SADC Course in Statistics

Risks and return periods

Module I3 Sessions 8 and 9

Learning objectives

• From this session you should be able to:

• Generalise the 5-number summary • to give any percentile, or risk level

• Explain risks in a variety of ways, • to suit different users.

• Be able to interpret a cumulative frequency curve to specify

• values for a given risk, • and risks for a given value.

Climate risks and other risks

• People have to take risks

• If they knew the size of the risk• e.g. 1 year in 10• or 10% chance

• They would have the information• To plan their action

• Without this information• they have to guess• often conservatively• sometimes rashly

• Can we help?• By interpreting the variability• As statements of risk• That people can use

Contents

• Activity 1: This presentation

• Activity 2: Peter Cooper interview• climate risks

• Activity 3: Demonstration of risks in CAST

• Activity 4: Practical 1• the results from the interview• learning about risks and return periods – CAST

• Activity 5: Practical 2• Calculating risks in Excel• To estimate the chance of solar cooking• Using sunshine data

• Activity 6: Review• Summarising data well

From DFID key sheet 6 2004, www.dfid.gov.uk

Peter Cooper

ICRISAT

Linking current climatic

variability

(using the historical data)

to climate change

Activity 2: Interview with Peter Cooper

• Particularly the points about data

• And risks for farmers

• Discussed on the next slides

Watch the interview or use the transcript

• Nitrogen recommended for maize (52kg/ha) – but not adopted

• Why not? – Too expensive and thought to be too risky. – We asked “how much could farmers afford”? – The answer was about 17kg N /ha

• ‘Risk and returns’ analyses was done – by a crop simulation program (APSIM)– with 47 years of daily historical climate data

• To compare the risks– with no fertilizer, 17kg and 52kg

Investment Returns on N-applicationto Maize - Masvingo, Zimbabwe

0%

20%

40%

60%

80%

100%

-10.0 -5.0 0.0 5.0 10.0 15.0

Z$ return /Z$ invested

%C

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1 bag AN/ha

recommended

An example of “accelerated learning, using historical climate data (Masvingo, Zimbabwe)

Simulated Maize Yield, Masvingo, Zimbabwe

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1952 1962 1972 1982 1992

Gra

in y

ield

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a)

N0

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N52

Investment Returns on N-applicationto Maize - Masvingo, Zimbabwe

0%

20%

40%

60%

80%

100%

-10.0 -5.0 0.0 5.0 10.0 15.0

Z$ return /Z$ invested

%C

han

ce o

f E

xcee

din

g

1 bag AN/ha

recommended

An example of “accelerated learning” - results

Fertilizer “failed” in a few years

Sometimes it increased yields a little

“Usually” it increased yields a lot

Probability or ‘Rates of Return’(how many years out of ten?)

Impact: Extension Services, Fertilizer Traders and ICRISAT,

•recently successfully evaluated nitrogen “micro-dosing”

•with 200,000 farmers in

Zimbabwe – still expanding.

rate of return on 52 kg/ha

rate of return on 17 kg/ha

Result: Good probability of higher rate of return with

lower inputs

Activity 3: Cast and risks

• Some risks have already been seen• For example with boxplots• See next slide

• CAST has a new chapter on risks and reurn periods

• Which we review here• And then investigate• in Practical 1

• How should you phrase risks• So they are easily understood

Starting points – some risks already

Boxplots and risks – sessions 2/3

CAST and risks

Expressing risks in appropriate ways

probability percentage

rate

Exercises too!

Activity 4: Practical 1

• Results from the Peter Cooper interview

• Then work on CAST• Working in pairs• To practice explanations to your partner

• If you can explain a topic• and explain your reasoning

• Then you probably understand it

Solar cooking Case study:Sunshine data

• Module B1 Session 8 describes the problem• Here we examine the risk of not having

enough sun• Data:

• The raw data has be made into variables for analysis• But they are still available as in the Zambia rainfall data

• Objectives:• Find proportion of days when cooking is possible• Find whether sunshine early morning is related to this

proportion• So can you reduce the risk, by knowing the state of

early part of the day?

Adopting a solar cooker

• The context• Adopting a solar cooker• depends on many things, some statistical, others not

• One statistical aspect• What proportion of days can it be used?• We therefore analyse the data to find out• What is the risk?

• Then, use the ideas from Session 7• Can we reduce the unexplained variability?• By using a related measurement, - early morning sunshine• We can not reduce the risk• But we can reduce the (last minute) risk• And hence help people to be able to plan better

Activity 5: Practical 2 – Excel for risks

Getting the summary

Plotting the summary

% of days with < 3hrs

Learning objectives

From these sessions you should be able to:

• Generalise the 5-number summary • to give any percentile, or risk level

• Explain risks in a variety of ways, • to suit different users.

• Be able to interpret a cumulative frequency curve to specify

• values for a given risk, • and risks for a given value.

Review

• Now you have the tools and skills to process– Factors (categorical or qualitative data)

• Using frequencies, proportions and percentages

– Variates (quantitative data)• Using means and medians• And quartiles, extremes, standard deviations• And proportions (risks), percentiles (return periods)

• You also know to use other measurements– to reduce the unexplained variation

Variability can partly be explained by the variety

Variability shown graphically (Sessions 2/3)

Variation shown numerically (Sessions 4/5)You can interpret measures of variation including s.d.

So are able to picture the data if given a summary

Limitations of each summary statistic, e.g.

Sessions 6/7: Reducing unexplained variation

If it could be done as well as this, then seasonal forecasting would be in good shape!

Overall variationVariation after forecast

The Analysis of variance was introduced

Showing both the variance and s.d. are used

Applying the information

• Swaziland crop cutting survey• Further analysis to be done

• To examine the relationships • between yield of maize and various inputs• like fertilizer and variety

• What might cause variation?• Perhaps early planting is an important variable?• Currently it has not been measured

• In the future• The discussions on explaining variation• Are leading to its measurement from now on!

In Sessions 8 and 9 here we looked at risks

Risks can be stated in different

ways

The cumulative frequency

curve is to be interpreted

Next we see how all these summaries can be displayed in tables