# Overview of Statistical Tests Available - PowerPoint PPT Presentation

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Overview of Statistical Tests Available. BIOL457/657 5 February 2014. Deciding Which Test to Use. 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?.

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Overview of Statistical Tests Available

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## Overview of Statistical Tests Available

BIOL457/657

5 February 2014

### Deciding Which Test to Use

• 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?

### Student’s t-Test

• Parametric test

• Compare two independent samples

• One version for equal variances

• Less powerful version for unequal variances

• H0: There is no difference in [DV] between two groups or treatments [IV]

### Paired t-test

• Parametric

• Data paired rather than drawn from independent populations

• Assumes equal variances

### Mann-Whitney U-test

• aka Rank-Sum Test

• Nonparametric comparison of two samples of meristic or mensural DV

### z-test

• 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]

### Chi-square (χ2) Tests

• χ2 Goodness-of-Fit Test

• Sample distribution vs. hypothesized/theoretical distribution

• χ2 Test for Independence

• Sample distribution vs. sample distribution

• Mantel-Haenszelχ2 Test for Independence

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

### One-way Analysis of Variance (ANOVA)

• 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

### HANDOUTGodfrey and Bryant, 2000European Robin Energy Expenditure

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

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

### Kruskal-Wallis Test

• Nonparametric equivalent of ANOVA

• Rejection of H0 requires nonparametric analog of post hoc testing

• Dunn’s Multiple Comparisons test

### Two-Way (or More) ANOVA

• 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

### Correlation Analysis

• 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

### Simple Linear Regression

• 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

### Multiple Linear Regression

• >1 continuous IV

• Multidimensional best-fitting line:

DV = a(IV1) + b(IV2) + c(IV3) … + z

(ac 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

### Analysis of Covariance

• 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.

### The General Linear Model (GLM)

• Mix of multiple linear regression (continuous IVs) and ANCOVA (allows for discrete IVs)

• Number of IVs limited only by sample size

• H0 for each IV states that its variation is not significantly related to variation in DV (given relationship of other IVs to DV)

• Interaction of IVs can also be examined in additional H0s

• ### Logistic Regression

• IV is continuous, but DV is discrete and categorical

• H0: Probability of categorization of DV is not correlated with IV

### Multivariate Analyses

• Variety of techniques that take large data sets with numerous variables and…

• …allow relatively simple graphical representations

• …identify interrelationships of variables

### Phylogenetic Comparative Methods

• 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

### Monte Carlo Randomizations

• 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