Year No. Offer Mode Description Cred. Pts 96 64001 S3 X DATA ANALYSIS 1.00
Practitioners in many disciplines are often required to deal with observations of variable phenomena and imprecise or approximate measurements. Statistics provides tools which help to identify the underlying nature of such phenomena, to evaluate the precision of the measurements, to discover the strength of the relationships between variables and to make predictions about the likelihood of particular events occurring in the future. This unit provides the statistical concepts, methods and skills necessary for students in business, engineering and the physical and social sciences to analyse and interpret data. Because these concepts are interdisciplinary in nature, students will encounter problems from many sources including their own area of interest. The statistical skills developed in this unit will form the basis for more advanced statistical methods and concepts in specialist fields.
Students will be introduced to the concepts involved in descriptive and inferential statistics. Topics include the role of statistics in a scientific investigation, methods of condensing, displaying, describing and presenting data, elementary descriptive statistics, elementary probability, the binomial, Poisson and normal distributions, single-sample inference, comparison of frequencies, regression and correlation, and inference for two or more samples.
Upon completion of this unit, students should be able to:
Description Weighting(%)
- Scientific method and the role of statistics. Statistics 1.00 in everyday life, Logic and statistical reasoning, a metho- dology for conducting an investigation and analysing the data obtained from such an investigation, statistical universe, population, sample error, descriptive statistics, inferential statistics.
- Data organization and models. Quantitative and 4.00 qualitative data, qualitative and quantitative variables, discrete and continuous variables, measurement scales, dependent and independent variables, univariate, bivariate and multi- variate data.
- Pictorial presentation of data. Data reduction, frequency 4.00 distributions, frequency polygons, histograms, bar graphs, ogive, pie charts, stem-and-leaf plots, pictograms, misuse of graphical techniques.
- Numerical descriptions of grouped and ungrouped data. 7.00 Measures of central tendency and dispersion - their properties, calculation and application. Mean, mode, median, range, standard deviation and quantiles. Coefficient of variation. Skewness and symmetry. Abuse of statistics.
- Elementary Probability. Sample space, sets, union, 9.00 intersection mutually exclusive sets. Classical, relative subjective approaches to probability. Laws of probability. Conditional probability and marginal probability, additive and multiplicative laws, dependent and independent events.
- Models for discrete random processes. Random variables. 7.00 Binomial and Poisson distributions as models. Determining probabilities associated with these distributions. Mean, variance and other characteristics of these distributions.
- A model for some continuous random processes. The normal 9.00 distribution, its characteristics and properties. The standardized normal distribution, tables, properties and applications. Sampling distributions and the Central Limit Theorem and its applications to the mean of a random sample and the sample proportion.
- Sampling and statistical inference. Reasons for sampling, 21.00 sampling schemes, types of sampling. Selecting a random sample. Point and interval estimation of sample means and proportions for large samples. The Student's t- distribution. Interval estimation for small samples when the population variance is unknown. Sample size determination. Hypothesis testing. Rationale, Type 1 and Type 2 errors. Framing hypotheses. One-tailed and two- tailed tests. Large and small sample tests concerning the population mean and proportion. Tests concerning the association between frequency data. The chi-squared distribution and its properties. Tests for independence in contingency tables.
- Regression and correlation. Concept of correlation, 14.00 measure of correlation, positive, negative and zero correlation. Pearson product-moment correlation. The coefficient of determination. Correct interpretation of correlation. Linear regression, the method of least squares, the line of best fit. Determination of the regression y = a + bx, interpretation of the slope and y- intercept of the regression line. Residuals, standard error of estimate. Prediction intervals. Cautions in the use of regression analysis.
- Statistical inference for two or more samples. Random 20.00 sampling distributions of the difference between two means. Independent and dependent sampling. Assumptions underlying inferences about the difference between two means. The pooled estimate of variance. Use of the t- distribution for inferences based on small samples. Degrees of freedom. Advantages and disadvantages of using dependent samples. Confidence intervals for the difference between two population means. Sources of variation in an experiment and their control. One-way Analysis of Variance. The F-distribution. Assumptions underlying the use of analysis of variance.
- Review and Revision. 4.00
Quinn, K J D, 'Eton Statistical and Mathematical Tables', 4th Edition,
Eton, Christchurch, NZ, 1974.
ACTIVITY HOURS Private Study 142 Examinations 3 Assessments 20
No *F/S Marks Due Description Wtg(%) LBL 1 S 100.00 13/12/96 ASSIGNMENT ON TOPICS 1, 2, 3, 4 8.00 Y 2 S 100.00 03/01/97 ASSIGNMENT ON TOPICS 5, 6, 7 8.00 Y 3 S 100.00 24/01/97 ASSIGNMENT ON TOPICS 8,9 8.00 Y 4 S 30.00 END S3 3 HOUR EXAM (OPEN BOOK) PT A 46.00 N 5 S 30.00 END S3 PART B OF ABOVE EXAM 30.00 N
1 To obtain a pass in the unit, students must perform
satisfactorily in all aspects of assessment.
2 The due date for assessments is the date by which a student must
despatch an assignment to the USQ. The onus is on the student to
provide proof of the despatch date, if requested by the Examiner.
3 Students MUST retain a copy of all assignments which must be
produced if and when required by the Examiner.
4 Extensions for assignment submission may be granted in
extenuating circumstances. The decision to grant or refuse an
extension is made by the Examiner. Students should be aware that
an application for an extension does not guarantee that an
extension will be granted.
5 Students apply for extension by either applying at the time of
submitting an assignment or applying in writing prior to
submitting an assignment. All relevant documentation should
accompany the application.
6 If assignments are submitted after the due date and no extension
is granted, then a penalty up to a maximum of 20% of the
assignment mark for each working day late may apply.
7 No further assignments will be accepted for assessment purposes
after assignments or model solutions have been released, except
in extenuating circumstances.