Information - Exercises - Solutions - Quizzes.

These lesson details include:

- outlines of the concepts to be delivered in each block of lessons
- references for resources to use in the teaching process
- exercises for pupils to practise the techniques
- notes of items to emphasise
- URL links to You Tube videos of selected explanations and proofs

*All the resources are offered without any warranty or guarantee of their accuracy, although every
effort has been made to make them as error-free as possible.*

CIMT Statistics eBook, with solutions and Excel data files.

CIMT Further Statistics eBook, with solutions and Excel data files.

These two eBooks are from the University of Plymouth's 'Centre for Innovation in Mathematics Teaching' (CIMT) and were originally written for A-Level Statistics and A-Level Further Statistics. They cover most of the content in the SQA Advanced Higher Statistics course and permission has been generously granted to host them here.

Each download .zip file contains:

- a single pdf copy of the eBook
- hand-written worked solutions to all relevant exercises and questions
- an Excel file with (nearly) all of the data sets

In the eBooks, a red line next to a question's printed data set means that the numbers are in the Excel file.

AH Statistics Worksheets and Teaching Materials.

This covers parts of the course that are not included in the CIMT eBooks.

It includes worksheets for:

- support materials for non-parametric tests
- normal approximations for non-parametric tests
- two sample proportion tests
- ... and many more!
- full worked solutions for all exercises

An interactive tool allows the user to visually and numerically interrogate the distributions of rank sums that underpin the Mann-Whitney Test and Wilcoxon Signed Rank Test.

This interactive tool supports the creation of annotated graphs of Normal Distribution.

This interactive demonstration highlights the effects of working with bivariate data that is a
sample of a
much larger population.

A video demonstration introducing it can be viewed [here].

By the end of the AH Statistics course, students have to make decisions about what type of analysis to perform on any given set of data. The list of choices and analysis techniques that they have to select from can be quite extensive.

The Analysis Decision Flowchart is an interactive web-page that prompts the user to decide which choice they wish to make at each stage, and it leads them through one possible decision making process. In essence, it's an attempt to train students to be 'thinking the right sort of thoughts' about what to look out for when faced with a data set.

It is not being presented here as necessarily the 'right way' to think about things, and it's certainly not intended to promote a linear or formulaic approach to the world of Statistical analysis. There will no doubt be other sequences of questions that a Statistician might ask themselves to arrive at similar conclusions.

For the technically minded, it's a single, standalone .html file. This means that you could choose 'Save as' in your browser to download a copy of it, and then run it locally on a device that has a web browser without being connected to the internet. Indeed, for the more coding-orientated teachers who want to edit the text that's contained within it or change the sequencing of the questions, then a standard html editor should reveal the file's inner workings and hopefully it's clear how things can be modified to suit your needs.

Multiple TI-Nspire documents have been authored to support delivering the SQA AH Statistics course content.

TI-Nspire Computer Software [Free 30 day trial].

using TI-Nspire software for past SQA AH Statistics exams.

TI-Nspire .tns files for CIMT eBooks, teaching resources and widgets

The download .zip file contains:

- .tns files of all data sets from both of the CIMT eBooks
- .tns files for demonstrating and simulating selected concepts from the course
- .tns 'Widget' files that can be installed in the 'MyWidgets' folder on a TI-Nspire Handheld. These Widgets provide extra functionality to support the teaching and checking of the course content. Note that when the handheld is in 'Press-to-Test' mode, these Widgets are disabled.

In addition, there are three pdf guides:

- 'Sampling Procedures using TI-Nspire OS4.2.pdf' shows how to simulate:
- Simple Random Sampling
- Systematic Sampling
- Stratified Random Sample
- 'Simple Coding of Statistical Simulations.pdf' shows how to simulate a wide variety of probability simulations
- 'Simulation of Chi-Squared Contingency Table.pdf' details the design of the .tns file 'ChiSquared Simulation RxC.tns'

Below is a list of all the .tns teaching files, by conceptual category:

General Background

- Statistician Timeline v1.tns

Probability

- Tree Diagrams.tns

Measures of Dispersion

- IQR vs StDev.tns
- Mean + Median + StDev.tns
- Standard Deviation Concept.tns
- Standard Deviation Divisor HH.tns
- Widget: StemAndLeaf.tns

Random Variables

- Binomial Distn.tns
- Normal Distn.tns
- Norm appx to Binomial.tns
- Poisson Distn.tns
- Poisson Simulation v3.tns
- Students t Distn.tns
- Sum of Normal RVs.tns
- Skewed Normal Distribution v2NH.tns
- Laws of Expectation and Variance.tns

Samples

- Normal Sample Boxplots.tns
- Stratified Random Sampling v2.tns
- Samples - Binomial.tns
- Samples - Normal.tns [for demonstrating normal sample mean is normally distributed]
- Samples - Uniform.tns [for demonstrating Central Limit Theorem]

Hypothesis Testing & Inference

- NonParametric Assumptions.tns
- Widget: MannWhitneyTest.tns
- Widget: Wilcoxon1Test.tns
- Widget: Wilcoxon2Test.tns
- Normal Approx to MW and Wilcoxon.tns
- Chi Squared Contingency Table.tns
- Chi Squared GOF.tns
- ChiSquared Simulation RxC.tns
- Confidence Intervals v2.tns

Bivariate Analysis

- Bivariate - Limitations.tns
- Bivariate - P and C Intervals.tns
- Bivariate - Regression Line.tns
- Bivariate - Residual Plots 1.tns
- Bivariate - Residual Plots 2.tns
- Bivariate - Sampling.tns
- Bivariate - Sxx Syy Sxy r.tns

Various software packages can support the delivery of AH Statistics - see the Software section of the Links page to access some of them.

some R code for past AH Statistics Exam Papers

With RStudio installed, you can run the .Rmd file, see the output and compare it to hand-written solutions.

The 2023 AH Statistics Conference at Glasgow University included sessions on using RStudio to ...

To support some of the exercises on this website, an Posit Cloud Workspace Project has been created to show how R can be used to perform many of the analysis techniques in the AH Statistics course.

The instructions given below will guide you through...

to access the Posit Cloud Project for the AH Statistics Course

You should be presented with a login screen for Posit Cloud.

Click on '**Sign up**'
in
the bottom right.

Enter an email address, and create a memorable password.

You will then be prompted for a name
for your
account - you can just leave this as your name.

Click on '**Create Account**'

You will see a 'Deploying Project' message. Wait until this ends.

Find the words 'Save a Permanent Copy' along the top right part of the screen. Click on these words.

You should see three main panes, called 'Console', 'Environment' and 'Files'

Find the toolbar that shows '**File Edit Code View Plots Session Build Debug Profile Tools
Help**'

Click on '**View**'

Select
'**Panes**'

Select
'**Pane Layout...**'

In the 4 panel display that appears, the top right panel
is labelled
'Environment, History, Connections....'

Click on this label and select
'**Console**'

Click '**OK**'

You should now see four main panes, called 'Untitled1', 'Console', 'Environment' and
'Files'.

The new
pane that has 'Untitled1' in it is called the 'Source' pane, and it is where the code that will
be run will
appear.

Locate the Toolbar again.

Click on '**Tools**'

Select '**Global
Options...**'

Select '**Appearance**' from the vertical list of
options

In
the Editor Theme box, select '**Cobalt**'

Click the '**OK**'
button

The four panes should now all go to a dark background.

In the 'Environment Pane', look to the far right corner and see two rectangular icons - one small and
one
large. These minimise and maximise the pane, respectively.

Click on the **small
rectangular
icon** in order to minimise the Environment pane.

Congratulations! You have now configured the Posit Cloud Interface to be optimised for running the
code.

You should not have to repeat any of the above steps, going forwards.

In the Files pane, you will see a list of files relating to the AH Statistics course.

Click on
the file
that you wish to use, and it will open in the Source pane.

You should see chunks of code that each have a
{yellow title inside curly brackets}

To the far right
of each title are three icons, the last of which is a green triangle 'play button': *play_arrow*

Clicking
on *play_arrow*
runs the code in that chunk.

The output from running a code chunk appears in two places -
just below
the code chunk in the Source pane, and also in the Console pane in the top right.

You can edit the code and re-run it at any time by clicking on the *play_arrow*

The download .zip file contains:

- Quick Sampling Quizzes
- 8 multiple choice homework quizzes, each of 10 questions
- issue to pupils roughly one every 1 or 2 weeks, after the teaching of sampling methods
- supports pupils consolidating their understanding of sampling techniques
- Which Test Quizzes
- 8 multiple choice quizzes, each of 4 scenarios
- designed to be used over 8 consecutive lessons, after all hypothesis testing methods have been taught.
- issue to individual pupils at the start of a lesson and discussed in that lesson
- pupils have to decide which analysis technique they'd likely use for each situation
- some situations have more than one answer, depending on the assumptions that are made!

Answers to these quizzes may be requested by sending an email to: statistics AT nhost DOT uk

SQA Advanced Higher Statistics course (Official SQA website)

SQA AH Statistics Google Group (Unofficial)

Not Awful and Boring Ideas for Teaching Statistics

Teaching Statistics is Awesome

Statistically, you shouldn't believe the news

Statisticians want to abandon science's standard measure of 'significance'

The likelihood of encountering two identical packs of Skittles

The Royal Statistical Society Schools Lecture 2004: 'Lies and Statistics', Part 1

The Royal Statistical Society Schools Lecture 2004: 'Lies and Statistics', Part 2

Should we worry that half of Americans trust their gut to tell them what's true?

How To Use Statistics To Improve Your Love Life

What Transport for London Learned From Tracking Your Phone On the Tube

Of Poohsticks and pâValues: Hypothesis Testing in the Hundred Acre Wood

How 'random' is Ryanair's seating allocation?

When U.S. Air Force discovered the Flaw of Averages

The shock of the mean: a missing element

How the Central Limit Theorem began

Heart surgery survival chances 'better in the afternoon'

When the normal approximation for Student t isn't good enough

Why You Should Love Statistics [TED talk 12m49s]

Statistical Hypothesis Test Mistakes [You Tube 6m00s]

How Juries are fooled by Statistics [TED talk 21m17s]

Hans Rosling: The best stats you've ever seen [TED talk 19m46s]

Hans Rosling: New insights on poverty [TED talk 18m54s]

Cambridge Mathematics (...how to teach Statistics)

Royal Statistical Society (Teaching Statistics Section)

This is Statistics (by the American Statistical Association)

Significance (by Royal Statistical Society)

CAUSE's collection of humorous statistics resources

Helping Engineers Learn Mathematics (HELM) Booklets 35-43, 45, 46

Simulation of Confidence Intervals for a Sample Mean

Open Middle (challenging stats problems worth solving)

Making Statistics Vital - Activities for the A-Level Statistics Classroom

Royal Statistical Society Significance Magazine

StatLect (a digital textbook on probability and statistics)

Resourceaholic (Statistics Compilation)

Risky Talk with David Spiegelhalter (Podcast)

Student-Made Interactive Learning with Educational Songs (in introductory statistics)

Data Science in a Box (using R)

TI-Nspire Computer Software (Free 30 day trial)

VassarStats: Website for Statistical Computation

Q: Why does this website exist?

A: The intention was for this collection of resources to support AH Statistics Teachers around Scotland in delivering the course, using free resources that are tailored to the course content. Currently, no single published textbook offers this.

Q: I have found a mistake in one of the resources - can it please be fixed?

A: Yes! Just send an email with as much detail as possible to: statistics AT nhost DOT uk

Q: Can I please obtain the original Word documents for the some of the worksheets?

A: That should be possible. Just send a nicely worded email to: statistics AT nhost DOT uk

Q: Who is the author of this website?

A: It's Nevil Hopley. He taught Statistics in Secondary Schools between 1996 and 2023. This website is not affiliated to any organisation.

Q: Does this site use any cookies?

A: No. The only data that is recorded from your visit is your IP address along with the date and time of what navigation tabs you clicked on or files that you downloaded.