Processing single and multiple variables

Processing single and multiple variables Module I3 Sessions 6 and 7

Learning objectives • Students should be able to: • Provide and interpret the appropriate summary statistics • for practical examples of quantitative data. • Relate the general ideas of statistics • in relation to variability, with the measures of variability • Recognise the role of statistics in “taming” variability • Construct and interpret a simple analysis of variance (ANOVA) table • Explain why both the standard deviation and variance • are used to summarise variation

Contents • Activity 1: This presentation • Activity 2: Practical 1 - Review • A further quick check that you are comfortable • with the summary statistics • Activity 3: Practical 2 • Apply the summaries to real data • And see what happens when there are outliers, etc • Activity 4: Practical 3 • Processing multiple variables • To see whether variation can be explained • Which introduces the “Analysis of Variance” (ANOVA) • As a descriptive tool • Activity 5: Review of the ideas

Why variation is SO important • From D. S. Moore • In Statistics: A Guide to the Unknown – 4th Edition • “Variation is everywhere • Individuals vary. • Repeated measurements on the same individual vary. • The science of statistics • provides tools for dealing with variation” • These are the tools we examine here

CAST and summary statistics We continue to use CAST in these sessions

The aim of Practical 1 • Understanding simple formulae remains important • See the examples in this session • e.g. stdev, mdev, cv • Can you calculate them in Excel • Using built-in functions • Or from first principles?

Practical 1 – using built-in functions Example using data from the statistics glossary These terms all use Excel’s built-in functions As we show on the next slide

Practical 1 - review The statistics as Excel functions The terms should be (or become) familiar

Practical 1 - continued Excel functions From first principles

DFID and climate – again! Reducing the vulnerability of the poor to current climate variability is the starting point for adaptation to climate change. Climatic variability is a fundamental driver of poverty in poor countries. The climate is changing and it is highly likely that it will worsen poverty and hinder efforts to achieve the Millennium Development Goals. The poor cannot cope with current climatic variation in many parts of the world, but this issue is often ignored in poverty assessments or national development planning. Responses to existing climatic variability should be mainstreamed into national development plans and processes. Current responses by individuals and governments to the impacts of climate variability can be used as the basis for adaptation to the increasing climatevariabilitythat will be associated with longer-term climate change. Interpreting variability is so important

Practical 2 – summaries for climatic data The start of the rains is important to many people And is very variable from year to year Consider the effect of “oddities” on the summary values

Practical 3 – Introducing ANOVA • The example of rice yields is used • The yields are very variable • The lowest is less than 20 (t/ha*10) • The highest is more than 60 (t/ha*10) • The standard deviation = 11 (t/ha*10) • The farmers use different varieties • Could knowing the varietyexplain some of the variation? • Variation is not so much the problem • Unexplained variation IS the problem

You use Excel and CAST ANOVA table Sums of squares Mean squares Degrees of freedom

The terms and an example

Understanding the terms Total corrected sum of squares devsq function in Excel – practical 1 d.f. = (n-1) Overall mean square This IS the variance

Understanding the terms continued Residual (unexplained) or within groups sum of squares Is much smaller than the overall SS Residual mean square (residual variance) Is therefore also much smaller than the overall variance

Understanding the terms continued again Overall standard deviation = √18.07 = 4.25 Residual (unexplained) standard deviation = √4.97 = 2.2 Is correspondingly much smaller

Most used measures of variation • This example is why the standard deviation • and the variance • Are the most used measures of variation • Even if they are not so simple to interpret • You can “do arithmetic” with them • You can split the variation • into explained • and unexplained • using these terms • This doesn’t work with the quartiles • or the mean deviation

Learning objectives • Are you now able to: • Provide and interpret the appropriate summary statistics • for practical examples of quantitative data. • Relate the general ideas of statistics • in relation to variability, with the measures of variability • Recognise the role of statistics in “taming” variability • Construct and interpret a simple analysis of variance (ANOVA) table • Explain why both the standard deviation and variance • are used to summarise variation

Now you know more about variability The next sessions show how to interpret the results as statements of risk etc

Processing single and multiple variables