Analysis of Variance

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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 NteSchool of Psychology : 

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 NteSchool of Psychology

Importance of Statistics in 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? Psych students + statistics =

A specific example : 

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)… Q: How can these be taught in a more integrated fashion? Histograms/ distributions Variance The F ratio “Significance” Type I error Underlying assumptions

Our idea : 

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

Slide 7: 

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 : 

ANOVA Demo Disk www 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

Evaluation : 

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 : 

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…

Evaluation : 

Evaluation

Conclusion : 

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… Math(s) anxiety

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” 3 principles

Demonstration of the normal distribution/ histograms : 

Demonstration of the normal distribution/ histograms Disk www 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.)

Using computer graphics to illustrate key concepts underlying basic statistics : 

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!

Slide 18: 

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