Week 3 Anova Assumptions PDF

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Anova assumptions...

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Week 3 ANOVA Assumptions, Power and Comparisons of Means • Adjust significance levels to account for the familywise error rate; • Know the different approaches to a priori tests, and when to use them; • Understand the different approaches to post hoc tests and when to use them; • Use jamovi to run different types of contrasts for a one-way ANOVA or main effect; • Use jamovi to run post-hoc tests; • Correctly interpret the jamovi output for these tests. Assumptions of ANOVA 1. Homogeneity of Variance - The scores in each group are normally distributed 2. Normality - The variances of the scores in each group should be similar – residual error is normally distributed 3. Independence of Observations - The observations in each group are independent of each other.

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Checking Assumption of Homogeneity of Variance Levenes Test – Standard Deviations of each group are similar. We want to see p>0.05 (non sig) which shows there are no differences. If sample sizes are equal this assumption can be violated without grave consequences. In Jamovi – ANOVA, Assumption Checks, Homogeneity Tests. If violated – look for outliers, check dataset or change test. Checking Assumption of Normality Check Histograms for each group – ANOVA is very robust in respect of normal distribution. o Distribution Shapes  Negative skew  Positive Skew  Normal o Kurtosis  Leptokurtic – positive kurtosis – most scores near the mean (looks pointy)  Platykurtic – negative kurtosis – wide spread of scores across (looks flat)

Skew and kurtosis can be checked in Jamovi – Analysis Descriptives. Remember that skew = 0 is perfectly symmetrical. Skew +1 ‘highly skewed’; skew between -1 and -0.5, or between 0.5 and 1 is ‘moderately skewed’; skew between -0.5 and +0.5 is approximately symmetric. Kurtosis is reported in terms of excess kurtosis, so the optimal value is 0. There’s no easy rule of thumb for how much skew is ‘too much’. 

Q-Q (Quantile-Quantile Plots) Plot of observed cumulative distribution of residuals (difference between value and mean) Vs. Distribution of residuals we would expect if the data is normally distributed.

If data is normally distributed, all points should be on the straight line. 3.   

Checking Assumption of Independence of Observations (residuals) Can be achieved by random allocation of participants to treatment groups. Violated if repeated measures taken on the same subject, use of intact groups (eg. Classmates, groups that may influence each others performance or outcomes). Do not explicitly test this assumption but build it into our experimental design.

POWER The power of a statistical test is defined as the probability of correctly rejecting the null hypothesis. Therefore, it is the probability of finding a difference between means, if there is one. Type1 Error or α (false positive) – refers to accepting a difference (or relationship) as significant when in fact it is due to something else (bias, sampling error, or chance) Type2 Error or β (false negative) – refers to occasions where the null hypothesis is false but we have decided to retain it. (set confidence limit too strictly eg....