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Overview of Statistical Tests Available

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Overview of Statistical Tests Available

BIOL457/657

5 February 2014

- Is DV meristic, mensural, or categorical?
- Is IV continuous or discrete in its variation?
- If IV is discrete, are two groups being compared, or more than two?

- Are there multiple IVs?

- Parametric test
- Compare two independent samples
- One version for equal variances
- Less powerful version for unequal variances

- Parametric
- Data paired rather than drawn from independent populations
- Assumes equal variances

- aka Rank-Sum Test
- Nonparametric comparison of two samples of meristic or mensural DV

- aka Binomial Test of Proportions
- Two samples
- DV occurs in two categories for each sample
- H0: There is no difference in binomial outcomes [DV] between two samples [IV]

- χ2 Goodness-of-Fit Test
- Sample distribution vs. hypothesized/theoretical distribution

- Sample distribution vs. sample distribution

- Compares distributions of samples with two or more IVs that may influence DV distribution

- Parametric
- H0: There is no difference in [DV] among three or more groups or treatments [IV]
- Rejection of H0 requires post hoc testing to identify which samples differ significantly from which other samples
- Fisher’s Least Significant Difference (LSD) test
- Tukey’s test
- Student-Newman-Keuls test
- Bonferroni t-tests
- Duncan’s Multiple Range test
- Sheffé comparisons

Note: For both tests, post hoc Scheffé comparisons show CHILLED was significantly

greater than other two treatments, which did not differ from one another.

- Nonparametric equivalent of ANOVA
- Rejection of H0 requires nonparametric analog of post hoc testing
- Dunn’s Multiple Comparisons test

- Two IVs analyzed simultaneously
- Multiple H0s:
- No difference in [DV] between/among groups as established by IV1
- No difference in [DV] between/among groups as established by IV2
- No difference in [DV] attributable to the interaction of IV1 and IV2

- More complex models for three or more IVs

- H0: There is no correlation of DV with IV
- Positive correlation: Direct relationship
- Negative correlation: Indirect relationship
- No correlation: Variation in DV not related to variation in IV

- If they are correlated, fit DV and IV data to a best-fitting line
y = ax + b

DV = a(IV) + b

a = slope

b = y-intercept

- >1 continuous IV
- Multidimensional best-fitting line:
DV = a(IV1) + b(IV2) + c(IV3) … + z

(ac are slopes in separate dimensions; z is intercept)

- With each added IV, partial correlation coefficient assesses whether it significantly improves fit to DV
- H0: There is no correlation of DV with IVx, after correction for correlation of DV with other IVs in model

- Two IVs: IVc continuous, IVd discrete
- Typically, IVc regarded as a confounding variable, known/suspected to be correlated with DV
- H0: No difference in DV between/among treatments or groups (IVd), after correction for correlation of DV with IVc.

- Mix of multiple linear regression (continuous IVs) and ANCOVA (allows for discrete IVs)
- Number of IVs limited only by sample size

- IV is continuous, but DV is discrete and categorical
- H0: Probability of categorization of DV is not correlated with IV

- Variety of techniques that take large data sets with numerous variables and…
- …allow relatively simple graphical representations
- …identify interrelationships of variables

- Used for analyzing data from related species
- Necessary because phylogenetic relationships cause violation of the assumption of independence of data points

- Primarily used for correlation analysis, but can be adapted for use in other types of analysis

- Uses 100s to 1000s of randomizations of the sample data to create a null distribution for the H0
- Parametric assumption thus not necessary

- Used to create highly specific H0s for particular scenarios one may wish to analyze