AQA Psychology: Research Mathematical
Concepts
The Exam
25% of the marks in your exams (72 marks total) will be research methods. Of that 72, at least 30
will be purely mathematical skills. This means that by number of marks research methods is by far
the most important topic in the course, and the mathematical component should be an easy way
to 30 marks.
Basic Arithmetic and Computation
Fractions may be encountered, with it being necessary to reduce fractions and calculate them
using given numbers. You must also be able to convert them into percentages by dividing the
numerator by the denominator and multiplying by 100, as well as expressing as decimals.
Ratios are also necessary and can be expressed either as a part-to-part ratio in which the ratio
expresses the likelihood of each event next to each other, or a part-to-whole ratio in which the
chosen event is expressed as a ration next to the total number of events. The former can easily be
changed into a fraction, the latter you must add both parts together to get the denominator. You
also need to be able to reduce ratios as with fractions.
Significant figure rounding just refers to making sure to round up when using significant figures,
but an extension of this is orders of magnitude and standard form. An easy way to remember how
to do this is that the power in, for example, 5.4 x 109, is always 1 more than the number of zeroes.
This would be 5,400,000,000. We have moved the decimal nine places. When using numbers
below 1 it will be the exact number of zeroes. We might write 0.0067 as 6.7 x 10 -3, again because
we have moved the decimal 3 places.
The last couple of areas in this section cover the use of mathematical symbols; as well as the
basics, you need approximately equal (~), much more than (>>), much less than (<<) and
proportional to (∝). Interestingly, you also need to be able to make mathematical estimates.
Quantitative Data Analysis
Perhaps the biggest part of the mathematical requirement concerns data analysis; the inspection
of data generated through research using mathematical techniques. This can be termed
descriptive statistics, as the techniques are used to describe patterns in the data. The different
types of data are as follows:
Nominal-The data are in separate non-hierarchical categories such as gender or
hometown. This is categorical and qualitative data.
Ordinal-The data are ordered in some way, but the difference between them is not unitary
such as military rankings or book reviews. This is like a mix between numerical and
categorical, as there is mathematical relationship between categories.
Interval-The data is measured in units of equal intervals, but the zero point is arbitrary. For
example, IQ level of zero would not necessarily mean no intelligence, and zero degrees
centigrade does not mean there is no temperature. IQ of 140 is not necessarily twice as
high as This is numerical data, and examples include height70, so there is no consistent
ratio between intervals.
, Ratio-The data has the above but also a true zero point. Height and pulse rate are easy
examples, as a true zero is meaningful and ratios between intervals are proportionate.
Numerical Data-This includes ratio and interval, and is quantitative. It can be further split
into discrete data, which can only take whole values (e.g. number of pets) or continuous,
which can take any value (e.g. time)
Measures of Central Tendency
Inform us about central, or typical, values for a data set. The mean is the sum of the data divided
by n, which considers all values but therefore misrepresents when there are extreme values, and
cannot be used with categorical data. It also makes little sense to use it with discrete data.
The median is the middle value in an ordered list (the average of the median scores if there are
multiple medians), is not affected by extreme scores, but doesn't reflect all values. The median can
be used for ratio, interval and ordinal data and is particularly useful for the latter.
The mode is the most common value, and is necessary when data is nominal (but there may be
several modes in which case the data is bi-modal). It is also thus useful for discrete data as it is not
affected by extreme values. Bi-modality creates issues.
Measures of Dispersion
These inform us about how spread out, or ‘dispersed’ a data set is.
Includes the range, which is the largest value minus the smallest value. It has become customary
to add 1 to this number, as the bottom number could be up to 0.5 lower and the top number 0.5
higher. As evaluation, it is affected by extreme values and doesn't consider the concentration of
observations; in other words, how closely grouped the data is from the mean.
A more precise method is standard deviation, or the average distance from the mean, which takes
all values into account but may hide extreme values.
Exercise: Consider the following three data sets A, B and C.
A = {9,10,11,7,13}
B = {10,10,10,10,10}
C = {1,1,10,19,19}
a) Calculate the mean of each data set.
b) Calculate the standard deviation of each data set.
c) Which set has the largest standard deviation?
Concepts
The Exam
25% of the marks in your exams (72 marks total) will be research methods. Of that 72, at least 30
will be purely mathematical skills. This means that by number of marks research methods is by far
the most important topic in the course, and the mathematical component should be an easy way
to 30 marks.
Basic Arithmetic and Computation
Fractions may be encountered, with it being necessary to reduce fractions and calculate them
using given numbers. You must also be able to convert them into percentages by dividing the
numerator by the denominator and multiplying by 100, as well as expressing as decimals.
Ratios are also necessary and can be expressed either as a part-to-part ratio in which the ratio
expresses the likelihood of each event next to each other, or a part-to-whole ratio in which the
chosen event is expressed as a ration next to the total number of events. The former can easily be
changed into a fraction, the latter you must add both parts together to get the denominator. You
also need to be able to reduce ratios as with fractions.
Significant figure rounding just refers to making sure to round up when using significant figures,
but an extension of this is orders of magnitude and standard form. An easy way to remember how
to do this is that the power in, for example, 5.4 x 109, is always 1 more than the number of zeroes.
This would be 5,400,000,000. We have moved the decimal nine places. When using numbers
below 1 it will be the exact number of zeroes. We might write 0.0067 as 6.7 x 10 -3, again because
we have moved the decimal 3 places.
The last couple of areas in this section cover the use of mathematical symbols; as well as the
basics, you need approximately equal (~), much more than (>>), much less than (<<) and
proportional to (∝). Interestingly, you also need to be able to make mathematical estimates.
Quantitative Data Analysis
Perhaps the biggest part of the mathematical requirement concerns data analysis; the inspection
of data generated through research using mathematical techniques. This can be termed
descriptive statistics, as the techniques are used to describe patterns in the data. The different
types of data are as follows:
Nominal-The data are in separate non-hierarchical categories such as gender or
hometown. This is categorical and qualitative data.
Ordinal-The data are ordered in some way, but the difference between them is not unitary
such as military rankings or book reviews. This is like a mix between numerical and
categorical, as there is mathematical relationship between categories.
Interval-The data is measured in units of equal intervals, but the zero point is arbitrary. For
example, IQ level of zero would not necessarily mean no intelligence, and zero degrees
centigrade does not mean there is no temperature. IQ of 140 is not necessarily twice as
high as This is numerical data, and examples include height70, so there is no consistent
ratio between intervals.
, Ratio-The data has the above but also a true zero point. Height and pulse rate are easy
examples, as a true zero is meaningful and ratios between intervals are proportionate.
Numerical Data-This includes ratio and interval, and is quantitative. It can be further split
into discrete data, which can only take whole values (e.g. number of pets) or continuous,
which can take any value (e.g. time)
Measures of Central Tendency
Inform us about central, or typical, values for a data set. The mean is the sum of the data divided
by n, which considers all values but therefore misrepresents when there are extreme values, and
cannot be used with categorical data. It also makes little sense to use it with discrete data.
The median is the middle value in an ordered list (the average of the median scores if there are
multiple medians), is not affected by extreme scores, but doesn't reflect all values. The median can
be used for ratio, interval and ordinal data and is particularly useful for the latter.
The mode is the most common value, and is necessary when data is nominal (but there may be
several modes in which case the data is bi-modal). It is also thus useful for discrete data as it is not
affected by extreme values. Bi-modality creates issues.
Measures of Dispersion
These inform us about how spread out, or ‘dispersed’ a data set is.
Includes the range, which is the largest value minus the smallest value. It has become customary
to add 1 to this number, as the bottom number could be up to 0.5 lower and the top number 0.5
higher. As evaluation, it is affected by extreme values and doesn't consider the concentration of
observations; in other words, how closely grouped the data is from the mean.
A more precise method is standard deviation, or the average distance from the mean, which takes
all values into account but may hide extreme values.
Exercise: Consider the following three data sets A, B and C.
A = {9,10,11,7,13}
B = {10,10,10,10,10}
C = {1,1,10,19,19}
a) Calculate the mean of each data set.
b) Calculate the standard deviation of each data set.
c) Which set has the largest standard deviation?
