Mathematical requirements in the NEW 2015 A Level Psychology Deb Gajic (CPsychol, AFBPsS) Head of Psychology The Polesworth School d.gajic@sky.com Thursday 24th September 2015

Mathematical Requirements What’s changed? 10% mathematical requirement at at least level 2 (GCSE) (take calculator into examination) – See specifications and maths appendix OFQUAL requirements refer to ALL specifications https://www.gov.uk/government/uploads/system/uploa ds/attachment_data/file/446829/A_level_science_subje ct_content.pdf Focus on the mathematical skills which are new or which in my opinion people will find most challenging.

Mathematical Requirements Changing mindsets Making I can’t become I can Why does Maths have this effect? People go to great lengths to hide illiteracy, but seem to have no problem saying ‘I can’t do maths’ The challenge: - make maths relevant to psychology, unthreatening, meaningful and active

Mathematical Requirements Changing mindsets Making I can’t become I can Being good at mental maths is not being a great mathematician

Mathematical Requirements Recommended texts Simple Statistics by Francis Clegg ISBN-13: 978-0521288026 Research Methods & Statistics in Psychology by Hugh Coolican ISBN-13: 978-1444170115

D.0 Arithmetic and Numerical Computation

D.0.1 Recognise and use expressions in decimal and standard form Standard form is a way of writing down very large numbers easily. E.g. 1000 = 103 (13 x10 = 103) Small numbers can also be written in standard form. However, instead of the index being positive (in the above example, the index was 3), it will be negative. E.g. 0.05 = 5 × 10-2 The rules when writing a number in standard form are that first you write down a number between 1 and 10, then you write × 10 (to the power of a number)

D.0.1 Recognise and use expressions in decimal and standard form The mean number of neurons in the human brain is 100,000,000,00. Express this in standard form One neuron may be as narrow as 0.004 centimeters in diameter. Express this in standard form

D.0.1 Recognise and use expressions in decimal and standard form e.g. Move the decimal point 11 places or 11 zeros 2) 0.004 = 4x10-3 e.g. Move the decimal point 3 places or 3 zeros.

D.1 Handling Data

D.1.4 Understand Simple Probability Complete the probability activity This activity also covers D.0.2 – Use ratios, fractions and percentages

D.1.4 Understand Simple Probability Type I Error False Positive. Rejecting the null hypothesis, when there is a possibility that the results were due to chance. Often caused by using a significance level that is too lenient e.g. 10%, 0.10, 1 in 10, p≤0.10. Not being cautious enough. Type II Error False Negative. Accepting the null hypothesis, when there is a possibility that the results were significant. Often caused by using a significance level that is too strict e.g. 1%, 0.01, 1 in 100, p≤0.01. Being over cautious.

D.1.4 Understand Simple Probability

D.1.6 Understand the terms mean, median and mode Haribo Sweet Activity Useful for understanding population and sampling and sample sizes, as well as calculating mean, median and mode

D.1.8 Use a statistical test Sign Test This test simply involves counting up the number of positive and negative signs.   Example: - A study was conducted to discover if students changed their attitude towards the death penalty after watching ‘The Green Mile’. Experimental Hypothesis: - Watching the film ‘The Green Mile’ will influence student’s attitudes to the death penalty. (non- directional – two-tailed) AQA Test of choice at AS

D.1.8 Use a statistical test

D.1.8 Use a statistical test Sign Test Add the number of times the least frequent sign appears. In this case the + sign, so S = 1. Look at the critical value tables to obtain the critical value for S, number of score = 9 (as pairs of scores with no change are omitted). Critical Value for a two tailed test = 1, therefore the Null hypothesis can be rejected the test result was statistically significant (most people did change their opinion after watching the film)

D.1.8 Use a statistical test Sign Test A researcher wished to find out if participants had a more positive image of statistics after they had been taught an introductory course. Experimental Hypothesis: - Participants will rate statistics more positively once they have been taught an introductory course. (1-tailed)   NB Ratings are ordinal data, but we are analyzing them at a nominal level, hence the sign test.

D.1.8 Use a statistical test

D.1.8 Use a statistical test

D.1.8 Use a statistical test Sign Test Add the number of times the least frequent sign appears. In this case the + sign, so S = 2. Look at the critical value tables to obtain the critical value for S, number of score = 10 (as pairs of scores with no change are omitted). Critical Value for a one tailed test = 1, therefore the Null hypothesis must be accepted the test result was not statistically significant (most people did not change their opinion after taking the introductory statistics course)

D.1.9 Make order of magnitude calculation Orders of magnitude are used to make very approximate comparisons and reflect very large differences. For example compare 387 with 40,262,030 387 is approximately 400 and 40,262,030 is approximately 40,000,000 Therefore 40,262,030 is approximately 10,000 times bigger than 387 (40,000,00 has 5 more zeros than 400)

D.1.10 Distinguish between levels of measurement Nominal data: a level of measurement where data are in separate categories (Frequencies). Ordinal data: a level of measurement where data are ordered in some way. (Interval & Ratio data can be converted to ordinal) Ordinal data is data that can be placed in rank order e.g. 1st, 2nd, 3rd etc. Used in non-parametric tests

D.1.10 Distinguish between levels of measurement Interval data: a level of measurement where units of equal measurements (a scale with equal intervals) are used e.g. minutes, kilograms, number of words recalled in a memory test or percentage score in an exam. Ratio data is also on a scale with equal intervals, but has a true zero e.g. weight/height, time, distance. Used in Parametric tests

D.1.11 Know the characteristics of normal and skewed distributions

D.1.11 Know the characteristics of normal and skewed distributions Characteristics of a normal distribution curve, also know as a bell- shaped curve or a Gaussian curve: - it is bell-shaped it is symmetrical the mean, median and mode all fall on the same central point. The two tails never touch the horizontal axis.

D.1.11 Know the characteristics of normal and skewed distributions As well as normal distributions, curves can be positively skewed, negatively skewed or bi-modal.

D.1.12 Select an appropriate test – Non-parametric

D.1.12 Select an appropriate test – parametric Conditions for Parametric Testing: - Data is interval or ratio Data is normally distributed Homogeneity of variances. (Standard deviations or variances for the two sets of data are equal)

D.1.12 Select an appropriate test – parametric

D.1.13 Use statistical tables to determine significance Critical Value Tables If there is a R in the name of the test the calculated value must be more than or equal to the critical value. If there is not a R in the name of the test the calculated value must be less than or equal to the critical value.

D.1.14 Understand measures of dispersion, including standard deviation and range Calculating Standard Deviation The requirement to calculate this is hidden in the exemplification for D.1.6. This also covers D.2.2 substitute values into a formula

D.1.14 Understand measures of dispersion, including standard deviation and range

D.1.14 Understand measures of dispersion, including standard deviation and range

D.1.14 Understand measures of dispersion, including standard deviation and range

D.1.14 Understand measures of dispersion, including standard deviation and range   10.233 is the variance

D.2 Algebra

D.2.1 Understand and use symbols Required symbols =, <, <<, >>, >, < Less than << much less than > Greater than >> much greater than Approximately equal to Proportional to Much less/greater use with probability e.g. much less than 5% Proportional to – Stratified sampling Approximately equal e.g. Baron-Cohen Normal = 20.3/25 Tourettes = 20.4/25

D.2.3 Solve simple algebraic equations Degrees of Freedom in a Chi-square Number of values that are free to vary df=(no: of rows-1)(no: of columns-1)

D.2.3 Solve simple algebraic equations Example of a contingency table: -  Piaget Conservation Experiment Hypothesis: 7 year olds will be more likely to be able to conserve than 5 year olds. (Directional - One-tailed)

D.2.3 Solve simple algebraic equations What is the df for the table? It is a 2 X 2 contingency table (2 rows and 2 columns with data) (2-1) X (2-1) 1 X 1 = 1 df = 1

D.3 Graphs

D.3.1 Translate information between graphical, numerical and algebraic forms Bar Chart, Scatter graph, Line graph, Pie Chart Sketching graphs - Remember to label all axis and put a title on it Interpreting graphs - Say what you see, relate to stimulus

D.3.1 Translate information between graphical, numerical and algebraic forms When constructing scattergraphs use mini jelly babies or smiley face stickers instead of crosses This ensures students understand that each point on the graph represents a participant.

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