What is statistics really about?

Neil Sheldon

Royal Statistical SocietyCentre for Statistical Education &

Manchester Grammar School

What is statistics really about?

What sorts of things should we, as teachers of statistics, be doing in schools?

What is statistics really about?

What sorts of things should we, as teachers of statistics, be doing in schools?

What technical knowledge do we need?

What is statistics really about?

What sorts of things should we, as teachers of statistics, be doing in schools?

What technical knowledge do we need?What practical understanding do we

need?

What is statistics really about?

What sorts of things should we, as teachers of statistics, be doing in schools?

What technical knowledge do we need?What practical understanding do we

need?What interpretative skills do we need?

What is statistics really about?

What sorts of things should we, as teachers of statistics, be doing in schools?

What technical knowledge do we need?What practical understanding do we

need?What interpretative skills do we need?How can we part of statistically sound

decision making in our schools?

Understanding data

What do you (and your students) know about the data of the world around us?

Understanding data

What do you (and your students) know about the data of the world around us?

What is the population of the world?

Understanding data

What do you (and your students) know about the data of the world around us?

What is the population of the world?At what rate is it growing?

Understanding data

What do you (and your students) know about the data of the world around us?

What is the population of the world?At what rate is it growing?At what rate, measured in planets, are we

consuming the Earth’s resources?

Understanding data

What do you (and your students) know about the data of the world around us?

What is the population of the world?At what rate is it growing?At what rate, measured in planets, are we

consuming the Earth’s resources?How does the rate of consumption vary

from country to country?

Understanding data

What about spotting, and correcting, inaccurate data?

Understanding data

What about spotting, and correcting, inaccurate data?

Trade between the US and Canada is reckoned to amount to $1 million per second (BBC). Is that correct? If not can you correct it?

Understanding data

What about spotting, and correcting, inaccurate data?

Trade between the US and Canada is reckoned to amount to $1 million per second (BBC). Is that correct? If not can you correct it?

People in Britain drop about half a tonne of litter each per year (Highways Agency). Is that correct or in need of correction?

Understanding data

The calorie counts used as the foundation for diet plans and healthy-eating guidance for the past 18 years may be wrong, a report suggests.

The recommended daily intake of calories could be increased by up to 16%, a draft report by the Scientific Advisory Committee on Nutrition said.

Intake levels are currently 2,000 calories for women and 2,500 for men.

Understanding concepts

What level of conceptual understanding do you have?

And how much of that conceptual understanding can you hope to convey to your students?

Understanding concepts

Too often statistics can be seen as a set of ‘recipes’. Plug the numbers into the formula and don’t ask too many questions.

Can you explain – would you expect your students to be able to explain – the principles of estimation or hypothesis testing or confidence intervals?

Consider some specific issues …

Understanding concepts

R A Fisher, one of the most distinguished of all statisticians, went to his death arguing that there is no role for the alternative hypothesis in significance tests.

So why do we have alternative hypotheses in specifications, textbooks, exam papers?

Understanding concepts

Suppose you are doing a chi-squared test for goodness of fit and the test statistic comes out to be very small – say, in the left hand 5% tail of the distribution.

Some books tell you to conclude that the fit is ‘too good to be true’ and that the data have been fiddled. Other books reject this interpretation.

Which is correct? And why?

Understanding concepts

Exam question:

Use the given data to find a 95% confidence interval for μ. State the probability that the true value of μ lies in your calculated interval.

Understanding concepts

Exam question:

Use the given data to find a 95% confidence interval for μ. State the probability that the true value of μ lies in your calculated interval.

Exam question:

A student says the probability that the true value of μ lies in a 95% confidence interval she has calculated is 0.95.

Explain why that is wrong and give a correct interpretation of the confidence interval for μ.

Making decisions

We live in information-based societies and an information-based age

Making decisions

We live in information-based societies and an information-based age

Decisions that affect all our lives should be based on evidence

Making decisions

We live in information-based societies and an information-based age

Decisions that affect all our lives should be based on evidence

(Almost all) evidence needs statistical interpretation

Making decisions

We live in information-based societies and an information-based age

Decisions that affect all our lives should be based on evidence

(Almost all) evidence needs statistical interpretation

Statistical understanding is a vital life skill

The problem solving approach

Case Study: Value Added

“The height of a man, in nine cases out of ten, can be told from the length of his stride. It is a simple enough calculation, though there is no use my boring you with figures.”

– Sherlock Holmes

in A Study in Scarlet

by Arthur Conan Doyle

Case Study: Value Added

stride

height

Case Study: Value Added

stride

height

Case Study: Value Added

Case Study: Value Added

Mean GCSE score plotted against baseline score

Case Study: Value Added

baseline

outcome

What is this line really telling us?

Case Study: Value Added

baseline

outcome

And shouldn’t we actually be thinking about lines like this?

Case Study: Value Added

A school sets pupils according to their performance on the baseline test, and keeps them in those sets.

How will eventual results compare from set to set?

How will value added compare from set to set?

Case Study: Value Added

baseline

outcome

Case Study: Value Added

A school sets pupils according to performance in end of year examinations (re-setting each year).

How will eventual results compare from set to set?

How will value added compare from set to set?

Case Study: Value Added

“Using Value Added allows fair comparisons to be made. Your pupils’ Maths results, for example, are compared with other pupils’ Maths results, so subject difficulty does not affect the outcome. Low ability pupils are compared with other low ability pupils, so a low ability intake is no disadvantage, while similarly a high ability intake is no advantage.”

Case Study: Value Added

So, re-setting each year, average value added will be …?

independent of set higher in the high ability sets higher in the low ability sets

Case Study: Value Added

baseline

outcome

Case Study: Value Added

Case Study: Value Added

“Standardised residuals are shown with confidence limits at 2 (95%) and 3 (99.7%) standard deviations.”

“If average standardised residual lies within [these] bounds you cannot draw any conclusions.”

What statistics is really about

Neil Sheldon

RSSCSE & Manchester Grammar School

The purpose of The purpose of statistics is statistics is insight, not insight, not

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