One-Way Anova - Lecture notes 10 PDF

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notes on the 1 way ANOVA test. all lectures by Dr Lawrence Bellamy...

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One-Way ANOVA

Week 7 with the number of groups increasing, the number of pairwise comparisons also increases, which will eventually get impractical with number of t tests performs, the chance of a type 1 error also increases (incorrectly rejecting the null hypothesis)

1 way ANOVA looks at effect of 1 categorical independent variable on 1 dependent variable 2 way ANOVA looks at influence of 2 different categorical independent variables on 1 dependent variable and can test their interaction ANOVA is a parametric test assumptions of ANOVA randomly drawn samples independent measurements samples are normally distributed homogeneity of variances Theory of ANOVA average of the 3 variances is 10 but total variance of all 3 data sets is 16 due to differences in means of the samples

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both slides is the null model which would have the same mean and variance as each other in this, the F would equal 1 Any differences in means between the samples will cause the ratio F to be greater than 1, making the variance larger A limitation of ANOVA is that it cant distinguish which how many of the sample means differ from one another and if one of the sample means do differ then you dont know which one it would be within each sample, the data has a variance about the sample mean As each sample has a mean value, this gives rise to a distribution of sample means this distribution of means is the variability between

How to do 1 way ANOVA Will never do these by hand but its good to understand them The null hypothesis: each of the samples are drawn from the same population so sample means should be equal Alternative hypothesis: at least 1 of the sample means is different to another

To reach a conclusion you check the calculated F against a critical value top row is the DF between left row is the DF within groups If observed FRatio > critical value: reject null hypothesis that means of all groups are equal this means variance between groups is greater than that within groups NOTE 1 way ANOVA is always 1 tailed as denominator is always the within sample variance

There is an agreed upon convention to display ANOVA results

Tukey Test Used to tell which means differ and need only be applied if the 1 way ANOVA was significant the version described can only be applied when the sample sizes of each group are the same There is a modified version for when the sample sizes are different for Tukey test you go straight to the critical value once you have the critical value you use the formula shown shown in the slide is a Tukey test for the previous data used if the difference in means is greater than T7.4 then the means differ (this is only for the example shown)...