# Mathematical requirements and exemplification

## AS

In order to be able to develop their skills, knowledge and understanding in Psychology, students need to have been taught, and to have acquired competence in, the appropriate areas of mathematics as indicated in the table of coverage below.

Overall, at least 10% of the marks in assessments for Psychology will require the use of mathematical skills. These skills will be applied in the context of AS Psychology and will be at least the standard of higher tier GCSE mathematics.

The following tables illustrate where these mathematical skills may be developed during teaching or could be assessed.

This list of examples is not exhaustive. These skills could be developed in other areas of specification content. Other areas where these skills could be developed have been exemplified throughout the specification.

Mathematical skills Exemplification of mathematical skill in the context of AS Psychology
Arithmetic and numerical computation
Recognise and use expressions in decimal and standard form. For example, converting data in standard form from a results table into decimal form in order to construct a pie chart.
Use ratios, fractions and percentages. For example, calculating the percentages of cases that fall into different categories in an observation study.
Estimate results. For example, commenting on the spread of scores for a set of data, which would require estimating the range.
Handling data
Use an appropriate number of significant figures. For example, expressing a correlation coefficient to two or three significant figures.
Find arithmetic means. For example, calculating the means for two conditions using raw data from a class experiment.
Construct and interpret frequency tables and diagrams, bar charts and histograms. For example, selecting and sketching an appropriate form of data display for a given set of data.
Understand simple probability. For example, explaining the difference between the 0.05 and 0.01 levels of significance.
Understand the principles of sampling as applied to scientific data. For example, explaining how a random or stratified sample could be obtained from a target population.
Understand the terms mean, median and mode. For example, explaining the differences between the mean, median and mode and selecting which measure of central tendency is most appropriate for a given set of data. Calculate standard deviation.
Use a scatter diagram to identify a correlation between two variables. For example, plotting two variables from an investigation on a scatter diagram and identifying the pattern as a positive correlation, a negative correlation or no correlation.
Use a statistical test. For example, calculating a non-parametric test of differences using the data from a given experiment.
Make order of magnitude calculations. For example, estimating the mean test score for a large number of participants on the basis of the total overall score.
Know the characteristics of normal and skewed distributions. For example, being presented with a set of scores from an experiment and being asked to indicate the position of the mean (or median, or mode).
Understand measures of dispersion, including standard deviation and range. For example, explaining why the standard deviation might be a more useful measure of dispersion for a given set of scores, eg where there is an outlying score.
Understand the differences between qualitative and quantitative data. For example, explaining how a given qualitative measure (for example, an interview transcript) might be converted into quantitative data.
Understand the difference between primary and secondary data. For example, stating whether data collected by a researcher dealing directly with participants is primary or secondary data.
Algebra
Understand and use the symbols: =, <, <<, >>, >, ∝, ~. For example, expressing the outcome of an inferential test in the conventional form by stating the level of significance at the 0.05 level or 0.01 level by using symbols appropriately.
Graphs
Translate information between graphical, numerical and algebraic forms. For example, using a set of numerical data (a set of scores) from a record sheet to construct a bar graph.
Plot two variables from experimental or other data. For example, sketching a scatter diagram using two sets of data from a correlational investigation.

## A-level

In order to be able to develop their skills, knowledge and understanding in Psychology, students need to have been taught, and to have acquired competence in, the appropriate areas of mathematics as indicated in the table of coverage below.

Overall, at least 10% of the marks in assessments for Psychology will require the use of mathematical skills. These skills will be applied in the context of A-level Psychology and will be at least the standard of higher tier GCSE mathematics.

The following tables illustrate where these mathematical skills may be developed during teaching or could be assessed.

This list of examples is not exhaustive. These skills could be developed in other areas of specification content. Other areas where these skills could be developed have been exemplified throughout the specification.

Mathematical skills Exemplification of mathematical skill in the context of A-level Psychology
Arithmetic and numerical computation
Recognise and use expressions in decimal and standard form. For example, converting data in standard form from a results table into decimal form in order to construct a pie chart.
Use ratios, fractions and percentages. For example, calculating the percentages of cases that fall into different categories in an observation study.
Estimate results. For example, commenting on the spread of scores for a set of data, which would require estimating the range.
Handling data
Use an appropriate number of significant figures. For example, expressing a correlation coefficient to two or three significant figures.
Find arithmetic means. For example, calculating the means for two conditions using raw data from a class experiment.
Construct and interpret frequency tables and diagrams, bar charts and histograms. For example, selecting and sketching an appropriate form of data display for a given set of data.
Understand simple probability. For example, explaining the difference between the 0.05 and 0.01 levels of significance.
Understand the principles of sampling as applied to scientific data. For example, explaining how a random or stratified sample could be obtained from a target population.
Understand the terms mean, median and mode. For example, explaining the differences between the mean, median and mode and selecting which measure of central tendency is most appropriate for a given set of data. Calculate standard deviation.
Use a scatter diagram to identify a correlation between two variables. For example, plotting two variables from an investigation on a scatter diagram and identifying the pattern as a positive correlation, a negative correlation or no correlation.
Use a statistical test. For example, calculating a non-parametric test of differences using data from a given experiment.
Make order of magnitude calculations. For example, estimating the mean test score for a large number of participants on the basis of the total overall score.
Distinguish between levels of measurement. For example, stating the level of measurement (nominal, ordinal or interval) that has been used in a study.
Know the characteristics of normal and skewed distributions. For example, being presented with a set of scores from an experiment and being asked to indicate the position of the mean (or median, or mode).
Select an appropriate statistical test. For example, selecting a suitable inferential test for a given practical investigation and explaining why the chosen test is appropriate.
Use statistical tables to determine significance. For example, using an extract from statistical tables to say whether or not a given observed value is significant at the 0.05 level of significance for a one-tailed test.
Understand measures of dispersion, including standard deviation and range. For example, explaining why the standard deviation might be a more useful measure of dispersion for a given set of scores, eg where there is an outlying score.
Understand the differences between qualitative and quantitative data. For example, explaining how a given qualitative measure (for example, an interview transcript) might be converted into quantitative data.
Understand the difference between primary and secondary data. For example, stating whether data collected by a researcher dealing directly with participants is primary or secondary data.
Algebra
Understand and use the symbols: =, <, <<, >>, >, ∝, ~. For example, expressing the outcome of an inferential test in the conventional form by stating the level of significance at the 0.05 level or 0.01 level by using symbols appropriately.
Substitute numerical values into algebraic equations using appropriate units for physical quantities. For example, inserting the appropriate values from a given set of data into the formula for a statistical test, eg inserting the N value (for the number of scores) into the Chi Square formula.
Solve simple algebraic equations. For example, calculating the degrees of freedom for a Chi Square test.
Graphs
Translate information between graphical, numerical and algebraic forms. For example, using a set of numerical data (a set of scores) from a record sheet to construct a bar graph.
Plot two variables from experimental or other data. For example, sketching a scatter diagram using two sets of data from a correlational investigation.