AQA 7387 SP 2017 v0 1

T

DRAFT 7387

Specification
For teaching from September 2017 onwards
For A-level exams in 2019 onwards

R
AF

DRAFT SPECIFICATION

A-LEVEL
STATISTICS

D

Version 0.1 11 August 2016


DRAFT SPECIFICATION

T

R
AF

D

A-level Statistics DRAFT 7387. A-level exams June 2019 onwards. Version 0.1 11 August 2016

Contents
1 Introduction

5

2.1 Subject content
2.2 Assessments

7
7
8

3 Subject content

9

3.1 Numerical measures, graphs and diagrams
3.2 Probability
3.3 Population and samples
3.4 Introduction to probability distributions
3.5 Binomial distribution
3.6 Normal distribution
3.7 Correlation and linear regression
3.8 Introduction to hypothesis testing
3.9 Contingency tables
3.10 One and two sample non-parametric tests
3.11 Bayes’ theorem
3.12 Probability distributions

3.13 Experimental design
3.14 Sampling, estimates and resampling
3.15 Hypothesis testing, significance testing, confidence
intervals and power
3.16 Hypothesis testing for 1 and 2 samples
3.17 Paired tests
3.18 Exponential and Poisson distributions
3.19 Goodness of fit
3.20 Analysis of variance
3.21 Effect size
3.22 Statistical Enquiry Cycle (SEC)

10
11
11
12
12
13
14
15
16
16
17
17
18
18

D

R

AF

DRAFT SPECIFICATION

2 Specification at a glance

5
5
6

T

1.1 Why choose AQA for A-level Statistics
1.2 Support and resources to help you teach
1.3 Draft specification

4 Scheme of assessment
4.1 Aims
4.2 Assessment objectives
4.3 Assessment weightings

5 General administration
5.1 Entries and codes
5.2 Overlaps with other qualifications

19
20
21
21
22

22
23
23

25
25
25
26

27
27
27

Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration 3


R
AF

D

Are you using the latest version of this specification?
•
•

You will always find the most up-to-date version of this specification on our website at
aqa.org.uk/7387
We will write to you if there are significant changes to the specification.

4 Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration

DRAFT SPECIFICATION

27
27
28
28
28
29
29

T

5.3 Awarding grades and reporting results
5.4 Re-sits and shelf life
5.5 Previous learning and prerequisites
5.6 Access to assessment: diversity and inclusion
5.7 Working with AQA for the first time
5.8 Private candidates
5.9 Use of calculators


A-level Statistics DRAFT 7387. A-level exams June 2019 onwards. Version 0.1 11 August 2016

1 Introduction
1.1 Why choose AQA for A-level Statistics
A-level Statistics is a fantastic choice for students who want to know the facts behind the figures
and want to make sense of the world around us.

T

The logical, problem-solving and numerical skills gained, are useful for many different areas of
employment; from working with a Formula One racing team on aerodynamics, to teaching or stock
market trading.

A specification designed for you and your students

R
AF

DRAFT SPECIFICATION

It goes well with subjects including A-level Biology, Psychology, Geography, Business Studies and
Economics.

This new qualification retains much of the content that we know you and your students enjoy and
you’ll recognise many of the topics. This means you can still use your existing resources. Topics
are clearly and logically structured and include:
•
•
•
•

numerical measures, graphs and diagrams
binomial distribution
correlation and linear regression
hypothesis testing.

Clear, well-structured exams, accessible for all

To enable your students to show their breadth of knowledge and understanding, we’ve created a
simple and straightforward structure and layout for our papers, using a mixture of question styles.
There is one exam paper for AS and there are two exam papers for A-level. Assessment remains
100% exam based.
You can find out about all our Statistics qualifications at aqa.org.uk/mathematics

D

1.2 Support and resources to help you teach

We’ve worked with experienced teachers to provide you with a range of resources that will help
you confidently plan, teach and prepare for exams.

1.2.1 Teaching resources
Visit aqa.org.uk/7387 to see all our teaching resources. They include:

•
•
•
•
•

sample schemes of work and lesson plans to help you plan your course with confidence
teachers' guide that have been checked by AQA
progress tests with engaging on-screen delivery and instant feedback
training courses to help you deliver AQA Statistics qualifications
subject expertise courses for all teachers, from newly qualified teachers who are just getting
started to experienced teachers looking for fresh inspiration.

Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration 5

1.2.2 Preparing for exams
Visit aqa.org.uk/7387 for everything you need to prepare for our exams, including:
•
•
•
•

past papers, mark schemes and examiners’ reports
specimen papers and mark schemes for new courses
Exampro: a searchable bank of past AQA exam questions
example student answers with examiner commentaries.

T

Find out which questions were the most challenging, how the results compare to previous years
and where your students need to improve. ERA, our free online results analysis tool, will help you
see where to focus your teaching. Register at aqa.org.uk/era

For information about results, including maintaining standards over time, grade boundaries and our
post-results services, visit aqa.org.uk/results

R
AF

1.2.4 Keep your skills up-to-date with professional development

Wherever you are in your career, there’s always something new to learn. As well as subject
specific training, we offer a range of courses to help boost your skills.

• Improve your teaching skills in areas including differentiation, teaching literacy and meeting
Ofsted requirements.
• Prepare for a new role with our leadership and management courses.
You can attend a course at venues around the country, in your school or online – whatever suits
your needs and availability. Find out more at coursesandevents.aqa.org.uk

1.2.5 Help and support

Visit our website for information, guidance, support and resources at aqa.org.uk/7387
If you'd like us to share news and information about this qualification, sign up for emails and
updates at aqa.org.uk/from-2017

Alternatively, you can call or email our subject team direct.

E:

D

T: 01483 477655

1.3 Draft specification

This draft qualification has not yet been accredited by Ofqual. It is published to enable teachers to
have early sight of our proposed approach to A-level Statistics. Further changes may be required
and no assurance can be given that this proposed qualification will be made available in its current
form, or that it will be accredited in time for first teaching in September 2017 and first award in
August 2018.

6 Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration

DRAFT SPECIFICATION

1.2.3 Analyse your students' results with Enhanced Results Analysis
(ERA)


A-level Statistics DRAFT 7387. A-level exams June 2019 onwards. Version 0.1 11 August 2016

2 Specification at a glance
This qualification is linear. Linear means that students will sit all their exams at the end of the
course.

Numerical measures, graphs and diagrams (page 10)
Probability (page 11)
Population and samples (page 11)
Introduction to probability distributions (page 12)
Binomial distribution (page 12)
Normal distribution (page 13)
Correlation and linear regression (page 14)
Introduction to hypothesis testing (page 15)
Contingency tables (page 16)
One and two sample non-parametric tests (page 16)
Bayes’ theorem (page 17)
Probability distributions (page 17)
Experimental design (page 18)
Sampling, estimates and resampling (page 18)
Hypothesis testing, significance testing, confidence intervals and power (page 19)
Hypothesis testing for 1 and 2 samples (page 20)
Paired tests (page 21)
Exponential and Poisson distributions (page 21)

Goodness of fit (page 22)
Analysis of variance (page 22)
Effect size (page 23)

T

•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•

D

R
AF

DRAFT SPECIFICATION

2.1 Subject content

Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration 7


2.2 Assessments
Paper 1
What's assessed
Specification content 3.1‒3.10

Questions

R
AF

• Questions requiring multiple choice, short, medium and extended answers including a
Statistical Enquiry Cycle (SEC) question.

Paper 2

What's assessed

Specification content 3.11‒3.21, not precluding 3.1‒3.10.

How it's assessed

• Written exam: 3 hours
• 120 marks
• 50% of A-level
Questions

D

• Questions requiring multiple choice, short, medium and extended answers including a
Statistical Enquiry Cycle (SEC) question.

8 Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration

DRAFT SPECIFICATION

• Written exam: 3 hours
• 120 marks
• 50% of A-level

T

How it's assessed


A-level Statistics DRAFT 7387. A-level exams June 2019 onwards. Version 0.1 11 August 2016

3 Subject content
The subject content of this specification matches that set out in the Department for Education’s
Statistics GCE subject content and assessment objectives document. This content is common to
all exam boards.

T

In addition to this subject content, students should be able to recall, select and apply mathematical
formulae. See Appendix 1 (page 31) and Appendix 2 (page 33) for a list of the DfE prescribed
formulae.

D

R
AF

DRAFT SPECIFICATION

The subject content, aims and learning outcomes, and assessment objectives sections of this
specification set out the knowledge, skills and understanding common to all GCE Statistics exams.

Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration 9


3.1 Numerical measures, graphs and diagrams
Subject content

Additional information

• Interpret statistical diagrams including bar
charts, stem and leaf diagrams, box and
whisker plots, cumulative frequency
diagrams, histograms (with either equal or
unequal class intervals), time series and

scatter diagrams.
• Know the features needed to ensure an
appropriate representation of data using
the above diagrams, and how
misrepresentation may occur.
• Justify appropriate graphical
representation and comment on those
published.
• Compare different data sets, using
appropriate diagrams or calculated
measures of central tendency and
spread: mean, median, mode, range,
interquartile range, percentiles, variance
and standard deviation.
• Calculate measures using calculators and
manual calculation as appropriate.
• Identify outliers by inspection and using
appropriate calculations.
• Determine the nature of outliers in
reference to the population and original
data collection process.
• Appreciate that data can be
misrepresented when used out of context
or through misleading visualisation.

Students will not be required to draw or construct
statistical diagrams.
Students must learn and recall the following:
• the angle in a pie chart is given by x × 360
total

f requency
class width

f requency densit y =

• the formula for calculating the arithmetic mean
is
∑fx
∑f

R
AF

−
x=

• range is

highest value–smallest value

• Interquartile range (IQR) = Q3 – Q1 where Q1 is
the lower quartile and Q3 is the upper quartile
• Outliers lie
• below Q1–1.5(Q3 – Q1) or above Q3+1.5(Q3 –
Q1), or
• outside the limits μ ± 3σ
Students will be given the following information
1

2

Population variance = N ∑ x − μ

1

Population standard deviation =

Sample variance = n − 1 ∑ x − −
x
1

D

Sample standard deviation =

10 Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration

N

2

1

n−1

∑ x−μ

∑ x−−
x

2

2

DRAFT SPECIFICATION

T

• in a histogram


A-level Statistics DRAFT 7387. A-level exams June 2019 onwards. Version 0.1 11 August 2016

Subject content

Additional information

• Know and use language and symbols
associated with set theory in the context of
probability.
• Represent and interpret probabilities using
tree diagrams, Venn diagrams and two-way
tables.
• Calculate and compare probabilities: single,
independent, mutually exclusive and
conditional probabilities.
• Use and apply the laws of probability to
include conditional probability.
• Determine if two events are statistically

independent.

The complement of the set A will be denoted by
the symbol A'.
Students must learn and recall that for A and B
to be independent events:

T

• P(A ∩B) = P(A) P(B)
• P(A|B)=P(A) and
• P(B|A)=P(B)

R
AF

DRAFT SPECIFICATION

3.2 Probability

3.3 Population and samples

Additional information

• Know both simple (without replacement) and
unrestricted (with replacement) random
samples.
• Know how to obtain a random sample using
random numbers tables or random numbers
generated on a calculator.

• Evaluate the practical application of random
and non-random sampling techniques: simple
random, systematic, cluster, judgmental and
snowball, including the use of stratification (in
proportional and disproportional ratios) prior to
sampling taking place.
• Know the advantages and limitations of
sampling methods.
• Make reasoned choices with reference to the
context in which the sampling is to take place.
Examples include, but are not limited to: market
research, exit polls, experiments and quality
assurance.
• Understand the practical constraints of
collecting unbiased data.

Students should know that for a random
sample of size n:

D

Subject content

• every member of the population is equally
likely to be included
• all subsets of the population of size n must
be possible
or that

• every possible sample of size n must be

equally likely to occur.
Students should appreciate that snowball
sampling can be used to reach populations
that are difficult to sample when using other
sampling methods eg drug users.

Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration 11


3.4 Introduction to probability distributions
Subject content

Additional information

• Know and use terms for variability: random,
discrete, continuous, dependent and
independent.
• Calculate probabilities and determine
expected values, variances and standard
deviations for discrete distributions.
• Use discrete random variables to model real
world situations.
• Know the properties of a continuous
distribution.
• Interpret graphical representations or
tabulated probabilities of characteristic
discrete random variables.
• Interpret rectilinear graphical
representations of continuous distributions.

Students will be expected to learn and recall the
formulae for calculating the expected value and
the variance of a discrete probability distribution,
namely:

T

E X = μ = ∑ xi pi

Variance:

2

2

Var X = σ = ∑ xi − μ pi
2
2
2
2
= ∑ xi pi − μ = E X − μ

R
AF

With reference to the uniform distribution.

3.5 Binomial distribution
Subject content

Additional information

• Know when a binomial model is appropriate (in
real world situations including modelling
assumptions).
• Know methods to evaluate or read probabilities
using formula and tables.
• Calculate and interpret the mean and variance.

Students may use calculator functions to
obtain binomial probabilities and are advised
to do so. Students will be given the formulae
for calculating individual binomial
probabilities:

P X =x =

n
x

px 1 − p n − x

and for the mean and variance of a binomial
distribution:

D

Mean = n p

Variance = n p 1 − p

Students will not be expected to derive the
formulae for the mean and variance.
Students may be asked to use the binomial
distribution in the context of simple
acceptance sampling used for batch quality
control.

12 Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration

DRAFT SPECIFICATION

Expectation mean :


A-level Statistics DRAFT 7387. A-level exams June 2019 onwards. Version 0.1 11 August 2016

3.6 Normal distribution
Subject content

Additional information

• Know the specific properties of the normal
distribution, and know that data from such an
underlying population would approximate to
having these properties, with different samples
showing variation.
• Apply knowledge that approximately 2 of

Students should learn and recall that

approximately 95% of observations lie within
μ ± 2σ and approximately 99.8% of
observations lie within μ ± 3σ

•
•

T

•

Students should learn and recall that the
normal distribution may be used to
approximate a binomial distribution when:
• n ≥ 20 and p ≈ 0.5
• or n p ˃10

R
AF

DRAFT SPECIFICATION

3

observations lie within μ ± σ , and equivalent
results for 2σ and 3σ .
Determine probabilities and unknown
parameters with a normal distribution.
Apply the normal distribution to model real world
situations.

−
Use the fact that the distribution of X has a
normal distribution if X has a normal
distribution.
Use the fact that the normal distribution can be
used to approximate a binominal distribution
under particular circumstances.

Students may use calculator functions to
obtain information for a normal distribution
directly and are advised to do so.

D

•

Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration 13


3.7 Correlation and linear regression
Subject content

Additional information

• Calculate (only using appropriate
technology ‒ calculator) and
interpret association using
Spearman’s rank correlation
coefficient or Pearson’s product
moment correlation coefficient.

• Use tables to test for significance of
a correlation coefficient.
• Know the appropriate conditions for
the use of each of these methods of
calculating correlation and determine
an appropriate approach to
assessing correlation in context.
• Calculate (only using appropriate
technology ‒ calculator) and
interpret the coefficients for a least
squares regression line in context;
interpolation and extrapolation, and
use of residuals to evaluate the
model and identify outliers.

When evaluating Spearman’s coefficient, candidates will
be expected to:
• rank both variables consistently
• rank tied values appropriately
• use a calculator to find the correlation coefficient.

R
AF

• find correlation coefficients and the coefficients for a
least squares regression line directly from the
calculator
• write the equation of a least squares regression line
in the form
• y = ax + b

• interpret correlation coefficients and the coefficients
in a least squares regression line in a given context.
Students will be given the following:
6∑ d

2

rs = 1 − n n2 −i1

Product moment correlation coefficient:

r=

=

S xy

S xx × S yy

∑ xi yi −

2

∑ xi −

∑ xi

n

2

∑ xi ∑ yi

n

2

∑ yi −

∑ yi

2

n

Coefficients for least squares regression line: least
squares regression line of y on x is y = a + bx where
a=−
y − b−
x

D

The regression coefficient of y on x is

b=

S xy
S xx

14 Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration

DRAFT SPECIFICATION

T

Students will be expected to:


A-level Statistics DRAFT 7387. A-level exams June 2019 onwards. Version 0.1 11 August 2016

Subject content

Additional information

• Use and demonstrate understanding of the
terms parameter, statistic, unbiased and
standard error.
• Know and use the language of statistical
hypothesis testing: null hypothesis, alternative
hypothesis, significance level, test statistic, 1tail test, 2-tail test, critical value, critical region,
and acceptance region and p-value.
• Know that a sample is being used to make an
inference about the population and appreciate
the need for a random sample and of the
necessary conditions.
• Choose the appropriate hypothesis test to
carry out in particular circumstances.
• Conduct a statistical hypothesis test for the
proportion in the binomial distribution and

interpret the results in context using exact
probabilities or, where appropriate, a normal
approximation.
• Conduct a statistical hypothesis test for the
mean of a normal distribution with known or
assumed variance, from a large sample, and
interpret the results in context.
• Know the importance of appropriate sampling
when using hypothesis tests and be able to
critique the conclusions drawn from rejecting
or failing to reject a null hypothesis by
considering the test performed.

Students will be expected to know and use
that:

T

• a parameter is a numerical property of a
population
• a statistic is a numerical property of a
sample and is a function only of the values
in the sample and contains no unknown
parameters.
In a hypothesis test on a population
proportion, candidates may use either π or p
as the parameter in their hypotheses.

The test statistic for a test on a binomial
proportion, using the normal distribution as an

approximation, will be given:

R
AF

DRAFT SPECIFICATION

3.8 Introduction to hypothesis testing

p− p

p 1− p
n

N 0,1

The test statistic for a mean using the normal
distribution will be given:
−

X −μ

N 0,1

D

σ
n

Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration 15

3.9 Contingency tables
Subject content

Additional information

• Construct contingency tables from real data,
combining data where appropriate, and
interpret results in context.
• Use a χ 2 test with the appropriate number of
degrees of freedom to test for independence in
a contingency table and interpret the results of
such a test.
• Know that expected frequencies must be
greater than, or equal to, 5 for a χ 2 test to be
carried out and understand the requirement for
combining classes if that is not the case.

The formula for a χ test statistic will be given

2

∑

Oi − Ei 2
Ei

T

Students will be expected to know how to find
the number of degrees of freedom and that
questions set will not require the use of Yates’
correction.

R
AF

Students must follow the rule to combine
classes when expected frequencies are
smaller than 5, and 'pooling' is permissible.
Students will not be required to use Yates’
correction.

3.10 One and two sample non-parametric tests
Additional information

• Use sign or Wilcoxon signed-rank tests to
investigate population median in single
sample tests and also to investigate for
differences using a paired model.
• Use the Wilcoxon rank-sum test to investigate
for difference between independent samples.

Students will be expected to use the sign test,
or the Wilcoxon signed-rank test to:

D

Subject content

• test the value of a single population median
based on a single sample
• test for a difference between two population
medians based on a sample of 'paired' data.
Students will be expected to test for a
difference between two population medians,
based on two independent samples, using the
Wilcoxon rank-sum test (this is also known as
the Mann-Whitney test).

16 Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration

DRAFT SPECIFICATION

Students may use either 'independent' or
'associated' in their hypotheses.


A-level Statistics DRAFT 7387. A-level exams June 2019 onwards. Version 0.1 11 August 2016

3.11 Bayes’ theorem
Subject content

Additional information

• Calculate and use conditional probabilities
to include Bayes’ theorem for up to three
events, including the use of tree diagrams.

Students will be given the formula for Bayes’
theorem and will be expected to use it in
problems that involve up to three events.

Subject content

T

3.12 Probability distributions

P Aj × P B Aj
∑3i = 1 P Ai × P B Ai

Additional information

• Know the use and validity of distributions which
could be appropriate in a particular real world
situation: binomial, normal, Poisson and
exponential.
• Evaluate the mean and variance of linear
combinations of independent random variables
through knowledge that if X i are independently

Students will be given the following:

R
AF

DRAFT SPECIFICATION

P Aj B =

distributed μi , σ 2i then ∑ ai X i is distributed
∑ ai μi ,  ∑ a2i σ 2i .

Poisson probability formula:
−λ λ

P X =x =e

x

x!

and knowledge of the mean and variance
both being λ

The exponential cumulative probability
formula:

D

• Evaluate probabilities for linear combinations of
P X ≤ x = 1 − e− λx
two or more independent normal distributions
and apply this knowledge to practical situations. and knowledge of the mean and variance
1
1
being λ and 2 respectively.
λ

The formulas

E X Y = E X E Y and
Var aX ± bY
2

2

= a Var X + b Var Y

will be given.
Students are expected to learn and recall
that:

E X ±Y = E X ±E Y

Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration 17


3.13 Experimental design
Additional information

T

Students will be expected to explain and
• Know and discuss issues involved in
discuss these concepts in a given context.
experimental design: experimental error,
randomisation, replication, control and

experimental groups, and blind and double
blind trials.
• Know the benefits of use of paired comparisons
and blocking to reduce experimental error.
• Use completely random and randomised block
designs.

R
AF

3.14 Sampling, estimates and resampling
Subject content

Additional information

• Use and demonstrate understanding of terms
parameter, statistic, unbiased and standard
error.
• Know the use of the central limit theorem in
−
the distribution of X where the initial
distribution, X , is not normally distributed and
the sample is large.

Students will be expected to know and use
that:

• a parameter is a numerical property of a
population
• a statistic is a numerical property of a

sample and is a function of only the values
in the sample and contains no unknown
parameters.
Students are expected to know that:

D

• the central limit theorem may be used when
the sample size (of random samples) is
sufficiently large (n ≥ 30)
• it is only necessary to use the central limit
theorem when the underlying population is
not normally distributed.

18 Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration

DRAFT SPECIFICATION

Subject content


A-level Statistics DRAFT 7387. A-level exams June 2019 onwards. Version 0.1 11 August 2016

Subject content

Additional information

• Use confidence intervals for the mean using z
or t as appropriate, interpreting results in
practical contexts.

• Know that a change in sample size will affect
the width of a confidence interval.
• Evaluate the strength of conclusions and
misreporting of findings from hypothesis
tests, including the calculation and
importance of the power of a hypothesis test.
• Know that sample size can be changed to
potentially elicit appropriate evidence in a
hypothesis test.
• Interpret Type I and Type II errors, in
hypothesis testing and know their practical
meaning.
• Calculate the risk of a Type II error.
• Know the difference and advantages of using
critical regions or p-values as appropriate in
real life contexts in all tests in this subject
content.

Students are expected to know and use the tdistribution when the sample size is small (n <
30) and the population standard deviation, σ, is
unknown.

T

Students will be expected to learn and recall
the formulae for constructing a confidence
interval on a population mean:

−
x ± z or t × standard error

Students will be expected to know and recall
that:

R
AF

DRAFT SPECIFICATION

3.15 Hypothesis testing, significance testing, confidence
intervals and power

• a Type I error is when the null hypothesis is
true but is rejected
• a Type II error is when the null hypothesis is
false but is accepted
and that these should be interpreted in the
given context.
Students are expected to know and recall that
the power of a test is given by

D

Power = 1 – P(Type II error).

Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration 19


3.16 Hypothesis testing for 1 and 2 samples
Subject content

Additional information

Know how to apply knowledge about carrying
out hypothesis testing to conduct tests for the:

Together with the content already mentioned in
A1.8, candidates will be given and expected to
select and use the following:
• test statistic for a mean using t distribution:

tn − 1

S
n

• test statistic for difference of two
independent normal means with known
variances :
−

−

X − Y − μx − μ y
σ2

N 0,1

+ ny
y

R
AF

σ 2x
nx

• test statistic for difference of two
independent normal means with unknown
but equal variance:
−

−

X − Y − μx − μ y
1

S 2p

S 2p =

nx

1

+n
y

tnx + n y − 2 where

nx − 1 S 2x + n y − 1 S 2y
nx + n y − 2

• test statistic for the difference in two
binomial proportions:
p1 p2
s . error

where s . error =

p1 × n1 + p2 × n2
n1 + n2

D

and where p =

p× 1− p ×

20 Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration

1

n1

1

+n
2

DRAFT SPECIFICATION

−

X −μ

T

• mean of a normal distribution with unknown
variance using the t distribution
• difference of two means for two independent
normal distributions with known variances
• difference of two means for two independent
normal distributions with unknown but equal
variances
• difference between two binomial proportions
• interpret results for these tests in context.


A-level Statistics DRAFT 7387. A-level exams June 2019 onwards. Version 0.1 11 August 2016

3.17 Paired tests
Subject content

Additional information

Use sign, Wilcoxon signed-rank or paired t-test,
understanding appropriate test selection and
interpreting the results in context.

Students will be expected to learn and recall
necessary conditions for the validity of these
tests, and may be required to use these to
select the test that is most appropriate in a
given context.
Students will be given:

T
−

X −μ
S
n

tn − 1

3.18 Exponential and Poisson distributions

R
AF

DRAFT SPECIFICATION

Paired t-test:

Additional information

• Determine when a Poisson model is appropriate
(in real world situations including modelling
assumptions).

• Determine when an exponential distribution is
appropriate (and its relationship to the Poisson
distribution as a model of the times between
randomly occurring Poisson events).
• Evaluate probabilities for Poisson and
exponential distributions and know the
corresponding mean and variance.

Students will be expected to know and recall
the conditions necessary for a Poisson
model to be appropriate and to explain or
discuss whether these conditions are likely
to be present in a given context.

D

Subject content

Students will be expected to know and use
the relationship between corresponding
Poisson and exponential distributions, in a
given context.
Students will be given the following:
in a Poisson distribution, Po(λ),

P X = x = e− λ ×

λx
x!

Mean = λ, variance = λ

In an exponential distribution with parameter
λ:
Probability density function = λe
1

mean = λ , variance =

1

− λx

λ2

Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration 21


3.19 Goodness of fit
Subject content

Additional information

Conduct a statistical goodness of fit test for
Students will be expected to know how to find
binomial, Poisson, normal and Exponential
the number of degrees of freedom and that
distributions or for a specified discrete distribution questions set will not require the use of Yates’
O−E 2
correction.

as an approximate χ 2 statistic.
using ∑ E

The formula for a chi-squared test statistic will
be given:
Oi − Ei 2
Ei

R
AF

∑

3.20 Analysis of variance

Additional information

• Conduct one way analysis of
variance, using a completely
randomised design with
appreciation of the underlying
model with additive effects
and experimental errors
distributed as N(0, σ 2 ).
• Conduct two-way analysis of
variance without replicates,
using a randomised block
design with blocking.
• Identify assumptions and
interpretations in context.

Students will only be required to use one-way ANOVA or twoway ANOVA (and will not be required to use a Latin square).

D

Subject content

Students will be given the following:

Analysis of variance (one-way and two-way):

one − factor model xi j = μ + ai + εi j, where εi j N 0, σ
2

T2

total sum of squares SS T = ∑i ∑ j xi j − n

T2

T2

between groups sum of squares SS B = ∑i ni − n
i

two − factor model with m rows and n columns

xi j = μ + ai + β j + εi j, where εi j N 0, σ 2
2

T2

total sum of squares SS T = ∑i ∑ j xi j − mn

R2

T2

between rows sum of squares SS R = ∑i ni − mn
C2

T2

between columns sum of squares SS c = ∑i mj − mn

22 Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration

2

DRAFT SPECIFICATION

T

Students must follow the rule to combine
classes when expected frequencies are
smaller than 5, and 'pooling' is permissible.


A-level Statistics DRAFT 7387. A-level exams June 2019 onwards. Version 0.1 11 August 2016

Subject content

Additional information

• Know the notion of effect size as a
complementary methodology to standard
significance testing, and apply in
authentic contexts.
• Know and use Cohen’s d in simple
situations.

Students will be given Cohen's formula:

d=

x−1 − x−2
s
n1 − 1 s21 + n2 − 1 s22
n1 + n2 − 2

T

where s =

3.22 Statistical Enquiry Cycle (SEC)

The Statistical Enquiry Cycle (SEC) underpins the study of Statistics. Students need to be able to
apply the knowledge and techniques outlined in this section within the framework of the SEC. The
cycle covers five stages:

R
AF

DRAFT SPECIFICATION

3.21 Effect size

•
•
•
•
•

initial planning
data collection
data processing and presentation
interpretation of results
evaluation and review.

The detail of the SEC that is common to all exam boards is provided in Appendix 4 (page 39).
During their learning students should develop their understanding of the SEC through a variety of
authentic contexts. Practical experience of the cycle is integral to their understanding of the
principles of the SEC.

3.22.1 Initial planning

Students must understand the importance of initial planning when designing a line of enquiry or
investigation including:
identifying factors that may be related to the problem under investigation
defining a question or hypothesis (or hypotheses) to investigate

deciding what data to collect, and how to collect and record it, giving reasons
engaging in exploratory data analysis in order to investigate the situation
developing a strategy for how to process and represent the data giving reasons
justifying the proposed plan with regards ensuring a lack of bias.

D

•
•
•
•
•
•

3.22.2 Data collection
Students must recognise the constraints involved in sourcing data including:
• when designing unbiased collection methods for primary sample data
• when researching sources of secondary data, including from reference publications, the internet
and the media
• the importance of declaring the data collection methodology, including appreciating the
importance of acknowledging sources
• appreciating the inherent bias that may be incorporated through the use of leading questions
either by accident or through agenda driven design.

Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration 23


3.22.3 Data processing and presentation
Students must understand a range of techniques in order to process, represent and discuss data
including:

• organising and processing data, including an understanding of how technology can be used
• make inferences about the population using appropriately chosen diagrams and summary
measures to represent data including an understanding of outputs generated by appropriate
technology
• appreciating how to avoid misrepresentation of data.

analysing/interpreting diagrams and calculations/measures
drawing together conclusions that relate to the questions and hypotheses addressed
using appropriate tests to determine the statistical significance of the findings
discussing the reliability of findings.

R
AF

•
•
•
•

T

Students must appreciate the need to consider the context of the problem when interpreting
results:

Students must show an understanding of the importance of the clear and concise communication
of findings and key ideas, and awareness of target audience.

3.22.5 Evaluation and review

Students must be able to understand the importance of evaluating statistical work including:

identifying weaknesses in approaches used to collect or display data
recognising the limitations of findings by considering sample size and sampling technique
suggesting improvements to statistical processes or presentation
refining processes to elicit further clarification of the initial hypothesis.

D

•
•
•
•

24 Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration

DRAFT SPECIFICATION

3.22.4 Interpretation of results


A-level Statistics DRAFT 7387. A-level exams June 2019 onwards. Version 0.1 11 August 2016

4 Scheme of assessment
Find past papers and mark schemes, and specimen papers for new courses, on our website at
aqa.org.uk/pastpapers
This specification is designed to be taken over two years.
This is a linear qualification. In order to achieve the award, students must complete all
assessments at the end of the course and in the same series.

T

All materials are available in English only.

Our A-level exams in Statistics include questions that allow students to demonstrate their ability to:
•
•
•
•

recall information
draw together information from different areas of the specification
apply their knowledge and understanding in practical and theoretical contexts
understanding of the Statistical Enquiry Cycle (SEC).

R
AF

DRAFT SPECIFICATION

A-level exams and certification for this specification are available for the first time in May/June
2019 and then every May/June for the life of the specification.

4.1 Aims

Courses based on this specification should encourage students to:

D

• understand the application of techniques within the framework of the statistical enquiry cycle
and the research methodologies used in experiments and surveys
• apply statistical techniques to data sourced from a variety of contexts, appreciating when

samples or population data could be used and applying appropriate sampling techniques
• generate and interpret the diagrams, graphs and measurement techniques used in performing
statistical investigations
• have an understanding of how visualisations of multivariate data are used to gain a qualitative
understanding of the multiple factors that interact in real life situations, including, but not limited
to, population characteristics, environmental considerations, production variables etc
• understand how technology has enabled the collection, visualisation and analysis of large data
sets to inform decision-making processes in public, commercial and academic sectors
• develop skills in interpretation and critical evaluation of methodology including justifying the
techniques used for statistical problem solving
• apply appropriate mathematical and statistical formulae, as set out in appendix 1 and appendix
2.

4.2 Assessment objectives
Assessment objectives (AOs) are set by Ofqual and are the same across all A-level Statistics
specifications and all exam boards.
The exams will measure how students have achieved the following assessment objectives.
• AO1: Demonstrate knowledge and understanding using appropriate terminology and notation,
of standard statistical techniques used:

Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration 25