Section 2 Flashcards
(32 cards)
What is statistical power?
The probability of detecting a true effect if it exists in our data
What are the factors that statistical power depends on?
Sample size
Background variation
Significance level
Effect size
How does sample size affect statistical power?
Larger samples sizes (with more independent observations) increases power
How does effect size influence statistical power?
Large effects are easier to detect than small ones
How does background variation affect statistical power?
More variation between “replicate” observations/experimental units decreases power
How does significance level (alpha) influence power?
Power increases is the significance is set e.g., at alpha = 0.1 -> this should be considered in all study designs with low replication
Which information do you need to include in addition to p-values?
Effect size
Effect direction
How does this extra information help avoid Type II errors?
Type II error is when an effect is not detected but it exists. This is more likely to happen when you have a p-value close to 0.05, which is an arbitrary number and should be adjusted accordingly for your sample size.
P-values alone only tell you if the effect was statistically significant, not biologically meaningful. Therefore, we are able to interpret results more thoughtfully.
If effect size is large and the direction is biologically meaningful, it suggests the result might be real and non-significance could be sue to small sample size, high variability, conservative trait
How does a fixed sample size affect statistical power?
Statistical power decreases with the total number of treatment combinations.
How do you maximise the power?
By allocating the available experimental units to fewer treatment combinations with more replicates per treatment level.
How do degrees of freedom impact statistical power?
The more degrees for freedom that are left over, the greater the statistical power
What do you need to include with the p-value for a GLM if the results are significant for categorical predictors?
Direction of categorical main effects -> bar graphs with SE’s.
Effect sizes (partial eta squared): for factor main effects and interactions.
Description of interaction patterns -> interaction plots
What do you need to include with the p-value for a GLM if the results are significant for continuous predictors?
Direction of the predictor main effects -> scatterplot for entire sample
Effect sizes (partial eta scared) -> for predictor main effects and interactions
Description of interaction patterns -> interaction scatterplots
When should you use a GLM?
When there are many levels to the treatment groups (predictor variables)
What should you do for a GLM if you have categorical variables?
Covert them into continuous variables
What happens to the statistical power when you use a GLM?
The power increases as it doesn’t use up as many DFs as an ANOVA
What assumptions are there for a GLM?
Homogeneity of variances, normality, no outliers, independence
What model checking do you need to do for a GLM?
Collinearity tests: VIFs and tolerance (1 - R2)
Homogeneity of variances: residual plot: Have to use these - trust the robustness of the test
What are the four types of residual plots?
Normal Q-Q
Residuals vs. fitted
Scale-location
Residuals vs. leverage
How do you deal with collinearity in general linear models?
Center the continuous predictor variables: Subtract the overall mean from each observation
What is the power for detecting effects in a GLM?
For all of the predictor main effects and all the interactive effects, the power is the same.
How do you interpret the significant main effects of predictors in the presence of significant interactions?
Where all significant higher-order interactions are present, interpretation of the lower-order interactions or main effecst of the experimental factors concerned must be done with care (effect sizes)
What happens is you have stronger interactions?
They override weaker factor man effects. But, if main effects are stronger both the main effect and the interaction remain valid.
What sums of squares do you use if you have a not fully balanced study design?
Type three sums of squares to calculate partial eta squared
