214 L3

• It is a parametric test 
• It has a set of assumptions which should be met- often ignored as theu are robust
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Will- marginally significant results

Will not- highly significant results- p <0.01

1. Assumption of independence 
2. Assumption of normality 
3. Assumption of homogeneity of variance

• Participants should be randomly assigned to a group 
• They should not cluster, share a classification variable- gender, skill level
• There should be no influence across one data point to another 

It becomes difficult to interpret results

• Always randomly allocate participants to a condition
• Try to allocate equal numbers to each condition 
• Test to see whether you have significant differences on important classification variables

• Overall data and data for each subgroup to be normally distributed
• Because: ANOVAs rely on the mean so if skewed and bimodal the mean is unlikely the best measure of central tendency

• If data are slightly skewed- no problem 
• If data skewed by same degree in the same direction - no problem 
• If skewed in different direction- problem, leads to type 1 and 2 errors

• Avoid measures which often have ceiling or floor effects
• Transform data, changing every score in a systematic way
• Use a robust ANOVA or non-parametric alternatives.

• Assumes variances of the distributions in the sample are equal 
• Therefore the variances for each sample should not significantly vary from one another

• The ANOVA tests the plausibility of the null hypothesis
• This is pointless to test when variance is already clearly different

• It is difficult to avoid but can be mitigated
• It is okay as long as largest variance is no more than 4x the size of the smallest
• Can transform data or use non-parametric alternative

Transform data

• Take every score from each participant and apply a uniform mathematical function to each
• Report both the original data and the transformed data

1. Log transformation (log(Xi))- whole numbers and covers wide range of values, small values with decimals
2. Square-root transformation (square root of Xi)- small whole number and percentage data where the range is between 0 and 30 % or 70 and 100 %

• Data points which significantly differ from other observations

• Can drastically bias/change predictive models
• Predictions can be exaggerated and present high error 
• Distort statistical analyses and violate assumption

It can be dishonest and misleading to do so if they are true scores

• Accept null hypothesis
• samples come from same population 
• no statistical difference in the population means
• experimental effect = 0

• Reject the null hypothesis
• sample comes from different populations 
• population means are statistically different 

1. Planned comparisons 
2. Post-hoc comparisons

Increases the probability of making a type 1 error

(rejecting null hypothesis when there was actually no effect)

• They are a focussed approach to examine specific group differences
• They should be pre-specified 

When certain hypotheses can be tested without comparing all combinations of means

To negate type 1 errors

1. Run t tests with a low number of pairs 
2. Run t tests with Bonferroni adjustment

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It makes the p value value more conservative

Generated from the prior significance level divided by the number of tests 

(p value / number of tests = bonferroni)

• Assess all possible combinations of differences between groups by comparing each mean with the other 
• They make adjustments to the p value, but more conservative than bonferroni.

Tukey-Kramer HSD

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When you don't have any pre set ideas on which group should differ

• Planned comparisons
• uses fewer combinations
• p value is less constrained 
• it is more powerful