QUALITATIVE AND QUANTITATIVE ASPECTS OF ANALYSIS
Description: QUALITATIVE AND QUANTITATIVE ASPECTS OF ANALYSIS Qualitative Analysis: It is the process of identification of components of material sample and impurities present. Quantitative Analysis: It is the process of determining the quantity of
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slide1. QUALITATIVE AND QUANTITATIVE ASPECTS OF ANALYSIS Qualitative Analysis: It is the process of identification of components of material sample and impurities present. Quantitative Analysis: It is the process of determining the quantity of components present in the sample material Analytical chemistry deals with the theory and practice of methods used to determine the composition of matter<br>
slide2. QUALITATIVE AND QUANTITATIVE ASPECTS OF ANALYSIS The analytical method involves using reason in a formal way to resolve problems. An analytical technique takes a problem, breaks it down into its constituent elements so that the problem may be understood, and then adds pieces that represent a solution. An analytical approach is required when dealing with complicated circumstances because they become too complex to resolve naturally. Every element must be formally recorded in writing,<br>
slide3. ERROR: A mistake is an action that you took that is considered incorrect, erroneous, or inappropriate. The word "error," which refers to a deviation from truth, accuracy, correctness, right, etc., is the most general in this comparison.<br>
slide4. Absolute Error: Relative Error:<br>
slide5. ACCURACY: Accuracy is generally the more significant characteristic of any quantitative analytical data that indicates the close proximity of the measurement to the true or expected value.
Higher accuracy of any measurement is associated with minimization of error.
Accuracy is a measure of how closely the result of an experiment agrees with the expected result.<br>
slide6. PRECISION: A substance's accuracy can be defined as the degree of agreement between two or more measurements.
Precision and accuracy have no connection. You can be exact without being accurate.<br>
slide7. EXPRESSION OF RELIABILITY OF DATA There are a few terms or terminologies with the analytical measurements to improve the reliability of the course of action. Replicate: It refer to the sample of about the same size, which are investigated through an analytical procedure in exactly identical manner.
For a set of replicate measurements, the mean or the median is used as a central value. MEAN:<br>
slide8. MEDIAN:
The middle result obtained when replicate data are arranged in ascending or descending order.
When the data set include an odd number of replicate measurements, the median is the middle value whereas for an even number of measurements, the median is the average of the N/2 and the (N/2)+1 measurements. Q. Calculate the mean and median values for the following set of measurements:
87.2, 87.8, 86.7, 88.1 and 87.3 Answer:
Mean= 87.4, Median= 87.3<br>
slide9. MEASURES OF SPREAD:
It deals with the variability of results connected with a particular analytical measurements. The three common measures of spread are Range, Standard Deviation and Variance. RANGE: STANDARD DEVIATION: The absolute standard deviation, s, describes the spread of individual measurements about the mean and is given as,<br>
slide10. RELATIVE STANDARD DEVIATION (RSD): RSD can be expressed in parts per thousand or in percent by multiplying this ratio by 1000 or by 100. The RSD when express in percent, then it is called the coefficient of variation (CV). Standard deviation are reported in relative terms rather than their absolute values. So, the RSD can be calculated by dividing the absolute value of Standard deviation by the mean value of the data set.<br>
slide11. VARIANCE: Average deviation from the Mean: The average deviation is expressed relative to the magnitude of the measured quantity, which is then termed as relative average deviation from the mean.<br>
slide12. Q. Calculate
i) Range(w) ii) Standard Deviation(s)
iii) Relative standard deviation(RSD) in ppt
iv) Variance v) Average deviation from the mean
using the given data: Answers:
Range = 1.74
Mean = 53.19
Standard Deviation = 0.7063
RSD in ppt= 13.28ppt
Variance= 0.4989
Average deviation from the mean = 0.595<br>
slide13. ERRORS IN ANALYTICAL MEASUREMENTS There are two types of error that mainly affects the accuracy of the results.
Systematic or determinate error
Random or indeterminate error Systematic or determinate error:
The error is reproducible and can be discovered and corrected. Random or indeterminate error:
Caused by uncontrollable variables, which can not be defined/eliminated.<br>
slide14. Instrument errors - failure to calibrate, degradation of parts in the instrument, power fluctuations, variation in temperature, etc.
Can be corrected by calibration or proper instrumentation maintenance.
2. Method errors - errors due to no ideal physical or chemical behavior –
completeness and speed of reaction, interfering side reactions, sampling problems
Can be corrected with proper method development.
3. Personal errors - occur where measurements require judgment, result from
prejudice, color acuity problems.
Can be minimized or eliminated with proper training and experience. Sources of Systematic or determinate error:<br>
slide15. Detection of Systematic Errors:
Instrumental errors can be detected and rectified by periodic calibration of the equipment.
Personal errors can be minimized by following strict discipline while carrying out the laboratory procedure.
Systematic Method errors are quite difficult to detect. The following steps are usually taken to identify and adjust this type of error:
Analysis of standard samples: Method error can be detected by carrying out the analysis of standard samples of Standard Reference Material (SRM).
Independent Analysis: If SRM are not available then method errors can possibly be detected by carrying out a parallel investigation of the sample along with the main evaluation technique with a different established and reliable procedure.
Blank determination: Method errors can be well resolved by analysing blank samples which refer to the sample with all the reagents and solvents used in the evaluating procedure except the analyte<br>
slide16. Random (indeterminate) Error
It is not identifiable. Always present and cannot be eliminated.
Ex. reading a scale on an instrument caused by the finite thickness of the lines on the scale; electrical noise NORMAL LAW OF DISTRIBUTION OF INDETERMINATE ERRORS: It states that if a large enough number replicate measurements are taken for a given analysis of the same sample under the same conditions, then the probability of occurrence of indeterminate errors follow a normal distribution. The accumulated effect causes replicate measurements to fluctuate randomly around the mean; Give rise to a normal or Gaussian curve.<br>
slide17. Statistical Analysis Data Treatment The picture here is the Norman Rockwell Saturday Evening Post cover ,The Holdout from February 14, 1959. One of the 12 jurors does not agree with the others, who are trying to convince her. In the jury room, we can make two types of errors.
An innocent person can be convicted, or
a guilty person can be set free. It is a more serious error to convict an innocent person than to acquit a guilty person.<br>
slide18. Similarly, in statistical tests to determine whether two quantities are the same, two types of errors are possible:
A type I error occurs when we reject the hypothesis that two quantities are the same, when they are statistically identical.
A type II error occurs when we accept that they are the same when they are not statistically identical. The characteristics of these errors in statistical testing and the ways we can minimize them are among the subjects of this chapter<br>
slide19. The most common applications of statistical data treatment : Defining a numerical interval, the confidence interval, around the mean of a set of replicate results within which the population mean can be expected to lie with a certain probability. This interval is related to the standard deviation of the mean.
Determining the number of replicate measurements required to ensure that an experimental mean falls within a certain range with a given level of probability.
Estimating the probability that a) an experimental mean and a true value or b)two experimental means are different. This test is particularly important for discovering systematic errors in a method and determining whether two samples come from the same source.
Determining at a given probability level whether the precision of two sets of measurements differs.
Comparing the means of more than two samples to determine whether differences in the means are real or the result of random error. This process is known as analysis of variance.
Deciding whether to reject or retain a result that appears to be an outlier in a set of replicate measurements.<br>
slide20. There are several ways to indicate the authentication or reliability of analytical data. Reliability of an experiment data can be indicated by giving a confidence interval at the 90% or 95% confidence level.
By reporting the absolute standard deviation or the coefficient of variation of the data. If one of these is reported, then the users will get some idea about the reliability of the standard deviation (s) as it reflects the number of data points that were used to obtain the standard deviation(s)
Another commonly used indicator of the quality of data, although not quite satisfactory to some extent, is significant figure convention.<br>
slide21. CONFIDENCE LIMITS AND CONFIDENCE INTERVALS Accuracy of the best estimate of the sample mean which is more likely to be in agreement with the population mean can be expressed in terms of confidence limits i.e. by setting limits at upper and lower end of a confidence interval.
A confidence interval actually reflects the probability that a population of will fall between the two set values.<br>
slide23. Q. A Group of 10 numbers of foot surgery patients had a mean weight of 240 pounds. The Sample standard deviation was pounds. The sample standard deviation was 25 pounds. Find the confidence interval for a sample, for a true mean weight of all foot surgery patients at 95% confidence level. Q. Construct a 99% Confidence Interval based on the following data:
45, 55, 67, 45, 68, 79, 98, 87, 84, 82. Q. If you increase the confidence level, the confidence interval
A) Decreases B) Increases
C) Stays the same D) May increases or decrease Q. Which of the following factors do not affect the width of the confidence interval?
A) Sample mean B) Population variance
C) Sample size D) Confidence Level<br>
slide24. STATISTICAL TEST OF DATA i) Q- test (Rejection of Outliers) Outliers are the results that appear in the data set whose values distinctly differ from all other data in a set of replicate measurements. So, keeping that value in the data set may affect calculations such as mean, standard deviation etc. Thus, rejection of outliers is very much essential in order to improve accuracy of the analytical result.<br>
slide25. Q. Test the presence of an outlier at 95% confidence level in the following data set.
32.07, 71.27, 49.21, 51.07, 48.95, 62.49, 87.49, 55.68<br>
slide26. ii) Test of Significance: a) F-test: F-test is employed to test the significance of the data obtained by following a new analytical procedure as compared to those obtained with the help of already adopted procedures.<br>
slide27. b) t-test This is used to determine whether there is a significant difference between the means of two groups of related samples. Q. The manufacturer of a certain LED claims that his bulb have a mean life of 20 months. A random sample of 7 such bulb gave the following values
Life of bulbs in months: 19, 21, 25, 16, 17, 14, 21
Apply the t-test to verify the producer’s claim to be valid at 1% significance (i.e. 99% confidence level)<br>
slide2. QUALITATIVE AND QUANTITATIVE ASPECTS OF ANALYSIS The analytical method involves using reason in a formal way to resolve problems. An analytical technique takes a problem, breaks it down into its constituent elements so that the problem may be understood, and then adds pieces that represent a solution. An analytical approach is required when dealing with complicated circumstances because they become too complex to resolve naturally. Every element must be formally recorded in writing,<br>
slide3. ERROR: A mistake is an action that you took that is considered incorrect, erroneous, or inappropriate. The word "error," which refers to a deviation from truth, accuracy, correctness, right, etc., is the most general in this comparison.<br>
slide4. Absolute Error: Relative Error:<br>
slide5. ACCURACY: Accuracy is generally the more significant characteristic of any quantitative analytical data that indicates the close proximity of the measurement to the true or expected value.
Higher accuracy of any measurement is associated with minimization of error.
Accuracy is a measure of how closely the result of an experiment agrees with the expected result.<br>
slide6. PRECISION: A substance's accuracy can be defined as the degree of agreement between two or more measurements.
Precision and accuracy have no connection. You can be exact without being accurate.<br>
slide7. EXPRESSION OF RELIABILITY OF DATA There are a few terms or terminologies with the analytical measurements to improve the reliability of the course of action. Replicate: It refer to the sample of about the same size, which are investigated through an analytical procedure in exactly identical manner.
For a set of replicate measurements, the mean or the median is used as a central value. MEAN:<br>
slide8. MEDIAN:
The middle result obtained when replicate data are arranged in ascending or descending order.
When the data set include an odd number of replicate measurements, the median is the middle value whereas for an even number of measurements, the median is the average of the N/2 and the (N/2)+1 measurements. Q. Calculate the mean and median values for the following set of measurements:
87.2, 87.8, 86.7, 88.1 and 87.3 Answer:
Mean= 87.4, Median= 87.3<br>
slide9. MEASURES OF SPREAD:
It deals with the variability of results connected with a particular analytical measurements. The three common measures of spread are Range, Standard Deviation and Variance. RANGE: STANDARD DEVIATION: The absolute standard deviation, s, describes the spread of individual measurements about the mean and is given as,<br>
slide10. RELATIVE STANDARD DEVIATION (RSD): RSD can be expressed in parts per thousand or in percent by multiplying this ratio by 1000 or by 100. The RSD when express in percent, then it is called the coefficient of variation (CV). Standard deviation are reported in relative terms rather than their absolute values. So, the RSD can be calculated by dividing the absolute value of Standard deviation by the mean value of the data set.<br>
slide11. VARIANCE: Average deviation from the Mean: The average deviation is expressed relative to the magnitude of the measured quantity, which is then termed as relative average deviation from the mean.<br>
slide12. Q. Calculate
i) Range(w) ii) Standard Deviation(s)
iii) Relative standard deviation(RSD) in ppt
iv) Variance v) Average deviation from the mean
using the given data: Answers:
Range = 1.74
Mean = 53.19
Standard Deviation = 0.7063
RSD in ppt= 13.28ppt
Variance= 0.4989
Average deviation from the mean = 0.595<br>
slide13. ERRORS IN ANALYTICAL MEASUREMENTS There are two types of error that mainly affects the accuracy of the results.
Systematic or determinate error
Random or indeterminate error Systematic or determinate error:
The error is reproducible and can be discovered and corrected. Random or indeterminate error:
Caused by uncontrollable variables, which can not be defined/eliminated.<br>
slide14. Instrument errors - failure to calibrate, degradation of parts in the instrument, power fluctuations, variation in temperature, etc.
Can be corrected by calibration or proper instrumentation maintenance.
2. Method errors - errors due to no ideal physical or chemical behavior –
completeness and speed of reaction, interfering side reactions, sampling problems
Can be corrected with proper method development.
3. Personal errors - occur where measurements require judgment, result from
prejudice, color acuity problems.
Can be minimized or eliminated with proper training and experience. Sources of Systematic or determinate error:<br>
slide15. Detection of Systematic Errors:
Instrumental errors can be detected and rectified by periodic calibration of the equipment.
Personal errors can be minimized by following strict discipline while carrying out the laboratory procedure.
Systematic Method errors are quite difficult to detect. The following steps are usually taken to identify and adjust this type of error:
Analysis of standard samples: Method error can be detected by carrying out the analysis of standard samples of Standard Reference Material (SRM).
Independent Analysis: If SRM are not available then method errors can possibly be detected by carrying out a parallel investigation of the sample along with the main evaluation technique with a different established and reliable procedure.
Blank determination: Method errors can be well resolved by analysing blank samples which refer to the sample with all the reagents and solvents used in the evaluating procedure except the analyte<br>
slide16. Random (indeterminate) Error
It is not identifiable. Always present and cannot be eliminated.
Ex. reading a scale on an instrument caused by the finite thickness of the lines on the scale; electrical noise NORMAL LAW OF DISTRIBUTION OF INDETERMINATE ERRORS: It states that if a large enough number replicate measurements are taken for a given analysis of the same sample under the same conditions, then the probability of occurrence of indeterminate errors follow a normal distribution. The accumulated effect causes replicate measurements to fluctuate randomly around the mean; Give rise to a normal or Gaussian curve.<br>
slide17. Statistical Analysis Data Treatment The picture here is the Norman Rockwell Saturday Evening Post cover ,The Holdout from February 14, 1959. One of the 12 jurors does not agree with the others, who are trying to convince her. In the jury room, we can make two types of errors.
An innocent person can be convicted, or
a guilty person can be set free. It is a more serious error to convict an innocent person than to acquit a guilty person.<br>
slide18. Similarly, in statistical tests to determine whether two quantities are the same, two types of errors are possible:
A type I error occurs when we reject the hypothesis that two quantities are the same, when they are statistically identical.
A type II error occurs when we accept that they are the same when they are not statistically identical. The characteristics of these errors in statistical testing and the ways we can minimize them are among the subjects of this chapter<br>
slide19. The most common applications of statistical data treatment : Defining a numerical interval, the confidence interval, around the mean of a set of replicate results within which the population mean can be expected to lie with a certain probability. This interval is related to the standard deviation of the mean.
Determining the number of replicate measurements required to ensure that an experimental mean falls within a certain range with a given level of probability.
Estimating the probability that a) an experimental mean and a true value or b)two experimental means are different. This test is particularly important for discovering systematic errors in a method and determining whether two samples come from the same source.
Determining at a given probability level whether the precision of two sets of measurements differs.
Comparing the means of more than two samples to determine whether differences in the means are real or the result of random error. This process is known as analysis of variance.
Deciding whether to reject or retain a result that appears to be an outlier in a set of replicate measurements.<br>
slide20. There are several ways to indicate the authentication or reliability of analytical data. Reliability of an experiment data can be indicated by giving a confidence interval at the 90% or 95% confidence level.
By reporting the absolute standard deviation or the coefficient of variation of the data. If one of these is reported, then the users will get some idea about the reliability of the standard deviation (s) as it reflects the number of data points that were used to obtain the standard deviation(s)
Another commonly used indicator of the quality of data, although not quite satisfactory to some extent, is significant figure convention.<br>
slide21. CONFIDENCE LIMITS AND CONFIDENCE INTERVALS Accuracy of the best estimate of the sample mean which is more likely to be in agreement with the population mean can be expressed in terms of confidence limits i.e. by setting limits at upper and lower end of a confidence interval.
A confidence interval actually reflects the probability that a population of will fall between the two set values.<br>
slide23. Q. A Group of 10 numbers of foot surgery patients had a mean weight of 240 pounds. The Sample standard deviation was pounds. The sample standard deviation was 25 pounds. Find the confidence interval for a sample, for a true mean weight of all foot surgery patients at 95% confidence level. Q. Construct a 99% Confidence Interval based on the following data:
45, 55, 67, 45, 68, 79, 98, 87, 84, 82. Q. If you increase the confidence level, the confidence interval
A) Decreases B) Increases
C) Stays the same D) May increases or decrease Q. Which of the following factors do not affect the width of the confidence interval?
A) Sample mean B) Population variance
C) Sample size D) Confidence Level<br>
slide24. STATISTICAL TEST OF DATA i) Q- test (Rejection of Outliers) Outliers are the results that appear in the data set whose values distinctly differ from all other data in a set of replicate measurements. So, keeping that value in the data set may affect calculations such as mean, standard deviation etc. Thus, rejection of outliers is very much essential in order to improve accuracy of the analytical result.<br>
slide25. Q. Test the presence of an outlier at 95% confidence level in the following data set.
32.07, 71.27, 49.21, 51.07, 48.95, 62.49, 87.49, 55.68<br>
slide26. ii) Test of Significance: a) F-test: F-test is employed to test the significance of the data obtained by following a new analytical procedure as compared to those obtained with the help of already adopted procedures.<br>
slide27. b) t-test This is used to determine whether there is a significant difference between the means of two groups of related samples. Q. The manufacturer of a certain LED claims that his bulb have a mean life of 20 months. A random sample of 7 such bulb gave the following values
Life of bulbs in months: 19, 21, 25, 16, 17, 14, 21
Apply the t-test to verify the producer’s claim to be valid at 1% significance (i.e. 99% confidence level)<br>