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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

Importance of Statistics in Psychology

- 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?”

Psych students + statistics =

- “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?

A specific example

- 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?

Our idea

- 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

Literature review

- 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

Two normal distributions

- 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

ANOVA Demo

- 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

Evaluation

- 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

Evaluation

Results

- 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…

Conclusion

- 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???

Math(s) anxiety

- “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…

3 principles

- 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”

Demonstration of the normal distribution/ histograms

- 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.)

Disk

www

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!

References

- 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

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