# BEES2041 Lecture Notes - Lecture 3: Dependent And Independent Variables

Transformations needed for highly skewed distributions

-Log transformation can

improve normality

remove outliers

-many questions better asked on log scales

-are relative / absolute differences more important?

-transformations change response variable and therefore your formal null & alternative

hypotheses

-Transformations must be done before analyses

-Choose transformation to best meet assumptions

-Do not choose transformation based on significance of test

Non-parametric tests

-wide variety of tests based on ranks rather than raw data

-ranks used because probability distribution of n ranks is always identical

-estimates of population parameters not used

The Mann-Whitney U test

-non-parametric equivalent of an independent samples t-tests

-ranks all data from two groups

-If Ho true, we would expect a similar mixture of rankings in each group

Wilcoxon signed-rank

-non-parametric equivalent of an paired samples t-test

-differences between pairs are ranked

Non-parametric tests are not free of assumptions

-still assume independence & homogeneity of variance

-use when assumption of normality cannot be met

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## Document Summary

Transformations change response variable and therefore your formal null & alternative hypotheses. Do not choose transformation based on significance of test. Wide variety of tests based on ranks rather than raw data. Ranks used because probability distribution of n ranks is always identical. If ho true, we would expect a similar mixture of rankings in each group. Use when assumption of normality cannot be met. Ranking loses information about size of differences among groups. Reshuffle the data collected to establish likelihood of any given outcome. Create a probability distribution rather than assume a known distribution. P values are proportion of data rearrangements that have differences equal to or more extreme than observed data. Null & alternative hypotheses deal with the samples only. Allow creation of (cid:862)home-gro(cid:449)(cid:374)(cid:863) test statistics to suit specific questions. Ofte(cid:374), (cid:449)e do(cid:374) t take (cid:373)easure(cid:373)e(cid:374)ts of (cid:272)o(cid:374)ti(cid:374)uous (cid:448)aria(cid:271)les (cid:271)ut (cid:272)lassify o(cid:271)ser(cid:448)atio(cid:374)s i(cid:374)to different categories.