cm x 3.10 cm x 85.75 cm = 5946.50525 cm3 We look to the original problem and check the number of significant digits in each of the original measurements: 22.37 shows 4 significant digits. 3.10 shows 3 significant digits. 85.75 shows 4 significant digits. 12 6  Multiplying and Dividing Our answer can only show 3 significant digits because that is the least number of significant digits in the original problem. 5946.50525 shows 9 significant digits, we must round to the tens place in order to show only 3 significant digits. Our final answer becomes 5950 cm3. 13 Adding and Subtracting RULE: When adding or subtracting your answer can only show as many decimal places as the measurement having the fewest number of decimal places. Example: When we add 3.76 g + 14.83 g + 2.1 g = 20.69 g We look to the original problem to see the number of decimal places shown in each of the original measurements. 2.1 show the least number of decimal places. We must round our answer, 20.69, to one decimal place (the tenth place). Our final answer is 20.7 g. 14 7  Rules for rounding off numbers (1) If the digit to be dropped is greater than 5, the last retained digit is increased by one. For example, 12.6 is rounded to 13. (2) If the digit to be dropped is less than 5, the last remaining digit is left as it is. For example, 12.4 is rounded to 12. (3) If the digit to be dropped is 5, and if any digit following it is not zero, the last remaining digit is increased by one. For example, 12.51 is rounded to 13. 15 Rules for rounding off numbers (4) If the digit to be dropped is 5 and is followed only by zeroes, the last remaining digit is increased by one if it is odd, but left as it is if even. For example, 11.5 is rounded to 12, 12.5 is rounded to 12. This rule means that if the digit to be dropped is 5 followed only by zeroes, the result is always rounded to the even digit. The rationale for this rule is to avoid bias in rounding: half of the time we round up, half the time we round down. 16 8  Percent Error measures the accuracy of a measurement % Error = (measured value – True value) x 100 True value Example What is the percent error if the length of a wire is 4.25 cm and the correct value should be 4.08 cm % Error = 4.25 – 4.08 x 100 = 4.17 % 4.08 17 Mean and Standard Deviation Mean and standard deviation are used to express accuracy and precision of the data. Mean : It is the "average" of a set of data. It is the sum of all of the data points divided by the number of data points. Example: what is the mean of 6, 11, 7 Add the numbers: 6 + 11 + 7 = 24 Divide by how many numbers (they are 3 numbers) 24 / 3 = 8. So the mean = 8 18 9  Standard Deviation: It is a number used to tell how measurements are spread out from the average (mean). A low standard deviation means that most of the numbers are very close to the average. A high standard deviation means that the numbers are spread out. 19 To find the standard deviation: 1-Find the mean. 2- Subtract this mean from each data point 3-Square the differences and add them 4-Divide the sum by one less than the number of data points 5-Finally take the square root. Where S = standard deviation X = each value in the sample X = the mean of the values N = the number of values (the sample size) 20 10  Reporting the Results of an Experimental Measurement The result of an experimental measurement of a quantity x should be reported with two parts. First, the best estimate of the measurement is reported. The best estimate of a set of measurements is usually reported as the “mean” of the measurements. Second, the variation of the measurements is reported. The variation in the measurements is usually reported by the “standard deviation” of the measurements. The measured quantity is reported in the following form: x = X ± S.D. 21 Straight line graphs Straight line graphs are useful in that they show data variables and trends very clearly and can help to make predictions about the results of data not yet recorded. They can also be used to display several dependent variables against one independent variable. Equation of a Straight Line: Equations of straight line correlating A and B variables is in the form A = mB + c where m is the “slope” of the straight line and c is the “y-intercept” (where the graph crosses the y-axis). 22 11  1- What is the international system of units (SI units)? what are the SI derived units? International system of units: (SI Units) It has seven base quantities & base units from which all other quantities can be derived: Quantity Unit Symbol Length Meter m Mass Kilogram kg Time Second s Temperature Kelvin K Amount of substance mole mol Electric current ampere A Luminous intensity candela cd 23 II- Derived SI units :- Quantity Symb. Expression SI unit Area A Length2 m2 Volume V Length3 m3 Density D Mass/volume Kg/m3 Velocity v Distance / time m.s-1 Acceleration A Velocity/ time m.s-2 Force F Mass x kg.m.s-2(newton N) acceleration pressure P Force/area kg.m-1.s-2(pascal pa) Energy E Force x kg.m2.s-2(joule J) distance 24 12  2-What are the SI prefixes? III- SI Prefixes Multiple Prefix Symbol 106 mega m 103 kilo k 102 hecto h 101 deka da 10-1 deci d 10-2 centi c 10-3 milli m 10-6 micro µ 10-9 nano n 10-12 pico p 25 Thank you 26 13