Analysis of Variance (ANOVA) is used to test a hypothesis of differences between the means of three or more groups. This teach yourself worksheet provides an introduction to Analysis of Variance including how to do this using SPSS.

This teach yourself worksheet will show you how to produce box and whisker plots by hand. Box Plots are summary plots based on the median and interquartile range.

5 questions. Qualitative, quantitative random variables, types of sampling, frequencies, stem and leaf plot, descriptive statistics. Numbas resources have been made available under a Creative Commons licence by Bill Foster and Christain Perfect, School of Mathematics & Statistics at Newcastle University.

. 1. Given descriptions of 3 random variables, decide whether or not each is from a Poisson or Binomial distribution. 2. Application of the Poisson distribution given expected number of events per interval. Finding probabilities using the Poisson distribution. 3. Application of the binomial distribution given probabilities of success of an event. Finding probabilities using the binomial distribution. 4. Given a random normal variable X as N(m, var) find P(X > a),a > m; P(X < b), b < m. 5. Given uniform distribution X, calculating the expectation and variance. Also finding P(X=a) for a given value a.6. Question on the exponential distribution involving a time intervals and arrivals application, finding expectation and variance. Also finding the probability that a time interval between arrivals is less than a given period. All parameters and times randomised. Numbas resources have been made available under a Creative Commons licence by the School of Mathematics & Statistics at Newcastle University.

5 questions. 1. Finding the confidence interval at either 90%, 95% or 99% for the mean given the mean and standard deviation of a sample. The population variance is not given and so the t test has to be used. Various scenarios are included. 2. Finding the confidence interval at either 90%, 95% or 99% for the mean given the mean of a sample. The population variance is given and so the z values are used. Various scenarios are included. 3. Provided with information on a sample with sample mean and standard deviation, but no information on the population variance, use the t test to either accept or reject a given null hypothesis. 4. Provided with information on a sample with sample mean and known population variance, use the z test to either accept or reject a given null hypothesis. 5. Given two sets of data, sample mean and sample standard deviation, on performance on the same task, make a decision as to whether or not the mean times differ. Population variance not given, so the t test has to be used in conjunction with the pooled sample standard deviation. Link to use of t tables and p-values in Show steps. Numbas resources have been made available under a Creative Commons licence by the School of Mathematics & Statistics at Newcastle University.

3 questions. 1. Uses the chi-squared test to see if there is any significant difference in preferences. 2. Find out whether the data presented in this question follows a Poisson distribution. Uses the chi-squared test. 3. The human resources department of a large finance company is attempting to determine if an employee's performance is influenced by their undergraduate degree subject. Personnel ratings are used to judge performance and the task is to use expected frequencies and the chi-squared statistic to test the null hypothesis that there is no association. Numbas resources have been made available under a Creative Commons licence by the School of Mathematics & Statistics at Newcastle University.

This teach yourself worksheet explains how to calculate the mean, median and mode, which are the most commonly used measures of central tendancy or average for a data set.

This is a Welsh language version of the Probability & Statistics Facts, Formulae and Information Leaflet. It is designed to be printed on A3 as a double-sided folded leaflet. Print quality is printer dependant. An onscreen version is available in mathcentre. The leaflets were translated by Dr Tudur Davies, a Coleg Cymraeg Cenedlaethol Lecturer of Mathematics, at the Institute of Mathematics, Physics & Computer Science, Aberystwyth University. Funding from the Coleg Cymraeg Cenedlaethol is gratefully acknowledged.

In this case study video, Analysis of Variance (ANOVA) is used to assess whether average student rent difffers by type of accommodation. The video was scripted by John Marriott (Royal Statistical Society Centre for Statistical Education) and presented by Dr Alun Owen (Loughborough University) and Steve Joiner and Nick Blenkin (both Coventry University). There is also an accompanying video resource listed with this case study which looks at the Problem Solving Approach (PSA) that should be used to handle this type of problem.

How to use SPSS to compute a chi-square test for 2-way tables and interpret the output (including coefficient, effect size and corresponding p-value). This resource from the "SPSS Tutorial Series" is contributed to the statstutor Community project by Christine Pereira, Brunel University and reviewed by Cheryl Voake-Jones, University of Bath. It was developed with sigma resource development funding.

A Quick Reference worksheet on the Chi-squared test for Two-Way Tables. The zip file contains the pdf worksheet and two Excel data files that accompany it. This resource has been contributed to the statstutor Community Project by Mollie Gilchrist and Peter Samuels, Birmingham City University and reviewed by Ellen Marshall, University of Sheffield. The zip file contains two associated data files.

This teach yourself worksheet will show you how to perform a Chi-Squared test for association when you have a contingency table formed from two categorical variables. The focus is on hand calculation but also includes some nots on how to do this using SPSS.

This is a zip file containing the SPSS data set called colours.sav for use with Chi-Squared tests of Association Using SPSS (Worksheet). Note: please save this file to your PC before extracting its contents.