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Mathematical requirements in the NEW 2015 A Level Psychology
Deb Gajic(CPsychol, AFBPsS)Head of Psychology
The Polesworth [email protected]
Thursday 24th September 2015
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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/upload
s/attachment_data/file/446829/A_level_science_subject_content.pdf
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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
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Mathematical Requirements
• Changing mindsets• Making I can’t become I can• Being good at mental maths is not being a great mathematician
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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
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D.0 Arithmetic and Numerical Computation
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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)
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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
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D.0.1 Recognise and use expressions in decimal and standard form
• Standard Form• 1) 100,000,000,000 = 1011 (111 x 10=1011)
• 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.
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D.1 Handling Data
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D.1.4 Understand Simple Probability
Probability
• Complete the probability activity • This activity also covers D.0.2 – Use ratios, fractions and
percentages
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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.
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D.1.4 Understand Simple Probability
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D.1.6 Understand the terms mean, median and mode
Haribo Sweet Activity
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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)
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D.1.8 Use a statistical test
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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)
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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.
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D.1.8 Use a statistical test
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D.1.8 Use a statistical test
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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)
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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)
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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.
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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.
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D.1.11 Know the characteristics of normal and skewed distributions
Normal Distribution of IQ
0
2
4
6
8
10
12
40 50 60 70 80 90 100
110
120
130
140
150
160
IQ (Mental/Chronological Age x 100)
Fre
qu
ency
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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.
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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.
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D.1.12 Select an appropriate test – Non-parametric
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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)
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D.1.12 Select an appropriate test – parametric
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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.
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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
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D.1.14 Understand measures of dispersion, including standard deviation and range
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D.1.14 Understand measures of dispersion, including standard deviation and range
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D.1.14 Understand measures of dispersion, including standard deviation and range
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D.1.14 Understand measures of dispersion, including standard deviation and range
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D.2 Algebra
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D.2.1 Understand and use symbols
• Required symbols• =, <, <<, >>, >, • < Less than << much less than• > Greater than >> much greater than• Approximately equal to• Proportional to
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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)
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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)
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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
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D.3 Graphs
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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
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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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Any Questions?
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