Experimental Design and Data Analysis for Biologists

“Ecologists know that the predictive ability of a model will always be constrained by the quality and quantity of the data entered into the model (‘garbage in – garbage out’) and the assumptions upon which the model is built (Quinn and Keough 2002).”

“We use Repeated Measures ANOVA (Quinn and Keough 2002) because the quadrats were repeatedly recorded in 1973, 1983, 1992, 1997, and 2002.”

“More precisely, we ran ANCOVA models (Quinn and Keough 2002; Zuur et al. 2009) with an interaction term in which the slope of one variable (describing soil, root or plant community characteristics) was evaluated at different levels of the SOC variable.”

“Asterisk represents significant differences (P ≤ 0.05) from nested 839 ANOVA.”

“…ancova, we visually checked the linearity assumption and tested for the homogeneity of slopes between the covariate and dependent variable by building preliminary models that included only deer density or the forest cover category and the interaction terms with the covariate (Quinn & Keough 2002).”

“Continuous variables were log10-transformed to improve normality, with the exception of milk composition (percentage) data, which were squarerooted and then arcsine-transformed (45).”

“As a result, hierarchical partitioning provides, for each explanatory variable separately, an estimate of the independent and conjoint contribution with all other variables (for more details see Chevan & Sutherland 1991; Mac Nally 2000; Quinn & Keough 2002).”

“Ordinary least-square regressions were used (after testing for normality of distributions, homogeneity of variance and independence of error terms; Quinn & Keough 2002) to examine relationships between arcsine square-root transformed skin reflectance (REFL) and MRAD, MAT, log 10 -transformed body…”

“To minimize the probability of detecting false positives ( i.e ., decrease Type I error) we selected a rejection alpha of 0.10 (Quinn and Keough 2002).”

“Two colonies were omitted to equalize the ranges of parental colony sizes (covariates) between both sites (Quinn and Keough 2002).”

“Further, we analysed scatterplots to check linearity of the relationships between the covariates and species richness (Quinn & Keough 2002).”

“We analysed population abundance and biomass of 31 species of medium to large-bodied mammal species at 38 Atlantic forest sites (including three islands, 26 forest fragments and six continuous forest sites) as related to forest type, level of hunting pressure and forest fragment size using ANCOVAs.”

“Similarly, the body condition index (BCI) of species did not vary significantly between tree-density categories (two-factor mixed-effects ANOVAs, P > 0.321 for all species).”

“The effects of five predictor variables (uapproach, θapproach, dstrike, dresponse and tresponse) on escape probability were evaluated by logistic regression (Quinn and Keough, 2002) for a binomial distribution (‘glmfit’ function in Matlab).”

“If significant differences among season, area, species and/or size factors were detected, a post hoc Bonferroni test was applied to identify the sources of the variation (Quinn and Keough 2002).”

“rately (Quinn and Keough 2002).”

“05) was used to test for the relation between the presence and absence of liver damage (as the binary response variable) and microcystin contents of fish liver (as the continuous predictor) [43].”

“A discriminant analysis (Quinn & Keough 2002) was carried out to assess the effect that each of these oceanographic parameters had on the presence of dolphins in the fjord.”

“Prior to analysis, all data were checked for homogeneity of variances and normality using Q-Q plots and box plots (46).”

“There were no significant relationships between the alien species relative abundance and biomass and (Quinn & Keough, 2002). the species richness, total numerical density and total biomass density of native fish observed at the study sites (Fig.”

“Statistical tests of our a priori directional hypothesis that problem-solving ability positively predicts mating success are one tailed (Quinn & Keough 2002).”

“Arbitrary values (X-axis) represent individuals’ loadings to component 1, reflective of Th2 activity as assessed by principal-components analysis (a standard technique for reducing multivariate data down to its main independent features [20]).”

“Although often difficult to implement in large-scale ecological studies, the basic principles of experimental design (e.g. Quinn & Keough, 2002) are generally also applicable to monitoring (Conroy & Carroll, 2009).”

“For interpreting the PCA results, Quinn & Keough (2002) suggest that independant variables with factor loading scores >0.7 are strongly correlated to the relevant PC, whereas factor loading scores between 0.4 and 0.6 indicate a moderate correlation, and scores <0.4 a weak or absent correlation.”

“The aim of principal component analysis is to reduce many correlated variables to a small number of new derived variables that adequately summarize the original information (Quinn & Keough 2002).”

“Mean values per hourly bin were treated as individual data points, and as we found no evidence of non-linearity, we considered Pearson’s coefficient appropriate (Quinn & Keough 2002).”

“We regarded all sensible twofold interactions (Quinn & Keough 2002) and we pre-selected those interactions with sufficient combinations (see Table S2 for full model).”

“In such an approach, the potential accumulation of decision errors is high and the adjustment of significance levels and/or p values is recommended [33].”

“(vectors; ES1, ES2, ES3, ES4, ES5, ES6) in the ordination graph for sites of two different land-use types (different colors). in which relationships between multiple services are approximately linear (see also Quinn and Keough, 2002).”

“Even when explanatory variables were centred or standardized, parameter tolerances were too low ( 0Æ1) to interpret their individual effects in full models (Quinn & Keough 2002).”

“Therefore, we followed Quinn and Keough’s [39] recommendation that individual main effects should be interpreted only where the effect size of the interaction is smaller than the size of the corresponding main effects, which was the case for the majority of response variables.”

“We evaluated candidate models starting from the fully saturated model and considered all interactions using likelihood ratio tests (LRT) and Akaike’s information criterion (AIC) to remove terms (Agresti 1996; Peng et al. 2002; Quinn & Keogh 2002).”

“Prior to performing factor analysis, we identified and removed any outliers (values greater than or equal to 1.5 times the interquartile range; Quinn and Keough 2002) and tested for independence of response variables by Bartlett’s test of sphericity (the null hypothesis of no correlation between variables was rejected…”

“Replication, randomization, blocking and independence are key, as with any good experiment (e.g. Quinn & Keough 2002).”

“Two-sample test for equality of proportions ( “ prop.test ” in statistical software “ R ” ; And (cid:2) el, 2007; Quinn & Keough, 2002) was used for comparison of percentages of students expressing positive attitude towards the seminar or the game.”

“data set (Quinn and Keough, 2002).”

“With path analysis, it is possible to distinguish the direct, independent effects of two related independent variables (LE and body mass) on a dependent variable (COT), while also calculating the indirect effect of covariance between independent variables (Quinn and Keough, 2002).”

“A one-way RANOVA was used to test the significance of PCA scores obtained for microbial communities (Quinn and Keough, 2004).”

“In the , P -values were derived using Pillai’s trace, which is more robust than other statistics (Quinn & Keough 2002).”

“Correlation values (r) above 0.8 indicate pairs or groups of parameters that tend to be strongly constrained together (Quinn & Keough, 2002).”

“We tested for collinearity among the independent variables by evaluating tolerance variables (Quinn and Keough 2002) and condition indices (Belsley et al. 1980) and found that it was not significant.”

“A multidimensional scaling (MDS) plot was constructed from the presence/absence matrix using Bray-Curtis dissimilarity, where similarity was only assigning to a joined presence and not a joined absence of bands (Quinn & Keough 2002).”

“) to test the entire model (Quinn and Keough, 2002; Zar, 1999) (Tables·2, 3).”

“We analyzed the effects of Bellamya, Orconectes and their interactions on the final abundance and wet mass of each native snail species using multivariate ANOVA (MANOVA) (log10-transformed ? 1 values; Quinn and Keough 2002). When evaluating the combined effects of two or more species, it is important to consider wheth…”

“Formal statistical identification of outliers or those observations with an undue influence on a fitted regression model using, for instance, Cook’s Distance (Quinn and Keough 2003) is recommended.”

“Principal Component Analysis (PCA, based on a correlation matrix; Quinn and Keough, 2002) was performed to determine which of the qualitative traits (origin, serotype and environmental persistence) and time/temperature conditions had the greatest influence on biofilm production.”

“Covariates were standardized (standard score) when assessed as an interaction to avoid intercorrelation with their lower order terms (Quinn and Keough, 2002).”

“A quasi-Poisson regression model was used in the F. serratus recruits model due to underlying distribution of the data and the overdispersion observed (Quinn and Keough 2002).”

“To examine the relationship between distance to B. nigra and captures of consumers, we used least-squares regression, after applying a square-root transformation to improve normality of capture data (Quinn and Keough 2002).”

“The UI was compared between passage types using a Kruskal–Wallis test since the assumptions for an ANOVAR were not met (Quinn and Keough, 2002).”

“Variance inflation factors (VIFs) (65) were less than 1.”

“We verified that there was no collinearity between the predictor variables (variance inflation factor\10; Quinn and Keough 2002).”

“Thus, a linear regression with weighted least squares was applied (Quinn & Keough 2002 ).”

“Nevertheless, power analysis (Quinn and Keough 2002) revealed that our level of replication generated a probability of 72% for statistically detecting a warming-induced increase in total algal biomass of 40%.”

“…ANOVA instead of an MANOVA as this combination of methods copes better with the large number of zeros, which is typical of species abundance data and post hoc comparisons of groups are more straightforward under a univariate ANOVA framework than under a MANOVA framwork (Quinn and Keough 2002).”

“A priori planned comparisons were conducted to compare certain measurement types using F tests (Quinn and Keough, 2002).”

“The effects of the predictor variables can be assessed by comparing these coefficients and their P - values (Quinn & Keough, 2002).”

“Analyses were conducted using canonical correspondence analyses (CCA; Quinn and Keough 2002) to graphically show how bird community composition differed among forest types.”

“The degree of settlement was calculated by using the critical values after Tukey’s B test (for zoospore and zoospore-adjusted) and t test (for Bpreferential^), whether 1 , 2 , 3 , or 4 greater than the test statistics, respectively [27].”

“To our knowledge, our study is the first to test explicitly the effects of tree diversity on this important plant–insect interaction for a very species-rich subtropical forest ecosystem.”

“However, because multivariate methods such as hierarchical clustering are sensitive to factors with relatively larger values [59], we standardized the expression values of opsins expressed within single and double cones separately.”