Transformations and Post Hoc test

Flashcards related to mathematical transformations and ANOVA assumptions.

Mathematical Transformation

Applying a mathematical function to raw data to satisfy ANOVA assumptions, such as normality or equal variances, while preserving relationships between observations.

Log Transformation

A mathematical transformation often used for negatively or strongly positively skewed data; can include a constant to accommodate zero values.

Square Root Transformation

A harsher mathematical transformation than the log transformation. It can be used if the log transformation is ineffective in normalizing data or achieving equal variances.

Arc Sine Transformation

A transformation specifically used for proportion data (e.g., percentages), where values are constrained between 0 and 1; percentages should be expressed as decimals (e.g., 50% as 0.5).

ANOVA Robustness

ANOVAs are generally robust against departures from normality, but equal variances are more critical; if assumptions cannot be met, results should be interpreted with caution.

Non-Parametric ANOVA

A distribution-free alternative to ANOVA, such as the Kruskal-Wallis test, which uses rank-based methods; it has less power and is typically used for one-way ANOVA designs.

Post Hoc Tests

Tests conducted after a significant ANOVA result to determine which specific groups differ significantly from each other; involve pairwise comparisons often using t-tests.

Confidence Intervals

Graphical approach for post hoc analysis, where overlapping 95% confidence intervals between groups indicate no significant difference, while divergence suggests a difference.

Family-Wise Error Rate

The increased probability of making at least one Type I error (false positive) when performing multiple statistical tests (e.g., post hoc tests); methods like Bonferroni correction or Tukey's test adjust for it.

Tukey's Test

A post hoc test that controls for the family-wise error rate, adjusting p-values to account for multiple comparisons; implemented using either the base R function or the e-means package.

Experimental Wise Error Rate

Same as family wise error rate; the probability of making one or more false discoveries, or type I errors, when performing multiple statistical tests.

Kruskal-Wallis Test

A non-parametric test used in place of ANOVA when the assumptions of normality are not met; it operates by ranking all the data points and then determining is the sum of ranks differs between groups