One way anova
Download
1 / 15

One way-ANOVA - PowerPoint PPT Presentation


  • 49 Views
  • Uploaded on

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?.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' One way-ANOVA' - hoai


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
One way anova

One way-ANOVA

Analysis of Variance



Basic design
Basic Design on memory

  • Grouping variable (IV, manipulation) with 2 or more levels

  • Continuous dependent/criterion variable

  • Ho: 1 = 2 = ... = k

  • WhatisHalt?

  • How many levels here?



Analysis
Analysis on memory

  • 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? on memory

  • 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 on memory

  • 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 )


F on memory

  • F = MSb/ MSw

  • If H is true, expect F = error/error = 1.

  • If H is false, expect


Anova results
ANOVA results on memory


What does anova do1
What does ANOVA do? on memory

  • 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 on memory

  • 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 on memory

  • 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 on memoryhomogeneity 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 on memory

  • 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 on memory

  • 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


ad