Basic Statistical Tests
Training session with Dr Helen Brown, Senior Statistician, at The Roslin Institute, December 2015.
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These training sessions were given to staff and research students at the Roslin Institute. The material is also used for the Animal Biosciences MSc course taught at the Institute.
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*Recommended YouTube playback settings for the best viewing experience:  1080p HD
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Content:
Analysis of Variance (ANOVA)
-Test if groups (eg genes) differ more than expected by chance
-Expressing the ANOVA model:
-Or equivalently expressed :
-This model is ‘Simple’ or ‘one-way’ ANOVA

Example: Compare level of expression between 6 genes, 3 observations per gene
Null hypothesis: groups have same expression levels

ANOVA table
One-way ANOVA: Gene versus Expression  (Minitab output)
F value
--compared to an F distribution under Null hypothesis of no difference

Note:
-F distribution has 2 degrees of freedom (DF)
--DF1 relates to number of groups
--DF2 relates to sample size
-Not essential to understand calculation of F and its DF
-ANOVA on 2 groups gives an identical p-value to a t-test (with pooled SD)

Comparing group pairs following an ANOVA
-Most packages optionally carry out t-tests to compare pairs of groups within the ANOVA
--By default these use a pooled SD for all groups
--Pooled SD may be more reliable than using individual group SDs
-Pairwise tests between groups (Minitab output)

Checking ANOVA assumptions
Assumptions for ANOVA:
--Residuals (errors) are normal, ie data normal within groups
--Each group has same variance
Calculating residuals (errors), recall ANOVA model expressed

Checking ANOVA assumptions
Residual plot
--Plot of residuals against predicted values
Check :
--Residuals have similar variability around zero over fitted values
--For outliers
Histogram
--Rough check of normality by examining histogram of all residuals