Ordinary Certificate in Statistics source:http://www.rss.org.uk/uploadedfiles/userfiles/files/Syllabus%20for%202012.pdf Paraphrase Two parts.
Objective: sound grounding in the principles and practice of statistics Emphasis on
- practical data collection,
- data presentation and
- data interpretation.
1: Collection and Compilation of Data
The origin, use and interpretation of published or administrative data.
Elementary ideas of sampling methods. Definitions of population and sampling frame. Methods of selecting samples (including practical problems) and implications of sample size: simple random sampling, systematic sampling, cluster sampling, quota sampling, stratified random sampling and multi-stage sampling. No formulae are required.
Advantages and disadvantages of each method, including considerations of cost and accuracy.
Pilot surveys, censuses, sample surveys, personal interviews, self-completion questionnaires, postal and telephone enquiries. Serial surveys - longitudinal or cross-sectional. Problems arising in the collection of data, late returns, 'freak' values and their treatment.
Non-sampling errors. Identification and interpretation of bias error (e.g. from non-response, errors in defining the population, enumerator distortion, etc).
Design of simple questionnaires and forms for collection of data. Formulation, classification and coding of questions, including verification.
Making questionnaires suitable for data processing and analysis; use of missing value codes.
Should be able to produce their own simple questionnaire and data form.
Distinction between observational and experimental studies.
Use of rough checks for order of magnitude and leading digits in results.
Check that their answer 'looks about right'.
Approximation, limits of accuracy, rounding and accuracy of recording. Percentages, ratios, rates and linear interpolation. Distinction between discrete and continuous data.
Error in the result of a simple expression when the consistent parts are all rounded. Construction and uses of frequency tables for one or more variables and contingency tables. Tables for presenting collections of results together with summary tables of frequencies, relevant averages, standard deviations, etc.
Graphs and diagrams, their use in analysis and presentation. Construction, uses and limitations of scatter diagrams, time charts, stem and leaf diagrams, histograms, bar charts, pie charts, frequency and cumulative frequency curves and boxplots (box and whisker plots).
Sample measures of location and dispersion.
Arithmetic mean, median, mode, percentiles, range, inter-quartile range, variance, standard deviation, coefficient of variation; their uses and limitations as measures; their calculation from frequency tables and raw data; graphical methods of estimation.
Distinction between inter- and intra-subject variation. Formulae should be known, except that the definition of 'hinges' is not required. Candidates should be able to estimate percentiles from a cumulative frequency curve (ogive). Probability as a measure of uncertainty. Link between probability and relative frequency. Allocation of probabilities in 'equally likely' cases. Mutually exclusive events. Independent events. Addition and multiplication of probabilities with simple applications. Use of Venn diagrams and tree diagrams. The long-run concept of probability, e.g. from tossing a coin repeatedly, should be understood. Permutations and combinations are not required. Calculation of least squares regression line and its interpretation. Correlation as a measure of linear association between two variables. Productmoment correlation coefficient. Spearman's rank correlation coefficient. Derivation of the least squares estimates (by calculus) is not required.
Simple moving averages for detecting trends and for smoothing time series. Seasonal data. Candidates should know when it is appropriate to use additive or multiplicative models for seasonality, and how each is calculated.Knowledge of weighted forms of moving average. No calculation is required.
Simple and weighted averages of price relatives. Construction of aggregate (Paasche, Laspeyres and Fisher) averages. Simple chain-based indices. Limitation and use of index numbers e.g. in assessment of productivity and prices.
Knowledge of how and why index members are used in real life is assumed.
Interpretation. Translation of written statements into tabular forms; simple fallacies, typical misleading distortion in popular published graphs. Answers to questions about tables and charts. Candidates may be asked to explain what the data presentation tells the reader. Writing of clear and concise reports on numerical data in different contexts. Candidates may be tested on their spelling and grammar as well as their logic