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One way-ANOVA

One way-ANOVA. Analysis of Variance. Let’s say we conduct this experiment: effects of alcohol on memory. Basic Design. Grouping variable (IV, manipulation) with 2 or more levels Continuous dependent/criterion variable H o :  1 =  2 = ... =  k What is H alt? How many levels here?.

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One way-ANOVA

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  1. One way-ANOVA Analysis of Variance

  2. Let’s say we conduct this experiment: effects of alcohol on memory

  3. Basic Design • Grouping variable (IV, manipulation) with 2 or more levels • Continuous dependent/criterion variable • Ho: 1 = 2 = ... = k • WhatisHalt? • How many levels here?

  4. Experiment results

  5. Analysis • Q: How do you know the effect was caused by the manipulation (vodka) rather than chance factors (e.g. brainier people happened to be in group B)? • Or: Do these two samples differ enough from each other to reject the null hypothesis that alcohol has no effect on mean memory? • A: A statistical test (such as ANOVA or a t-test) is usually applied to decide this.

  6. What does ANOVA do? • ANOVA assesses the extent to which the distributions of two or more variables overlap • The more the distributions overlap the less likely it is that they are different • What is 2.6? 3.2? What should it be in our case?

  7. F-ratio • ANOVA involves calculating a statistic called the “F ratio” • (the between groups variance=MSb/ the within groups variance=MSw) • The F ratio gets larger as the distribution overlap gets smaller (i.e. a larger F indicates a difference in the group means )

  8. F • F = MSb/ MSw • If H is true, expect F = error/error = 1. • If H is false, expect

  9. ANOVA results

  10. What does ANOVA do? • You have calculated F - what next? • Someone somewhere ran numerous ANOVAs on random data and worked out what values of F occur by chance alone • We check our calculated F ratio statistic against this chance value; if it is greater than the tabulated value we reject chance and argue that the manipulation is the most likely explanation for the data The p-value is the probability of obtaining an F value as extreme or even more extreme than the one actually observed. So, p-value = P(F > Fobs).

  11. Writing up ANOVA results • A one-way ANOVA was calculated on participants' memory rating. The analysis was significant or n.s?, F(  ,    ) =          , p = .xxx .

  12. ANOVA doesn’t always give a true result • ANOVA can only be applied under certain conditions, i.e…. • Certain assumptions must be met: • Homogeneity of variance of the measured variable (e.g. memory score) • Normal distribution of the measured variable

  13. Assumption of homogeneity of variance • The dependent variable scores show the same degree of variability across the treatments, i.e. • The treatment variances are of similar magnitude • This diagram represents data from two treatments that meet the assumption of homogeneity of variance • The spread of data within each treatment is similar hence the variances of the treatments are similar also

  14. Assumption of normality • The normal distribution.. • Symmetrical about its mean therefore the mean is a good estimate of central tendency • There are fixed percentages of scores falling between points that can be defined using the SD (e.g. 68.26% of scores fall within 1 SD of the mean) therefore the SD and/or the variance are good estimates of spread around the mean • Sensible to employ ANOVA, i.e. to analyse for differences in treatment means using estimates of variance

  15. Consequences of violating assumption of normality • A common violation of the normal distribution is skew • Here is a figure showing a positively skewed distribution • Not symmetrical about its mean therefore the mean is NOT a good estimate of central tendency • The relationship between the percentages of scores falling between SD points is NOT FIXED therefore the SD/ variance is NOT a good estimate of spread around the mean • NO LONGER sensible to employ ANOVA, i.e. to analyse for differences in treatment means using estimates of variance

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