OPEN COURSES
Statistical Methods in Practice
Day 1: Confidence Intervals, Significance Testing and the Normal Distribution
The need to specify the statistical population before sampling and the need to ensure samples are representative of the population. How to summarise statistics using means, standard deviations, histograms, blob diagrams and box plots. Obtaining a margin of error for a sample mean and drawing inferences about the population. Using significance testing to check theories and principles of a significance testing procedure which can be applied to any situation. Using the one sample t-test for the mean and the F-test for differences between two standard deviations.
Day 2: T-tests, Regression and Correlation
Looking at how data is distributed over a set of values and the circumstances under which a Normal distribution occurs. Predicting from a small set of data using the Normal distribution. Outliers and tolerance intervals. The use of the t-test to determine whether two means are significantly different or whether the difference could be due to chance. Designing and analysing a paired sample trial. The meaning and interpretation of the correlation coefficient. Fitting of lines using regression techniques. Checking the validity of the line using residuals. Predicting from a regression equation. Determining the validity of a regression equation.
Day 3: Qualitative Data and Trend Analysis
Analysing qualitative data and checking whether two percentages are significantly different. The pattern of qualitative data and obtaining a margin of error for sample percentage. Examining patterns in qualitative data and seeing whether they fit a Poisson or Binomial distribution. The use of these distributions. Carrying out Analysis of Variance to separate sources of error (eg, sampling and testing) and using this knowledge to determine sampling schemes or improving processes. Applying cusums to analyse trends and determine when a step change occurred and deciding on reasons for the change.
For details of the date, venue and fee of our next open course, please see our Course Dates page.
Note: At the end of each module in the course there is a discussion on the effectiveness of the designs outlined in the chapter, and the limitations of the conclusions drawn from the analysis.
Day 1: Some Simple but Effective Experimental Designs
A discussion on why bother to design an experiment. Comparing two processes or methods using a design based on testing two independent samples and a more effective design involving paired samples. Simple designs involving two input variables. The importance of interactions (synergistic effects) in design and analysis. Designs with three or four variables. Obtaining a measure of repeatability without replication.
Day 2: Fractional Designs and Multiple Regression Analysis
Obtaining a fractional design in which the number of variables is too large for a full design. How to choose the best fraction. The use of saturated designs, say investigating 12 variables in 16 trials. Regression analysis to relate a response to one independent variable. The importance of residuals in the analysis. Multiple regression relating a response to many variables. How to determine which independent variables are important.
Day 3: Response Surfaces and Computer-aided Experimental Designs
Designs to generate response surfaces including variables at more than two levels. Central composite designs involving more than two levels and the ability to split a trial into two runs. Computer aided designs to cope with non-standard conditions, for example, an odd number of trials, where some trials have already been completed, or where a constraint limits conditions in a standard design. A discussion on 23 ways of messing up an experiment.
OPTIONAL Day 4 - Designing & Analysing Qualitative Experiments using Analysis of Variance
Obtaining Analysis of Variance table and determining the significance of the variables from the table. Using one-way Analysis of Variance to determine significant differences between formulations, treatments, assessors, etc. Designing experiments in blocks to cope with nuisance variables, that is, variables which have a great effect on the result, eg, different assessors, but are not a variable of interest to the experiments. Two-way designs. Incomplete block designs used where it is impossible for all machines, assessors, etc, to test every treatment.
Day 1: SPC: Improving the Capability of a Process
Assessing process capability and test method capability. Improving process capability by improving test method. Establishing whether the process is stable. Determining step changes in performance and the reasons for them. Assessing the stability of a process using the Normal Distribution.
Day 2: SPC: Getting the most out of Control Charts
Assessing process variability so that correct limits can be used on control charts. Setting-up control charts for the mean and the range. Using control charts to control processes and obtain information to improve the process. An easy-to-use adaptive control chart. When and where not to use control charts. 23 ways to mess-up SPC.
Day 1: Significance Testing
Sampling: determining the margin of error and sample size. Determining whether two samples have significantly different means or standard deviations. The advantages of using a paired sample design. Deciding whether tests are valid in relation to the assumption of Normal distribution. Robust significant tests which do not depend upon the assumption of a Normal distribution. Sample size required to design an effective trial.
Day 2: Multiple Regression and Trend Analysis
Assessing curvature. Assessing the effect on a response of several input variables. Modelling the process using stepwise multiple regression to determine the important input variables. Assessing curvature and synergistic effects between input variables. Use diagnostic statistics such as residuals to validate the model. Using response surfaces to locate optimal conditions. Trend analysis using cusums.
Day 3: Multivariate Analysis
Analysing and displaying sensory profiles or chemical spectra using principal component analysis. Describing the underlying dimensions using factor analysis. Determining the discrimination between two or more sets of data using discriminant analysis. Relating a multidimensional profile to a multivariate set of analytical or physical data using PLS regression.
Day 1: Significance Testing
Sampling: determining the margin of error and sample size. Determining whether two samples have significantly different means or standard deviations. The advantages of using a paired sample design. Deciding whether tests are valid in relation to the assumption of Normal distribution. Robust significant tests which do not depend upon the assumption of a Normal distribution. Sample size required to design an effective trial.
Day 2: Analysis of Sensory Panel Data
Choosing the right type of sensory scale for an experiment. Determining differences and preferences using single sensory tests. Comparing several products using scales. Analysing panel data taking into account differences between panellists. Analysis of multi-factor experiments. Relating two methods of evaluation. Monitoring panel performance.
Day 3: Multivariate Analysis
Analysing and displaying sensory profiles or chemical spectra using principal component analysis. Describing the underlying dimensions using factor analysis. Determining the discrimination between two or more sets of data using discriminant analysis. Relating a multidimensional profile to a multivariate set of analytical or physical data using PLS regression.
Day 1: Estimating and Reducing the Sources of Error of Test Methods
Improving an analytical method in terms of precision and bias. Improving the estimate of precision. Determining the magnitude of bias using a margin of error. Testing for outliers using the Normal distribution. Determining whether there is a significant difference between a measured bacterial density and a reference value. Improving a method by determining the magnitude of several sources of error, eg, operator, instruments.
Day 2: Analytical Method Validation, Method Transfer and Calibration
How to determine a relevant specification for method validation based on need and expected performance. Designing a method transfer study. The application of statistics to validate a method in terms of specification, precision, bias, outliers, calibration, selectivity, specificity and limit of detection. Designs to determine uncertainty. Determining the margin of error for an unknown sample from a calibration curve. The precision of the calibration factor. Deciding whether a calibration is linear and, if not, determining the limit of linearity. Calibration when the absolute error increases with concentration.
Day 3: Control Charts, Capability and Spectral Analysis
Spectral Analysis – the use of Multiple Regression and Principal Component Analysis in obtaining multiple calibrations. Determining test method capability. Setting-up control charts for the mean (bias) and the standard deviation (precision). Evaluating how to use a control chart to improve the quality of analytical results as well as improving precision and reducing bias. Improving capability using trend analysis (cumulative sum techniques).
Day 1: Estimating and Reducing the Sources of Error of Test Methods
Improving a microbiological method in terms of precision and bias. Obtaining better estimates of precision. Determining the magnitude of bias using a margin of error. Testing for outliers using the Normal distribution. Finding whether there is a significant difference between a measured bacterial density and a reference value. Improving a method by determining the magnitude of several sources of error, eg, operator, instruments.
Day 2: Analysis of Microbiological Data & Validation using ISO 16140Comparing an automatic method with a traditional method for colony counts. Determining the accuracy of a measurement with a calibration curve. Estimating bacterial density from a number of dilutions. Using MPN to determine bacterial density. Understanding the distribution of microorganisms in solids and liquids. Using a significance test to determine whether two methods are giving different means or standard deviations. Improving capability by looking for trends using cusum analysis. Determining test method capability.
Day 3: Control Charts and Capability of Test MethodsSetting-up control charts for the mean (bias) and the standard deviation (precision). Evaluating how to use a control chart to improve the quality of microbiological results as well as improving precision and reducing bias. Limit of detection. Understanding ISO 16140 by using the knowledge gained in the course. How to apply it successfully.
Day 1: Introductory Statistics and Inspection Schemes
The need to specify the statistical population before sampling and the need to ensure samples are representative of the population. How to summarise statistics using means, standard deviations, histograms, blob diagrams and box plots. Obtaining a margin of error for a sample mean and drawing inferences about the population. The pattern of qualitative data and do they fit binomial and Poisson distributions? The use of binomial distribution in acceptance sampling schemes. Determining the Operating Characteristic (OC) Curve for sampling scheme procedures and consumers' risks. Designing sampling schemes to obtain a scheme which meets the requirements for producers' and consumers' risks. Double sampling schemes.
Day 2: International and British Standards for Inspection Schemes
How to use ISO 2859 and BS6001 for inspection sampling by attribute. The measuring of Acceptable Quality Level (AQL). Switching rules. Choosing the batch size. Obtaining OC curves. A critique of the Standard. Looking how data is distributed over a set of values and the circumstances under which a Normal distribution occurs. Predicting from a small set of data using the Normal distribution. Acceptance sampling by variable. Obtaining OC curves. Using ISO 3951: BS6002 for sampling inspection by variable. The huge gains by using variable instead of attribute sampling. Trend analysis to assess performance using cumulative sum techniques.