-SQA- SCOTTISH QUALIFICATIONS AUTHORITY HIGHER NATIONAL UNIT SPECIFICATION GENERAL INFORMATION -Number- 7481554 -Superclass- -Title- RB DESCRIPTIVE STATISTICS FOR SCIENCE ---------------------------------------- -DESCRIPTION- GENERAL COMPETENCE FOR UNIT: Using a practical approach to apply the concepts of data collection, display and analysis with special emphasis on small data sets for the biological and chemical sciences. OUTCOMES 1 select suitable methods of data collection; 2 use descriptive statistics; 3 investigate bivariate data; 4 use statistical software to investigate data. CREDIT VALUE: 1 HN Credit ACCESS STATEMENT: Access is at the discretion of the centre. However, it would be beneficial if the candidate had skills in mathematics as evidenced by possession of National Certificate Module 7180331 Core Mathematics 4, or SCE Standard Grade Mathematics at 1/2, or an equivalent level of experience. ---------------------------------------- For further information contact: Committee and Administration Unit, SQA, Hanover House, 24 Douglas Street, Glasgow G2 7NQ. Additional copies of this unit may be purchased from SQA (Sales and Despatch section). At the time of publication, the cost is 1.50 (minimum order 5).
UNIT NUMBER: 7481554 HIGHER NATIONAL UNIT SPECIFICATION STATEMENT OF STANDARDS UNIT TITLE: DESCRIPTIVE STATISTICS FOR SCIENCE Acceptable performance in this unit will be the satisfactory achievement of the standards set out in this part of the specification. All sections of the statement of standards are mandatory and cannot be altered without reference to SQA. OUTCOME 1 SELECT SUITABLE METHODS OF DATA COLLECTION PERFORMANCE CRITERIA The choice of data collection method is appropriate to the context. The selection of a sample using random number tables is correct. RANGE STATEMENT The range for this outcome is fully expressed within the performance criteria. EVIDENCE REQUIREMENTS Evidence of candidate's ability to select suitable methods of data collection on at least 3 occasions and use random number tables on at least 2 occasions. OUTCOME 2 USE DESCRIPTIVE STATISTICS PERFORMANCE CRITERIA The construction of diagrams is appropriate to the context. The calculation of measures of central tendency and spread appropriate to the context is correct. RANGE STATEMENT The range for this outcome is fully expressed within the performance criteria. 2
EVIDENCE REQUIREMENTS Minimum of two different types of diagram. PC. Minimum of two different pairs of measures of central tendency and spread, which must include mean and standard deviation. PC. OUTCOME 3 INVESTIGATE BIVARIATE DATA PERFORMANCE CRITERIA The plotting and interpretation of scatter diagrams are correct. The calculation and interpretation of regression line and correlation coefficient are correct. RANGE STATEMENT The range for this outcome is fully expressed within the performance criteria. EVIDENCE REQUIREMENTS At lease one piece of written evidence that the candidate can fulfil PCs and. The calculations for PC should be carried out using the linear regression facility of a suitable calculator. OUTCOME 4 USE STATISTICAL SOFTWARE TO INVESTIGATE DATA PERFORMANCE CRITERIA The interpretation of the output from a statistical package to investigate univariate data is correct. The interpretation of the output from a statistical package to investigate bivariate data is correct. RANGE STATEMENT The range for this outcome is fully expressed within the performance criteria. 3
EVIDENCE REQUIREMENTS Output and/or written evidence derived from a statistical package for each performance criterion. MERIT A candidate who achieves all performance criteria for all outcomes will be awarded a pass. A pass with merit may be awarded to a candidate who demonstrates superior performance throughout the unit in each of the following aspects: consistently high level of accuracy outstanding skills of analysis consistently logical presentation of work Evidence which satisfies the criteria for merit may be generated by either: solving the problem to a level beyond that defined as pass or where this is not possible, including in the assessment a further section which would allow the candidate to demonstrate skills which satisfy the criteria for merit. ASSESSMENT ---------------------------------------- In order to achieve this unit, candidates are required to present sufficient evidence that they have met all the performance criteria for each outcome within the range specified. Details of these requirements are given for each outcome. The assessment instruments used should follow the general guidance offered by the SQA assessment model and an integrative approach to assessment is encouraged. (See references at the end of support notes.) Accurate records should be made of the assessment instruments used showing how evidence is generated for each outcome and giving marking schemes and/or checklists, etc. Records of candidates' achievements should also be kept. The records will be required for external verification. SPECIAL NEEDS Proposals to modify outcomes, range statements or agreed assessment arrangements should be discussed in the first place with the external verifier. Copyright SQA 1994 Please note that this publication may be reproduced in whole or in part for educational purposes provided that: (i) (ii) no profit is derived from the reproduction; if reproduced in part, the source is acknowledged. 4
UNIT NUMBER: 7481554 HIGHER NATIONAL UNIT SPECIFICATION SUPPORT NOTES UNIT TITLE: DESCRIPTIVE STATISTICS FOR SCIENCE SUPPORT NOTES: This part of the unit specification is offered as guidance. None of the sections of the support notes is mandatory. NOTIONAL DESIGN LENGTH: SQA allocates a notional design length to a unit on the basis of the time estimated for achievement of the stated standards by a candidate whose starting point is as described in the access statement. The notional design length for this unit is 40 hours. The use of notional design length for programme design and timetabling is advisory only. PURPOSE: This unit enables candidates to use statistics in a range of practical contexts within their chosen science discipline. The emphasis of the unit is on the application of statistics in a vocational context and it can be used by candidates who are not accustomed to a rigorous mathematical approach. CONTENT/CONTEXT: All assessments should conform to the relevant standards laid down by the British Standards Institute. Currently these include: BS 2846 BSISO 3534-1: Guide to statistical interpretation of data Part 1 Routine analysis of data 1993 Statistical terminology Part 1 Glossary of terms relating to probability and general terms relating to statistics There are many further British Standards which give sampling schemes to different substances. The term `statistical package' used in Outcome 4 is intended to include all of the following: (i) (ii) (iii) (iv) dedicated statistical packages available for computers; statistical functions incorporated in spreadsheet packages for computers; statistical functions incorporated in computer algebras for computers; statistical functions incorporated in graphic calculators. It is not intended that any programming should be carried out nor should the computer or graphic calculator be used merely to evaluate formulae. 5
Corresponding to outcomes: 1 Need for sampling. Population samples. Sampling frames. Sampling methods: census; simple random sampling; systematic sampling; multistage sampling; cluster sampling; stratified random sampling; quota sampling; convenience sampling. 2 Types of data: qualitative, ordinal, quantitative discrete, quantitative continuous. Tabulation of data: contingency tables, frequency distributions, relative frequency distributions; cumulative frequency tables. Display of data: dot plots, stem and leaf diagrams, bar charts, line graphs, histograms, frequency polygons, ogives and box plots. Symmetrical, skew and other distributions. Calculations: mean, mode and median from raw data and from frequency distributions; range, quartiles, inter-quartile range, variance and standard deviation; choice of statistics. 3 Dependent and explanatory variables, plotting scatter diagrams. Calculating regression lines and correlation coefficients using the regression facility on a suitable calculator/computer. Plotting the calculated regression line on the scatter diagram. Interpretation: gradient, intercept, interpolation, extrapolation, appropriateness of fitted linear relationship; limitations of regression and correlation. 4 As for Outcomes 2 and 3. APPROACHES TO GENERATING EVIDENCE It is recommended that candidates be given real-life examples to illustrate the statistical concepts and techniques used in this unit. These examples could be linked to the biological or chemical sciences subjects being studied. The design of the unit is such that it requires both the use of a calculator with statistical and linear regression facilities and the use of appropriate software packages. Large data sets should be set up in advance. It is recommended that the consolidation of skills be achieved by including problem-solving in a practical and vocational context and not only by mechanical exercises. Group investigations are to be encouraged. 6
Candidates are advised to maintain a workfile. This could comprise the candidate's own notes, class handouts, worksheets, exercises, a logbook of computer activities and other relevant material. It is important that non-statistical terms are used to explain the significance of results. ASSESSMENT PROCEDURES: Centres may use the instruments of assessment which are considered by tutors/trainers to be most appropriate. Examples of instruments of assessment which could be used are illustrated by the exemplars. 7
EXEMPLARS Outcome 1 1 Match the correct sampling method from the given list to the following situations: An experiment is conducted in which each of 10 different antiscalants is added to an aliquot of brine. One of the 10 brine solutions is to be selected, filtered and the amount of silica determined. How would you select the brine sample so that the choice is random? It has been decided that in addition to the nationwide Census of Population, a nationwide sample survey is to be carried out, with questions additional to the census ones. How would you go about selecting the households for this? (c) Suppose you want to sample 10 syringe needles from a shipment of 10,000. How would you set about sampling the syringe needles? (d) (e) You wish to find out how Inverness veterinary practices use antibiotics to treat farm animals. You have been asked by a company which manufactures water filters how their product is viewed by consumers. The manufacturer wishes his results quickly, and he has a limited budget. Sampling Methods (i) (ii) (iii) (iv) (v) (vi) (vii) (viii) census simple random systematic multistage cluster stratified random quota convenience sampling 2 Select a simple random sample of 3 students from the members of your class. Use random number tables and ask your lecturer for a starting point in the tables. Use the sampling frame given to you to select a sample of 20. Ask your lecturer for a starting point in the random number tables. 8
Outcome 2 1 SCRAM is the term used by nuclear engineers to describe a rapid emergency shut down of a nuclear reactor. The nuclear industry has made a concerted effort to reduce significantly the number of unplanned scrams. The table gives the number of scrams at each of 56 US nuclear reactor units in a recent year. Summarise the data with a graphical descriptive technique. (Source: Statistics for Engineering and the Sciences, Third Edition, by Mendenhall and Sincich, published by Maxwell MacMillan). 4 5 5 2 4 2 3 1 1 2 3 4 7 2 2 2 3 4 2 2 4 5 4 6 1 2 3 5 3 6 1 4 5 6 2 5 5 3 1 7 2 4 6 4 2 2 3 2 3 4 6 5 5 6 3 2 2 Calculate an appropriate measure of central tendency for the data in Question 1. 3 Calculate an appropriate measure of spread for the data in Question 1. 4 In the following table, the weights of 40 male students at Anycity University are recorded to the nearest pound. Summarise the data with a graphical descriptive technique (but not the same one as used for Question 1). 139 165 151 133 145 126 150 158 145 157 139 146 135 147 151 143 169 127 139 177 164 120 155 166 145 172 141 146 134 152 139 134 162 146 136 143 151 157 146 129 5 Calculate an appropriate measure of central tendency for the data in Question 4. 6 Calculate an appropriate measure of spread for the data in Question 4. 9
Outcome 3 The weights and bill lengths of 10 Dunlin are recorded below: Weight (gm) Bill Length (mm) 51 33.5 59 38.0 49 32.0 54 37.5 50 31.7 55 33.0 48 31.0 53 36.5 52 34.0 57 35.0 1 Plot a scatter diagram of bill length against weight. 2 From your scatter diagram, does there appear to be a relationship between bill length and weight? If so, what kind of relationship is there? 3 Calculate Pearson's Product Moment Correlation Coefficient for weight and bill length of the 10 Dunlin. 4 Calculate the Least Squares regression line for the above data and estimate the bill length of a bird weighing 56 gm. Outcome 4 The following questions should be answered using a graphics calculator with statistical and linear regression modes, or a suitable computing package. 1 In the table below are the wing length measurements (to the nearest whole mm) of 100 birds. 77 74 76 74 75 75 75 75 75 78 75 73 76 77 74 72 74 72 74 81 76 76 69 73 79 75 76 75 70 78 78 73 73 77 77 78 71 78 73 75 78 77 79 73 71 75 77 73 74 72 75 75 76 80 76 75 76 75 72 74 76 74 76 71 74 76 71 73 73 72 77 74 75 77 75 76 75 77 76 76 74 74 79 75 74 76 75 74 73 77 74 77 75 72 73 72 80 79 70 78 10
NB Select a suitable method of displaying this data. Calculate suitable measures of location and dispersion. If using a graphics calculator, intermediate totals should be recorded, ie number of variables, sum of variables, sum of squares. 2 A study of another type of bird gives wing lengths at known ages. The results are recorded below. Age (days) Wing Length (mm) 2 26.0 4 29.2 6 33.9 8 37.0 10 41.6 13 57.4 16 73.7 19 81.5 22 105.0 25 164.0 (c) (d) (e) Plot a scatter diagram of wing length against age. Does a relationship exist between these data? If so, what sort of relationship is it? What kind of transformation is required to produce a straight line graph? Calculate the correlation coefficient and regression coefficients of the transformed data. Estimate the wing length of a 30 day old bird, stating any reservations you have about the accuracy of this estimate. PROGRESSION: For information on how this unit relates to National Certificate mathematics provision and to other units in the Higher National mathematics framework, please refer to the following grid: Higher National mathematics grid for science 11
REFERENCES 1 Guide to unit writing. 2 For a full discussion on assessment issues, please refer to SQA's Guide to Assessment. 3 Information for centres on SQA's operating procedures is contained in SQA's Guide to Procedures. 4 For details of other SQA publications, please consult SQA's publications list. 5 For an up-to-date list of suitable computer packages, please contact SQA's Product Development Department. Copyright SQA 1994 Please note that this publication may be reproduced in whole or in part for educational purposes provided that: (i) (ii) no profit is derived from the reproduction; if reproduced in part, the source is acknowledged. 12
HIGHER NATIONAL MATHEMATICS GRID FOR SCIENCE National Certificate Higher National 7180331 Core Maths 4 7481534 Mathematics for Science 1 7481554 Descriptive Stats for Science 7481544 Mathematics for Science 2 7481564 Inferential Stats for Science HNGRID.DOC 13