SADC Course in Statistics Graphical summaries for quantitative data Module I3: Sessions 2 and 3

SADC Course in Statistics

Graphical summaries for quantitative data

Module I3: Sessions 2 and 3

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Learning ObjectivesStudents should be able to:

• Present data in a histogram – and interpret data when shown a histogram

• Present data in a boxplot – and interpret data in a boxplot

• Recognise advantages and limitations – of each method of presentation

• Explain what is gained and lost from data summary• Interpret graphical summaries to answer questions

– concerning proportions, – extremes, – medians – and quartiles

• Resolve simple problems with graphical displays– when real data (not text-book examples) are used

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Session Overview

Activity 1: Presentation to introduce the sessions

Activity 2: Demonstration on histograms in Excel

Activity 3: Practical covering the same ideas– CAST Chapter 2.1– Histograms– Population pyramids

Activity 4: Practical on boxplots and percentage points– CAST Chapter 2.2– Boxplots in Excel

Activity 5: Presentation continued

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Activity 1- Case studies• Case studies used in these sessions are:

– Rice Survey– Zambia Rainfall Data – The Swaziland Crop Cutting Survey

• The were introduced in Modules B1 and B2 – so for many this will be a reminder.

• The rice survey and the Swaziland Crop Cutting– were already used in Session 1 of this Module.

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Rice surveyUsed repeatedly

in slightly different forms

In CAST as shown here

In demonstration

And in Excel

Qualitative and quantitative variables to analyse

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Zambia Rainfall data

• Farmers are migrating from Southern Zambia– citing climate change as the reason– they can no longer grow the crops as before

• A local NGO – acknowledges climate change in general, – but believes improved farming practices is more

important– wherever farmers locate

• They question the evidence– for climate change in the pattern of rainfall– as it affects farming strategy

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Data analysed in these sessions

Total rainfall from 1 Jan to 31 March – called SeasonTot

Number of rain days in the same period - Scount

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Original daily values are also available

Not needed for analysis here, but used for checking

Also useful if further questions posed

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Zambia rainfall continued:

• Here we use the annual data – on the final worksheet– preparing data for analysis is done in Module I2

• We have access to the raw data – for checking purposes – and in case other variables are needed on a

later occasion

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Swaziland Crop Cutting Survey

• Annual survey– Of agricultural holdings– And areas planted– Then yields from a crop-cutting exercise

• Data from 2005 made available

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Person-level data

Ages will be analysed in these sessions

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Yield data

The dry weights will be analysed

Analysis overall and just for maize

The zero yields cause a slight problem

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Activity 2 – demonstration of histograms

• Before the practical (which is activity 3)• Follow the demonstration• On histograms and population pyramids in Excel

• It shows• Use of Excel• But keeping control – you must remain in charge• And not be limited by the software

• So it shows how to resolve problems• As well as how to use Excel

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Activity 3 – practical with CAST and Excel

• Using CAST to understand histograms

• Then use Excel to construct them• Being observant – as was shown in the demonstration• And keeping control

• Remember the aims• Are more to understand statistics• Rather than to practice with Excel• Excel is just the tool

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An example with CAST

Practice with small data sets – as shown here and also with large data sets

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Population pyramid in CAST

How close to this display can you get with Excel?

Interpret this display

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Activity 4: Boxplots and data summary

• Now do the demonstration

• And these two practical exercises

• Then return to the remaining slides

• For a discussion of the key points

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Topics for the class discussion

• What was interesting?

• What did you discover

• What was difficult?

• What needs further discussion?

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Boxplots and histograms – CAST page 2.2.3

Are you clear how boxplots and histograms relate?

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Boxplots show outliers – CAST page 2.2.4

And this makes them very useful for data exploration as well as summary

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You can calculate percentage points

• The formula

r * (n + 1)/100

• for the r’th % point

• Should now hold no fears

• For example– when there are 11 observations– and you want the median– use 50 * (11+1)/100 = 6– the median is the 6th highest in the sorted data

• If necessary look again at practical 2

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Practical problems with real data

• This always happens

• You saw a problem – with the rainfall data– and with the crop yields

• The solution always involves being observant

• You can follow guidelines for a good analysis

• But not always simply obey rules

• Become a data detective instead!

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Learning ObjectivesAre you now able to:• Present data in a histogram

– and interpret data when shown a histogram

• Present data in a boxplot – and interpret data in a boxplot

• Recognise advantages and limitations – of each method of presentation

• Explain what is gained and lost from data summary• Interpret graphical summaries to answer questions

– concerning proportions, – extremes, – medians – and quartiles

• Resolve simple problems with graphical displays– when real data (not text-book examples) are used

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These sessions were largely on graphical summaries

The next sessions consider numerical summaries of the data