Course: Statistics
Level: Advanced Higher
March 2015
This advice and guidance has been produced for teachers and other staff who
provide learning, teaching and support as learners work towards qualifications.
These materials have been designed to assist teachers and others with the
delivery of programmes of learning within the new qualifications framework.
These support materials, which are neither prescriptive nor exhaustive,
provide suggestions on approaches to teaching and learning which will
promote development of the necessary knowledge, understanding and skills.
Staff are encouraged to draw on these materials, and existing materials, to
develop their own programmes of learning which are appropriate to the needs
of learners within their own context.
Staff should also refer to the course and unit specifications and support notes
which have been issued by the Scottish Qualifications Authority.
http://www.sqa.org.uk
Acknowledgement
© Crown copyright 2015. You may re-use this information (excluding logos) free of
charge in any format or medium, under the terms of the Open Government Licence.
To view this licence, visit http://www.nationalarchives.gov.uk/doc/open-governmentlicence/ or e-mail: psi@nationalarchives.gsi.gov.uk.
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Contents
Introduction
4
Resources
8
Additional resources
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INTRODUCTION
Introduction
Understanding statistics is an important skill for everyday life, allowing us to
make sense of the information around us. It is an essential feature of the
modern workplace and is crucial to competitiveness in the global market.
The majority of academic subjects rely on knowledge and understanding of
data and statistics.
The course content includes applying skills in data analysis and modelling,
statistical inference and hypothesis testing, and the interpretation of situations
involving data collections, probability and sampling.
This advice and guidance provides online links to a range of resources,
including simulators, games, e-books, case studies, experiments and data
sets, to support the learning and teaching of:
 data analysis and modelling
 statistical inference
 hypothesis testing
within the context of Advanced Higher Statistics.
The resources incorporate opportunities for collaborative and independent
learning using a range of real-life situations. Learners will be expected to use
statistical reasoning skills to make and explain their decisions within a given
relevant context.
Assumed prior knowledge, skills and understanding from the National 5
mathematics course are:
Comparing data sets using statistics
Applications
Forming a linear model from a given set of data
Applications
These are needed to provide a firm foundation for further learning within
SCQF level 7.
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Increased emphasis on skills development
Advanced Higher Statistics has an increased emphasis on skills development
and higher-order thinking skills, which are developed through the selection
and application of operational skills in:
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data presentation and interpretation
probability theory
discrete random variables
probability distributions
sampling and central limit theorem
intervals and estimation
bivariate analysis and tests
parametric and non-parametric tests
to a variety of statistical and real-life situations.
Learning and teaching approaches should provide opportunities to build
progressively through these higher-order thinking skills:
Image courtesy of Me and My Laptop blog
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Active learning
Learners will be expected to take an active role in the learning process,
extending their reasoning and analytical skills through a range of statistical
tasks and activities. Learning activities, linked to their own interests or
aspirations, will develop their ability to analyse, evaluate, solve problems and
apply learning in other aspects of their lives.
Through engaging learning, learners should experience tasks and activities
that require them to analyse and justify decisions, explain their thinking and
synthesise aspects of their existing skills. When learners are increasingly
active in their learning, they think deeply about statistical ideas and concepts,
and construct their own understanding about them. They use existing skills
and knowledge in different contexts, test out their ideas and solve problems.
Independence, responsibility and collaboration
Learners undertaking Advanced Higher Statistics will continue to develop as
independent learners either working on their own or in groups. They can
develop confidence and self-motivation through activities that offer a choice of
approaches and resources, and which encourage them to be self-reliant. This
could nurture their leadership skills and promote responsibility and team
working – essential skills for learning, life and work.
Learners should be expected to take responsibility for, and plan, their own
learning based on an understanding of how best they themselves learn.
Opportunities for personalisation and choice will enable learners to show what
they can do. This will promote motivation and ensure individuals are
challenged appropriately.
Collaborative learning challenges learners to think independently and engage
in discussion, debate and activity to achieve specific outcomes. For example,
collaborative approaches will support learners to develop confidence in the
application of hypothesis tests and the use of statistical language to explore
statistical ideas. In planning activities, staff should provide opportunities for
learners to collaborate more widely with others. This is a key change that
recognises that learning takes place both within and beyond the classroom.
Working with business partners provides the relevant and real-life contexts
and situations that promote investigative and problem-solving approaches.
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Areas of change and points of stability
Advanced Higher Statistics is now a course in its own right, rather than part of
Advanced Higher Mathematics.
Two-sample t-tests have been introduced as new content to this course.
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RESOURCES
Resources
SQA Statistical Formulae and Tables booklet, for use in NQ examinations
http://www.sqa.org.uk/files_ccc/2004_Applied_Maths_Stats_and_Tables.pdf
Unit
Resources
Data Analysis and
Modelling
Applying skills to data
presentation and
interpretation
Undertaking the
exploratory data
analysis of univariate
data
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http://www.statgraphics.com/eda.htm
Data presentation – examples include stem and leaf diagrams, boxplots and scattergraphs.
http://www.abs.gov.au/websitedbs/a3121120.nsf/home/statistical+language+-+census+and+sample
Animation explains the concept of census and sample. Information on when to use a census and
sample and on selecting samples.
http://surfstat.anu.edu.au/surfstat-home/cont1.html
Summarising and presenting data by topic. Information and explanation, progress check and links to
glossary for each topic: types of data, discrete data, continuous data (Java needed for applet),
characteristics of a distribution, measure of central tendency (Java needed for applet), measure of
variability, normal distribution, two continuous measurements, exploring data in tables.
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Data Analysis and
Modelling
Applying skills to
probability theory
Working with
theoretical and
experimental
probabilities
Calculating
conditional
probabilities
http://www.censusatschool.org.uk/resources/probability/173-too-many-boys
Probability of gender at birth. Real data contrasted with theoretical probabilities of family make-up. Can
extend to using Bayes’ theorem.
http://interactivemaths.net/index.php?q=category/1/75
A selection of probability activities and experiments: Are you a psychic? Cereal box problem, The
birthday problem, Stick or switch. Some of these need Java to run applets.
Also included are random generators for numbers, coins, dice and playing cards.
http://cims.nyu.edu/~kiryl/Elementary%20Statistics/Chapter_6.pdf
Some rules of probability – a useful reference for learners.
http://www.statlect.com/bayes_rule.htm
Bayes’ rule – proof, worked example in a practical context, terminology, examples with solutions.
https://onlinecourses.science.psu.edu/stat464/node/27
Probability and distribution functions information. Useful for revision and support.
http://www.cimt.plymouth.ac.uk/projects/mepres/alevel/stats_ch1.pdf
Probability – theoretical and empirical – ideas for activities and experiments.
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Data Analysis and
Modelling
Applying skills to
discrete random
variables
Modelling a discrete
random variable
Using the laws of
expectation and
variance
http://phet.colorado.edu/en/simulation/plinko-probability
‘Run Now’ and see balls drop randomly through a triangular grid of pegs. Watch the histogram build up
and approach the binomial distribution. Balls can be released one at a time or continuously. Encourage
discussion on expected distribution as the histogram builds.
http://www.mathsrevision.net/advanced-level-maths-revision/statistics/expectation-and-variance
Worked example and explanations for expectation and variation. Could be used as an introduction or for
independent revision.
http://www.s-cool.co.uk/a-level/maths/probability-distributions/revise-it/expectation-and-variance
Worked examples and prompts on expectation and variance. Good for revision.
http://www.sciencebuddies.org/science-fairprojects/project_data_analysis_variance_std_deviation.shtml
Detailed worked example and explanation of variance and standard deviation.
http://www.cimt.plymouth.ac.uk/projects/mepres/alevel/fstats_ch1.pdf
Continuous probability distributions – worked examples and questions on expectation, mean and
variance, and distributions.
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Data Analysis and
Modelling
Applying skills to
particular probability
distributions
http://www.socr.ucla.edu/htmls/SOCR_Distributions.html
Interactive distribution applets (Java) which allow the user to vary parameters and visualise the change
in shape of the distribution. A snapshot can also be taken and saved as a JPG image. The range of
distributions include:
 binomial – select number of trials and success probability
 chi-squared – select number of degrees of freedom
 normal – select mean and standard deviation
 Poisson – select shift and lambda
 Student’s t-distribution – select degrees of freedom.
http://www.socr.ucla.edu/htmls/SOCR_Experiments.html
A selection of interactive simulations and experiments (Java) using a range of distributions, including:
binomial coin, binomial timeline, chi-square dice, Poisson, two-dimensional Poisson, uniform estimate,
bivariate normal and bivariate uniform. The user can update the frequency and select whether the
number of trials is discrete or continuous. The changes can be visualised in graphs and tables. A
snapshot can also be taken and saved as a JPG image.
http://www.onlinemathlearning.com/statistics.html
Section F – More Advanced Statistics – contains a series of statistics lessons which comprise theory
and videos.
 Bayes’ theorem – Laws of probability: addition law, multiplication law and Bayes’ theorem. Two
videos introduce Bayes’ theorem (10.02 minutes and 7.24 minutes).
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 Binomial distribution – Video 1 (12.16 minutes) and video 2 (11.05 minutes) introduce the binomial
distribution in the context of a flipped coin experiment. Video 3 (13.27 minutes) and video 4 (10.45
minutes) use basketball shots and visualise the distribution using Excel. Video 5 discusses what a
binomial experiment is and the formula for finding the probability associated with the experiment, and
gives an example to illustrate the concepts.
 Poisson distribution – Video 1 (11.01 minutes) and video 2 (12.42 minutes) show how to derive the
Poisson formula from the binomial formula. Video 3 (5.58 minutes) discusses simulation that can be
modelled by a Poisson distribution to give the formula and do a simple example illustrating Poisson
distribution, based on customers entering a fast-food restaurant.
Using discrete
probability
distributions
http://www.distributome.org/V3/exp/BinomialExperiment.html
Binomial distribution interactive experiment.
http://www.distributome.org/V3/exp/PoissonExperiment.html
Poisson interactive experiment.
http://distributome.org/blog/?cat=4
Colourblindness activity (binomial and normal distributions).
Homicide trends activity (Poisson distribution).
http://www.distributome.org/V3/exp/DiscreteUniformExperiment.html
Uniform distribution interactive experiment – discrete.
http://www.censusatschool.org.uk/resources/probability/387-secrets-of-the-talent-show
Introduction to the binomial distribution, based on a popular talent show.
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http://www.censusatschool.org.uk/resources/probability/176-fillings-what-are-the-chances
Use of the Poisson distribution with real-life data on dental health and number of fillings for school
children.
http://www.distributome.org/V3/exp/ContinuousUniformExperiment.html
Continuous uniform distribution interactive experiment.
http://www.cimt.plymouth.ac.uk/projects/mepres/alevel/stats_ch6.pdf
Poisson distributions – ideas for activities and examples to try.
http://www.umass.edu/wsp/resources/poisson/
Poisson distribution – computing probabilities, contextual examples, approximation to binomial,
problems with solutions (including the king’s coiner, Ozzie’s risk, the prisoner’s dilemma), tables of
numbers (including Pascal’s triangle, factorials, Poisson table). Historical information is also given about
statisticians such as Simeon-Denis Poisson, Jacob Bernouilli and Carl Friedrich Gauss.
https://onlinecourses.science.psu.edu/stat464/node/19
Binomial distribution information. Useful for revision and support.
http://www.distributome.org/V3/exp/NormalExperiment.html
Normal distribution interactive experiment.
http://www.cimt.plymouth.ac.uk/projects/mepres/alevel/stats_ch5.pdf (will need to paste url into address
bar)
Binomial distribution – ideas for activities and examples to try.
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http://opl.apa.org/contributions/Rice/rvls_sim/main.htm
Applets (Java) to simulate experiments and show their distributions. These include:
 robustness of t-test and ANOVA – simulates t-test/ANOVA with normality and homogeneity of
variance assumptions violated
 normal approximation to the binomial distribution – view binomial distribution and the normal
approximation to it as a function of the probability of success on a given trial and the number of
trials
 chi-square test of deviations from expected frequencies – sample from either a uniform or normal
distribution; applet does the sampling and tests the significance of deviations
 repeated measures – investigate differences between correlated and independent t-tests.
Using continuous
probability
distributions
https://onlinecourses.science.psu.edu/stat464/node/20
Normal distribution information. Useful for revision and support.
http://www.cimt.plymouth.ac.uk/projects/mepres/alevel/stats_ch7.pdf
Continuous probability distributions – ideas for activities and examples to try.
http://www.cimt.plymouth.ac.uk/projects/mepres/alevel/stats_ch8.pdf
Normal distribution – ideas for activities and examples to try.
Using the normal
approximation to
discrete probability
distribution
http://simulation-math.com/_ElementaryStatistics/BinomialVSNormal4.cshtml
Binomial distribution versus normal distribution – series of comparisons between binomial distribution
calculations and normal distribution calculations examples.
Link to simulation (top of page) – program designed to run with Firefox or Google Chrome.
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Statistical Inference
Applying skills to
sampling and the
central limit theorem
http://wadsworth.cengage.com/psychology_d/templates/student_resources/workshops/res_methd/samp
ling/sampling_01.html
Research methods workshop resource – sampling strategies and test your knowledge workshop quiz.
Identifying and using
appropriate random
sampling methods
http://www.cimt.plymouth.ac.uk/projects/mepres/alevel/stats_ch2.pdf
Data collection – ideas for activities and examples to try.
http://www.cimt.plymouth.ac.uk/projects/mepres/alevel/stats_ch9.pdf
Estimation – ideas for activities and examples to try.
Working with the
distribution of sample
means
http://interactivemaths.net/index.php?q=category/1/76/107
Sampling distributions (Java), applet estimates and plots sampling distributions of various statistics.
Sampling pennies (Java) applet shows the difference between the distribution of the members of a
dataset and the distribution of sample means.
Sampling distribution of the mean simulation shows the consistency of sample means from variously
shaped populations.
http://wadsworth.cengage.com/psychology_d/templates/student_resources/workshops/stat_workshp/sta
nd_error/stand_error_01.html
Standard error workshop resource – sampling distribution and standard error of the mean, calculate
standard error and test your knowledge workshop quiz.
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http://wadsworth.cengage.com/psychology_d/templates/student_resources/workshops/stat_workshp/cnt
_lim_therm/cnt_lim_therm_01.html
Central limit theorem workshop resource – sampling, populations, distributions and test your knowledge
workshop quiz.
http://wadsworth.cengage.com/psychology_d/templates/student_resources/workshops/stat_workshp/sa
mpling_dist/sampling_dist_01.html
Sampling distribution workshop resource – samples and hypotheses, hypothesis testing, variance,
distributions and test your knowledge workshop quiz.
Statistical Inference
Applying skills to
intervals and
estimation
Obtaining confidence
intervals
http://sphweb.bumc.bu.edu/otlt/MPHModules/BS/BS704_Confidence_Intervals/BS704_Confidence_Intervals_print.html
Comprehensive information on confidence intervals taking account of number of groups, outcome
variable and parameter.
http://www.math.usu.edu/~schneit/CTIS/CI/
Confidence intervals (Java) applet. Estimate the proportion of orange balls in a jar, with questions to
consider.
https://www.usablestats.com/lessons/SamplesVary
Interactive tutorial to introduce confidence intervals.
https://explorable.com/statistics-confidence-interval
Information on what confidence intervals mean. Useful for an introduction.
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http://www.ditutor.com/inference/confidence_interval.html
Information and examples on confidence intervals and critical values.
http://www.measuringu.com/blog/ci-10things.php
Ten things to know about confidence intervals, including the location and precision of a measure and
the width of the confidence interval.
http://www.cimt.plymouth.ac.uk/projects/mepres/alevel/fstats_ch2.pdf
Estimation/confidence intervals – ideas for activities and examples to try.
Using control charts
http://www.cimt.plymouth.ac.uk/projects/mepres/alevel/fstats_ch8.pdf
Statistical process control – ideas for activities and examples to try.
http://www.qimacros.com/control-chart/shewhart-control-chart-excel/
Shewhart control charts – creating the seven Shewhart control charts in Excel. Information given on
purpose and when to use each of these control charts.
http://www.micquality.com/six_sigma_glossary/western_electric.htm
Western Electric rules limits displayed graphically.
http://www.micquality.com/six_sigma_glossary/control_charts.htm
Purpose of control charts with links to the glossary for each of the different types of control charts.
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Statistical Inference
Applying skills to
bivariate analysis
Fitting a linear model
to bivariate data
Measuring the
strength of the linear
association between
two variables
http://wadsworth.cengage.com/psychology_d/templates/student_resources/workshops/stat_workshp/sc
atter/scatter_01.html
Bivariate scatter plots workshop resource – scatter plots and bivariate plots, correlation coefficient and
regression, and test your knowledge workshop quiz.
http://geographyfieldwork.com/SpearmansRank.htm
Spearman’s rank correlation coefficient – real-life example which looks at the strength of the price of a
convenience item (bottle of water) and distance from a museum. Considers the hypothesis, calculating
the coefficient and what this value means
http://changingminds.org/explanations/research/analysis/pearson.htm
Description of Pearson correlation with worked example and what the result indicates.
Estimating with
bivariate data
http://www.uvm.edu/~naguiar/courses/lessons_111/Lecture_10_1.html
Correlation and simple linear regression – explanations and examples on scatterplots, Pearson
correlation coefficient, regression models and analysis.
https://www.ma.utexas.edu/users/mks/statmistakes/CIvsPI.html
http://www.physics.csbsju.edu/stats/least_squares.html
Least-squares fitting worked example on comparing the diameter of an oak tree with its age.
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Hypothesis Testing
http://www.zoology.ubc.ca/~whitlock/bio300/lecturenotes/HypothesisTesting/HypothesisTesting.html
Introduction to hypothesis testing – explanation of null and alternative hypotheses and using test
statistics.
http://www.cimt.plymouth.ac.uk/projects/mepres/alevel/stats_ch10.pdf
Hypothesis testing – ideas for activities and examples to try.
http://www.nuffieldfoundation.org/fsmqs/level-3-hypothesis-testing
Hypothesis testing activities:
Successful HE applicants – carry out significance tests on proportions to test hypotheses about
applicants to higher education.
Gender differences – carry out significance tests on means in order to test hypotheses about the body
measurements of boys and girls at different ages.
Appling skills to
parametric tests
http://wadsworth.cengage.com/psychology_d/templates/student_resources/workshops/stat_workshp/hy
pth_test/hypth_test_01.html
Hypothesis testing workshop resource – null and alternative hypotheses, power and statistical errors,
and test your knowledge workshop quiz.
http://wadsworth.cengage.com/psychology_d/templates/student_resources/workshops/stat_workshp/tes
t_means/test_means_01.html
Test of means workshop resource – one-sample z-test, one-sample t-test, t-test for dependent and
independent means, selecting the appropriate test, and test your knowledge workshop quiz.
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Identifying and
applying an
appropriate onesample test for the
population mean and
proportion
http://wadsworth.cengage.com/psychology_d/templates/student_resources/workshops/stat_workshp/zs
cores/zscores_01.html
z-scores workshop resource – data types, examples and big ideas, and test your knowledge workshop
quiz.
http://www.cimt.plymouth.ac.uk/projects/mepres/alevel/fstats_ch3.pdf
Hypothesis testing: one-sample t-test, normal, binomial and Poisson populations, population medians –
ideas for activities and examples to try.
http://wadsworth.cengage.com/psychology_d/templates/student_resources/workshops/stat_workshp/tte
st_one/ttest_one_01.html
Single sample t-test workshop resource – use the t-test to reject or fail to reject the null hypothesis, and
test your knowledge workshop quiz.
Identifying and
applying an
appropriate twosample test
(independent or
paired) for population
means or proportions
http://www.amstat.org/education/stew/pdfs/AnAmazingComparison.pdf
This demonstrates an investigation using the two-sample t-test and can easily be modified for this
course. The two-sample t-test is new content.
http://www.gla.ac.uk/sums/users/jdbmcdonald/PrePost_TTest/chooset1.html
Statistics tutorial on choosing a t-test. Explanation given on when to choose a paired or independent ttest. Test your knowledge of choice of t-test type, tail number and experimental design.
http://www.gla.ac.uk/sums/users/jdbmcdonald/PrePost_TTest/pairedt1.html
Statistics tutorial on paired t-tests. Explanation given on what a paired t-test does, what it measures and
how to use it. Test your knowledge of whether a paired t-test should be used for given scenarios, the
most useful average for comparing pairs of values and experiment conclusions.
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http://www.cimt.plymouth.ac.uk/projects/mepres/alevel/fstats_ch4.pdf
Hypothesis testing – two-sample tests, normal populations, sign test for paired samples, results of
paired samples design – ideas for activities and examples to try.
Hypothesis Testing
Applying skills to nonparametric tests
Identifying and
carrying out an
appropriate test for
population median/s
http://sphweb.bumc.bu.edu/otlt/MPH-Modules/BS/BS704_Nonparametric/BS704_Nonparametric5.html
Non-parametric tests to compare two groups for matched or paired samples. Real-life example of a
clinical investigation which looks at the effectiveness of a new drug for children with autism. One-sided
versus two-sided tests and the special circumstance of the sign test giving zero difference scores are
considered.
http://sphweb.bumc.bu.edu/otlt/MPH-Modules/BS/BS704_Nonparametric/BS704_Nonparametric6.html
Wilcoxon signed rank test. Re-analyses the clinical investigation example above (previous page of this
website). Comprehensive worked examples. Useful for instructional phase in class, revision and
support.
https://onlinecourses.science.psu.edu/stat464/node/32
One-sample test: the sign test information. Useful for revision and support.
http://geographyfieldwork.com/Mann%20Whitney.htm
Mann–Whitney U test of significance – real-life example which compares and contrasts the differences
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of two urban areas. There are eight pairs of data, one of which is the quality of the architecture.
https://onlinecourses.science.psu.edu/stat464/node/37
Mann–Whitney test and confidence information. Useful for revision and support.
https://onlinecourses.science.psu.edu/stat464/node/36
Wilcoxon rank sum test information. Useful for revision and support.
Identifying and
carrying out an
appropriate chisquared test
http://wadsworth.cengage.com/psychology_d/templates/student_resources/workshops/stat_workshp/chi
_sqr/chi_sqr_01.html
Chi-squared workshop resource – example on workplace discrimination, test of independence, visual
chi-square and test your knowledge workshop quiz.
http://www.cimt.plymouth.ac.uk/projects/mepres/alevel/fstats_ch5.pdf
Goodness-of-fit tests – calculating expected frequencies, using the chi-squared distribution to test if a
set of observations fits an appropriate probability model, discrete and continuous probability models –
ideas for activities and examples to try.
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Hypothesis Testing
Applying skills to
bivariate tests
Identifying and
carrying out an
appropriate
hypothesis test on
bivariate data
http://www.cimt.plymouth.ac.uk/projects/mepres/alevel/stats_ch12.pdf
Correlation and regression – investigate strength and direction of a relationship between two variables,
evaluate and interpret Pearson’s product moment correlation coefficient and the Spearman’s rank
correlation coefficient, find equations of regression lines, bivariate distributions – ideas for activities and
examples to try.
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Additional resources
http://www.mathportal.org/calculators/statistics-calculator/
Free online statistics calculators, with optional step-by-step explanations:
 descriptive statistics: find the arithmetic mean, mode, median, minimum
and maximum of a data set
 standard deviation: find the standard deviation, variance and range of a
data set
 discrete probability distributions: find the mean, standard deviation and
variance of a discrete probability distribution
 z-score: find the area under a standard normal curve
 normal distribution: find the area under a normal distribution curve
 t-test: one-sample and two-sample t-test calculator
 correlation and regression: find the linear correlation coefficient and
regression line. Calculator generates a graph of a regression line as well as
a detailed explanation.
http://wiki.stat.ucla.edu/socr/index.php/EBook
Statistics eBook which is a useful reference for definitions, methods and
examples in probability and statistics.
This could be used for home study or in the classroom.
http://web.grinnell.edu/individuals/kuipers/stat2labs/Labs.html
Activities and games based on labs that allow learners to develop their own
research questions, use their own unique data to make decisions and then tie
their conclusions to actual research (hypothesis testing).
Tangrams: one-sample and two-sample t-tests.
Memorathon game: z-test or one-sample t-test.
Statistically grounded game: understanding p-values and introducing
multivariate issues in a simplified game environment.
http://lib.stat.cmu.edu/DASL/allmethods.html
Data files for stories that illustrate the use of statistical methods. The data
could be used in investigations in the Hypothesis Testing and Statistical
Inference units.
Data for use with chi-squared test, Mann–Whitney U test, paired t-test,
ANOVA, t-test and two-sample t-test methods are included.
http://www.censusatschool.org.uk/resources/relevant-a-engaging-stats
Free downloadable booklet, by chapter, which provides practical advice and
suggestions:
 statistical facts, formulae and information
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data visualisation
examples of curriculum resources
teaching through statistical investigations
using random samples of real data
using spreadsheets
using the whole problem-solving approach
using your learners’ own data.
http://www.censusatschool.org.uk/resources/simulationsA selection of statistical simulations in Excel. Numerous examples can be
randomly generated:
 S1 binomial hypothesis test – one-tail and two-tail tests
 S1 dot plots – same size samples from two populations with the same
mean and standard deviation. Which is normal and which is uniform?
 S2 CLT simulation – graphs of distributions of sample means. Central limit
theorem in action
 S2 normal approximation to binomial – how do values for n and p affect the
graphs?
 S2 normal approximation to Poisson – how does value of lambda (λ) affect
the graph?
 S2 Poisson approximation to binomial – how do binomial parameters for n
and p affect the graphs?
 S3 die chi-squared – chi-squared statistic for rolling a fair die
 S3 t and normal distributions – comparing these distributions
 stats random dots – dots scattered across grid. Amount in any square has
Poisson distribution. Look at extreme values.
http://www.amstat.org/education/stew/
A website of lesson plans for staff use. Lessons are organised around four
elements: formulate a statistical question, design and implement a plan to
collect data, analyse the data by measures and graphs, and interpret the data
in the context of the original question.
Some of the Grades 9–12 section would correspond with this course,
including:
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10000 steps – paired t-test
Double stuffed – two-sample t-test
An A-MAZE-ING comparison – two-sample t-test
I always feel like somebody’s watching me – hypothesis test on proportion,
chi-squared test, binomial distribution, binomial test
 The case of the careless zookeeper – chi-squared test
 When 95% accurate isn’t – Bayes’ theorem
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© Education Scotland 2015
RESOURCES
Maths is Fun – Statistics
These pages provide learners with the opportunity to review and consolidate
their learning. Clearly explained key information and worked examples,
followed by ten questions to check knowledge and understanding.
http://www.mathsisfun.com/data/binomial-distribution.html
Binomial distribution and a link to a game which demonstrates this.
http://www.mathsisfun.com/data/standard-normal-distribution.html
Normal distribution.
http://www.mathsisfun.com/data/standard-normal-distribution-table.html
Standard normal distribution table.
Excel simulations
The change to the shape of the distributions can be seen by altering the
variables in these spreadsheets.
http://wps.prenhall.com/bp_groebner_busstats_8/145/37312/9551949.cw/cont
ent/index.html
Binomial distribution, chi-square distribution, confidence interval distribution, fdistribution, hypothesis distribution, normal curve distribution, t- distribution.
http://www.quantitativeskills.com/sisa/
A collection of procedures to do simple interactive statistical calculations
online. Useful as a tool for checking.
http://www.socscistatistics.com/tests/
Online statistical test calculators. Useful as a tool for checking.
http://www.socscistatistics.com/pvalues/
Online p-value calculators. Useful as a tool for checking.
http://davidmlane.com/hyperstat/glossary.html
Glossary of statistical terms.
http://www.stats.gla.ac.uk/glossary/
Useful glossary of statistical terms, many of which are more advanced than
required for this course. Clear concise explanations, many with
exemplification.
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© Education Scotland 2015