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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 l.jpg

Overview of Statistical Tests Available

BIOL457/657

5 February 2014


Deciding which test to use l.jpg

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?


Textbook rear inside cover l.jpg

Textbook Rear Inside Cover


No difference h 0 or no correlation h 0 is dv meristic mensural or categorical l.jpg

No-difference H0 or no-correlation H0?Is DV meristic/mensural or categorical?


Ii normal or non normal data l.jpg

II. Normal or non-normal data?


Iii sample data compared to what l.jpg

III. Sample data compared to what?


Iv one comparison or more than one l.jpg

IV. One comparison or more than one?


V paired or unpaired data l.jpg

V. Paired or unpaired data?


Vi testing for cause and effect x y l.jpg

VI. Testing for cause-and-effect [XY]?


Vii eureka l.jpg

VII.Eureka


Comparing two sets of data with meristic or mensural data l.jpg

Comparing Two Sets of DatawithMeristic or Mensural Data


Student s t test l.jpg

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]


  • Handout iverson 2002 razorback musk turtles of ok and ar l.jpg

    HANDOUTIverson, 2002Razorback Musk Turtles of OK and AR


    Paired t test l.jpg

    Paired t-test

    • Parametric

    • Data paired rather than drawn from independent populations

    • Assumes equal variances


    Handout long et al 1998 hemlocks on tip up mounds l.jpg

    HANDOUTLong et al., 1998Hemlocks on Tip-up Mounds


    Mann whitney u test l.jpg

    Mann-Whitney U-test

    • aka Rank-Sum Test

    • Nonparametric comparison of two samples of meristic or mensural DV


    Handout godfrey and bryant 2000 european robin energy expenditure l.jpg

    HANDOUTGodfrey and Bryant, 2000European Robin Energy Expenditure


    Comparing two or more sets of data with categorical data l.jpg

    Comparing Two (or More) Sets of DatawithCategorical Data


    Z test l.jpg

    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]


    Handout hoikkala and aspi 1993 drosophila mating l.jpg

    HANDOUTHoikkala and Aspi, 1993Drosophila Mating


    Chi square 2 tests l.jpg

    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


  • Handout spinks et al 2000 mole rat sex ratios l.jpg

    HANDOUTSpinks et al., 2000Mole Rat Sex Ratios


    Handout harrold 1982 snails and starfish predation l.jpg

    HANDOUTHarrold, 1982Snails and Starfish Predation


    Handout carney et al 1996 iris seeds l.jpg

    HANDOUTCarney et al., 1996Iris Seeds


    Comparing three or more sets of data with meristic or mensural data l.jpg

    Comparing Three or More Sets of DatawithMeristic or Mensural Data


    One way analysis of variance anova l.jpg

    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


    Handout godfrey and bryant 2000 european robin energy expenditure27 l.jpg

    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 l.jpg

    Kruskal-Wallis Test

    • Nonparametric equivalent of ANOVA

    • Rejection of H0 requires nonparametric analog of post hoc testing

      • Dunn’s Multiple Comparisons test


    Handout zaviezo and mills 2000 parasitoid clutch size l.jpg

    HANDOUTZaviezo and Mills, 2000Parasitoid Clutch Size


    Two way or more anova l.jpg

    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


    Handout paradise 2000 artificial treeholes l.jpg

    HANDOUTParadise, 2000Artificial Treeholes


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    Examining the Correlation of Variables with Continuous Variation


    Correlation analysis l.jpg

    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


    Handout ellers et al 1998 parasitoid body size and fitness l.jpg

    HANDOUTEllers et al., 1998Parasitoid Body Size and Fitness


    Simple linear regression l.jpg

    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


    Handout beukema et al 2000 polychaete worm biomass l.jpg

    HANDOUTBeukema et al., 2000Polychaete Worm Biomass


    Multiple linear regression l.jpg

    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


    Handout long et al 2005 arctic ground squirrel activity l.jpg

    HANDOUTLong et al., 2005Arctic Ground Squirrel Activity


    Analysis of covariance l.jpg

    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.


    Handout crespi 1988 thrip fitness l.jpg

    HANDOUTCrespi, 1988Thrip Fitness


    The general linear model glm l.jpg

    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 l.jpg

    Logistic Regression

    • IV is continuous, but DV is discrete and categorical

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


    Handout vi uela 1997 black kite nesting l.jpg

    HANDOUTViñuela, 1997Black Kite Nesting


    Multivariate analyses l.jpg

    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 l.jpg

    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 l.jpg

    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


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