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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

One way-ANOVA

Analysis of Variance

basic design
Basic Design
  • Grouping variable (IV, manipulation) with 2 or more levels
  • Continuous dependent/criterion variable
  • Ho: 1 = 2 = ... = k
  • WhatisHalt?
  • How many levels here?
analysis
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.
what does anova do
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?
f ratio
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 )
slide8
F
  • F = MSb/ MSw
  • If H is true, expect F = error/error = 1.
  • If H is false, expect
what does anova do1
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).

writing up anova results
Writing up ANOVA results
  • A one-way ANOVA was calculated on participants\' memory rating. The analysis was significant or n.s?, F(  ,    ) =          , p = .xxx .
anova doesn t always give a true result
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
assumption of homogeneity of variance
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
assumption of normality
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
consequences of violating assumption of normality
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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