# Advanced statistics teaching resources: Chi-squared distribution

Resources and ideas for mathematics, advanced statistics, chi-squared distribution, written by teachers to support teaching and learning

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#### A-level (Post 16) Statistics Revision Worksheets

These worksheets are useful revision aids that include mixed questions to different a-level statistic topics. Solution sheets are provided.

#### S2 EDEXCEL Powerpoints

These are powerpoints and associated pupil notes I have used to deliver S2 to my Y12 further mathematics class. They are tailored to the EDEXCEL S2 syllabus. Please contact me if you notice errors or you have any other comments and please leave feedback - would be nice to know if people are using them or find them useful.

#### Higher C1, C2 Revision PowerPoint - Post 16.

An interactive PowerPoint which goes over each topic and exam type questions of C1 and C2. It has full solutions and markers comments. I usually give pupils a copy of this as a revision aid, it’s an excellent resource!

#### Hypothesis testing and Chi-squared

This presentation introduces the students to hypothesis testing using normal distribution. It starts by explaining what a hypothesis test is, the key language used and also covers type 1 and type 2 errors.Also included is a presentation that shows students how to use Chi-squared test to find a goodness of fit. It covers all parts of chi-squared from a basic introduction to very clear examples, including using the standard results tables (don't forget to move them to show the answers underneath). It also goes on to contingency tables including Yates' correction.SMART Notebook Express presentations can be used for free by using SMART online or by downloading SMART software, also free, I use it because it allows a more interactive presentation than a powerpoint. Just search 'SMART Notebook Express' and try it with my free SMART resource.

#### Statistics 2 powerpoints

A set of powerpoints covering all topics in S2. Examples labelled WB correspond to the separately attached 'Workbook&' (I give this as a single booklet so pupils have a clear model answer to each topic). References to Exercises are from the Pearson Edexcel S2 textbook.

#### Chi squared test of independence

Power Point presentation, 29 slides, Explaining what is Chi squared test of independence, using examples to show how to perform the test, and show how to use GDC to calculate chi-squared, based on IB Standard Level Mathematical Studies Syllabus. For a preview of the power point copy the following link on your browser: https://drive.google.com/file/d/0B8z00qLZV7OlV1cxZFBGQjZXZG8/view?usp=sharing

#### Limitations of the chi-squared test

Power Point presentation, 9 slides, Explaining what are the limitations when performing the Chi squared test of independence, using examples to show how to overcome those limitations, based on IB Standard Level Mathematical Studies Syllabus. For a preview of the power point copy the following link on your browser: https://drive.google.com/file/d/0B8z00qLZV7Olb2YwcUlqb1g3UGs/view?usp=sharing

#### Statistics and Probability

Discrete and continuous random variables, expectation algebra, chi-squares and goodness of fit, hypothesis testing, confidence levels CLT and distribution of sample means..

#### Goodness of Fit and Chi Squared.

Introduction to the concept of testing for independence, goodness of fit for discrete and continuous distributions combined with hypothesis testing.

#### A Level Biology- Stats

A collection of resources I have picked up and adapted along the way when teaching statistic elements of A Level Biology. These resources focus on Chi Squared and Students T Test. The stats booklet I refer to is an unedited version from another user which can be found via a TES search.

#### Statistics 2

This bundle includes all the topics needed to cover the S2 AQA course including; Discrete and Continuous Random Variables Poisson Distribution Estimation Hypothesis Testing Chi-squared

#### Chi squared worksheet- A level geography- Rivers

Chi squared worksheet- A level geography- Rivers.Contains an introduction to the purpose of chi squared and then gives a partially blank table to fill in, complete with a writing frame with gaps to fill in the analysis from the critical value table.

#### Edexcel S2 Revision Cards

These S2 revision cards can be used as an individual or class activity. Individuals can ask friends/relatives to test them using these cards. For use in class, hand out one laminated card per pupil. They circulate round the class, pairing up to ask and answer their questions, then swapping cards and pairing up with someone else. It's a nice active revision lesson. Please do let me know if I&'ve made any errors on these cards.

#### MEI stats 2 power point presentation

This presentation covers the Poisson distribution, The normal distribution, samples and hypothesis testing and Bivariate data. Including approximations and hints and tips. The resource is also extremely useful just before exams if printed out as flash cards to induce mathematical thinking before students enter an exam

#### Chi squared test and contingency table (Biology and maths focus)

Powerpoint and examples on turning maggots and fingerprint types

#### Binomial Distribution

Introduction, formula, mean and variance

#### Binomial Distribution

Using Binomial Distribution cumulative probability tables

#### Confidence Intervals Worksheet

Short Exercise with brief solutions

#### S2 Definitions

These definitions are based on past edexcel paper mark schemes. I think getting your students to learn these definitions the night before the exam should ensure they get all the marks for the definitions in the exam.

#### Poisson Distribution

Formula, tables, mean, variance

#### S2 Revision sheets

A collection of summary/revision sheets for S2

#### Continuous Random Variables

Probability density functions and cumulative distribution functions

#### A level Statistics: Poisson Distribution worksheet

Examples with full worked solutions for the students to annotate and follow.

#### Sampling

Notes and worksheets on sampling

#### Interactive graphs of the Binomial and Poisson Distributions - spreadsheet

An interactive Excel spreadsheet that graphs the Binomial and Poisson distributions, with sliders to affect the probability for the Binomial, and lambda for the Poisson. The graphs update instantly so that you can see how the distributions change as the parameters change. Two further sheets overlays the normal distribution (with the relevant mean and standard deviation), showing how well the normal curve models these distributions. I suggest that it is shown via projector/SWB, and the teacher manipulates the slider to give students a more intuitive grasp of the distributions.

#### Maths Further Statistics:Hypothesis Testing sheet

Binomial and Poisson

#### Central Limit Theorem Simulation. Post 16.

Illustrates the Central Limit Theorem in Statistics, by means of a simulation, where you can add up to 10 Uniform(0,1) random variables and observe the shape of the resulting distribution (shown with a histogram and a frequency polygon) getting closer to the Bell Shaped Curve as you increase the number of random variables, intervals and simulations.

#### Statistics: Hypothesis Testing worksheet

Examples with full worked solutions for the students to annotate and follow.

CLT and CI

#### Identifying Distributions

Classification activity to identify the appropriate statistical model for different situations (Binomial, Poisson, Normal, Continuous Uniform Distributions)