Higher Education Academy Psychology Learning and Teaching Conference, Bath, July 2008
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Higher Education Academy Psychology Learning and Teaching Conference, Bath, July 2008 Development of an interactive visual workspace to aid the intuitive understanding of ANOVA (Analysis of Variance) Richard Stephens & Sol Nte School of Psychology. Importance of Statistics in Psychology.

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Higher Education Academy Psychology Learning and Teaching Conference, Bath, July 2008Development of an interactive visual workspace to aid the intuitive understanding of ANOVA (Analysis of Variance)Richard Stephens & Sol NteSchool of Psychology

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Importance of Statistics in Psychology Conference, Bath, July 2008

  • People are the subjects in Psychology research

  • People vary e.g. cleverness, speediness, attention to detail, etc.

  • Statistics offer a counter-argument to: “What if all the brainy people were in the experimental group?”

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Psych students + statistics = Conference, Bath, July 2008

  • “Surface learning" (Marton & Saljo, 1984) v.“Deep learning" (e.g. Richardson, 2005)

  • How to encourage psych students to process statistics at a deep(er) level?

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A specific example Conference, Bath, July 2008

  • ANOVA (Analysis of Variance)

  • Used where a study includes groups and we want to know whether group means are different

  • I think you need to grasp 6 concepts to understand ANOVA properly (to integrate info and process it more deeply)…

  • Histograms/ distributions

  • Variance

  • The F ratio

  • “Significance”

  • Type I error

  • Underlying assumptions

  • Q: How can these be taught in a more integrated fashion?

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Our idea Conference, Bath, July 2008

  • A software applet and tutorial package presenting a medium rendering ANOVA and its assumptions visually and dynamically

  • Aimed to demonstrate key concepts, so facilitating in students a more intuitive grasp of ANOVA and its assumptions

  • Mills (2002; Journal of Statistics Education) recommends computer simulation methods for teaching statistics (but notes absence of empirical evaluation studies)

  • Existing web-based ANOVA demonstration applets (see links on final slide) criticised:

    • lack an intuitive interface

    • omit assumptions of ANOVA

    • not evaluated

  • We tried to rectify these problems and we included an empirical evaluation study

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Literature review Conference, Bath, July 2008

  • We could find no formal evaluations of comparable software applets

  • But there are reports of positive student evaluations of other demonstrative teaching methods applied to ANOVA...

  • Software that graphically presented ANOVA designs (Rasmussen, 1996);

  • A demonstration of ANOVA sources of variance using cardboard boxes of different weights (Sciutto, 2000)

  • A classroom exercise demonstrating the effects of violations of ANOVA assumptions (Refinetti, 1996)

  • Conclusion: there is pedagogic merit in developing and empirically evaluating a novel software applet for teaching ANOVA and its assumptions

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  • Two normal distributions Conference, Bath, July 2008

  • Right is moveable, morphable and can be viewed as a curve or histogram

  • The distributions are generated algorithmically in real-time (i.e. NOT animations)

  • Generated using the highly skewable log-normal distribution, given by the formula

  • Controls vary the location (), shape () and scale (m), adjusting the core properties of the blue distribution

  • Added an algorithm allowing adjustment of N to explore sample size and power

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ANOVA Demo Conference, Bath, July 2008

  • Learning outcomes:

    • How ANOVA works: F = between grps / within grps variance

    • Homogeneity of variance assumption

    • Normality assumption & kurtosis

    • Normality assumption & skewness

    • Relationship between sample size and statistical power

  • Disk

  • www

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Evaluation Conference, Bath, July 2008

  • A classroom comparison study in Y1 Psyc research methods module

  • Aimed to assess, empirically, the dynamic interactive aspect, so

    • 59 experimental group participants used the software online (moveable)

    • 52 control participants studied paper copies (static)

  • 10-item MCQ class test applied twice: immediately and after a 1 hour delay

  • An 8-item qualitative feedback questionnaire inbetween

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Evaluation Conference, Bath, July 2008


  • P’pants answered 6.54 items on the class test correctly (standard deviation 2.3), but..

  • No effect of group, F(1,106) < 1, no effect of delay, F(1,106) = 1.238, p = 0.268, and no group x delay interaction, F(1,106) < 1

  • The control group responded slightly more favourably on the qualitative items (chi-sq p>0.05)

  • 89 subsequent Blackboard (VLE)visits, average visit time 2.5 minutes – the longest average visit time of all course items

  • We did see improvements on the module examination…

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Evaluation Conference, Bath, July 2008

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Conclusion Conference, Bath, July 2008

  • Likely to be an improvement (exam perf), but could not pinpoint the interactive aspect as necessary

  • Over-stringent control condition???

  • Useful class exercise + in lectures

  • Significant amount of assumed knowledge, e.g. the normal distribution and its depiction in a histogram???

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Math(s) anxiety Conference, Bath, July 2008

  • “A general fear of contact with mathematics, including classes, homework and tests” (Hembree, 1990)

  • Predicted maths performance in a mixed sample of adults (Miller & Bichsel, 2004)

  • In the late 80s classroom interventions (e.g. using microcomputers) were not effective at reducing maths anxiety (Hembree, 1990)

  • But…

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3 principles Conference, Bath, July 2008

  • Appearance should be the antithesis of anxiety; cuteness (Marcus, 2002)

  • NOT abstract; metaphor of data drifting down from the real world to the statistics world

  • Incorporated a game mode to address the need to achieve “deep learning”by allowing students to “learn by doing”

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Demonstration of the normal distribution/ histograms Conference, Bath, July 2008

  • Learning outcomes – to explain:

    • What the normal distribution is;

    • How it is depicted with a histogram;

    • How to produce a histogram;

    • Properties of the normal distribution that make it useful in statistics (e.g. 68% of values fall within 1 standard deviation of the mean; the mean is at the centre, etc.)



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Using computer graphics to illustrate key concepts underlying basic statistics

  • People seem to think it’s a good idea even if there’s not much empirical support

  • Attractive to funders

  • Don’t be too stringent in your choice of control when doing a first evaluation

  • Can be creative – good to be so

  • Need a good programmer!

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References underlying basic statistics

  • Dancey, C.P. & Reidy, J. (2002). Statistics without maths for psychology. 2nd Edition. Harlow: Prentice Hall.

  • Hembree, R. (1990). The nature, effects, and relief of mathematics anxiety. Journal For Research In Mathematics Education, 21, 33-46.

  • Marcus, A. (2002). The cult of cute: the challenge of user experience. Interactions 9(6), 29 - 34. 

  • Marton, F. & Saljo, R. (1984). Approaches to Learning. In Marton, F., Hounsell, D. and Entwistle, N.J. (eds), The Experience of Learning: Implications for Teaching and Studying in Higher Education, 2nd ed, Edinburgh: Scottish Academic Press.

  • Miller, H. & Bichsel, J. (2004). Anxiety, working memory, gender, and math performance. Personality and Individual Differences, 37, 591-606.

  • Mills, J.D. (2002). Using computer simulation methods to teach statistics: A review of the literature. Journal of Statistics Education [Online], 10(1).(http://www.amstat.org/publications/jse/v10n1/mills.html)

  • Rasmussen, J.L. (1996). ANOVA MultiMedia: A program for teaching ANOVA designs. Teaching of Psychology, 23, 55-56.

  • Refinetti, R. (1996). Demonstrating the consequences of violations of assumptions in between-subjects analysis of variance. Teaching of Psychology, 23, 51-54.

  • Richardson, J.T.E. (2005). Students’ approaches to learning and teachers’ approaches to teaching in higher education. Educational Psychology, 25, 673-680.

  • Sciutto, M.J. (2000).Demonstration of factors affecting the F ratio. Teaching of Psychology, 27, 52-53.

    Link to our ANOVA demo

  • http://www.psychology.heacademy.ac.uk/miniprojects/anova/anova1.html

    Link to our Normal Distribution demo

  • http://www.keele.ac.uk/depts/ps/RSStat/index.html

    Links to other online statistics demos

  • http://www.ruf.rice.edu/~lane/stat_sim/one_way/index.html

  • http://www.psych.utah.edu/stat/introstats/anovaflash.html

  • http://www.csustan.edu/ppa/llg/stat_demos.htm