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Hypothesis Testing: Univariate Parametric Tests
Published in Shayne C. Gad, Carrol S. Weil, Statistics and Experimental Design for Toxicologists, 1988
Analysis of covariance (ANCOVA) is a method for comparing sets of data which consist of two variables (treatment and effect, with our effect variable being called the “variate”), when a third variable (called the “covariate”) exists which can be measured but not controlled and which has a definite effect on the variable of interest. In other words, it provides an indirect type of statistical control, allowing us to increase the precision of a study and to remove a potential source of bias. One common example of this is in the analysis of organ weights in toxicity studies. Our true interest here is the effect of our dose or exposure level on the specific organ weights, but most organ weights also increase (in the young, growing animals most commonly used in such studies) in proportion to increases in animal body weight. As we are not here interested in the effect of this covariate (body weight), we measure it to allow adjustment of the measurement of the variate in which we are interested (the organ weights). Analysis of covariance allows us to make this adjustment. We must be careful before using ANCOVA, however, to ensure that the underlying nature of the correspondence between the variate and covariate is such that we can rely on it as a tool for adjustments (Anderson et al.,1980 and Kotz and Johnson, 1982).
Generalized linear models
Published in Kenneth G. Russell, Design of Experiments for Generalized Linear Models, 2018
Earlier examples described situations where the explanatory variables in a linear model were all real variables (Example 1.1.1) or were all indicator variables (Example 1.1.2). However, in some experimental situations, the explanatory variables in a linear model would include both categorical or ordinal variables and also “real” variables. The latter variables were known as covariates, and the analysis of such linear models was called analysis of covariance (ANCOVA).
Effects of different dosages of caffeine administration on wrestling performance during a simulated tournament
Published in European Journal of Sport Science, 2019
Raoof Negaresh, Juan Del Coso, Motahare Mokhtarzade, Adriano Eduardo Lima-Silva, Julien S. Baker, Mark E. T. Willems, Sina Talebvand, Mostafa Khodadoost, Farid Farhani
SPSS21 software (IBM, USA) was used for statistical analysis. Initially, the normality in the data distribution was checked with the Shapiro–Wilk test for each variable. The effect of the different forms of caffeine administration on variables measured in each experimental trial was assessed using a two-way repeated-measures analysis of variance (condition × time). The effect of the different caffeine forms of administration on urine osmolality and urine specific gravity was assessed using analysis of covariance. Furthermore, the effects of the different caffeine forms of administration on gastrointestinal complaints, urine volume and dehydration index were measured using a one-way analysis of variance. When violations to the assumptions of sphericity were observed in analysis of variance or covariance, the degrees of freedom were corrected using Greenhouse-Geisser corrections. The partial Eta squared (ηp2) was used as effect size in analysis of variance and analysis of covariance tests. Bonferroni post hoc tests were applied when necessary. Statistical significance was set at p < .05. Values are expressed as mean ± SD for the study sample.
Effects of movement velocity and training frequency of resistance exercise on functional performance in older adults: a randomised controlled trial
Published in European Journal of Sport Science, 2019
Darren L. Richardson, Michael J. Duncan, Alfonso Jimenez, Paul M. Juris, Neil D. Clarke
All data were analysed using IBM SPSS Statistics, Version 24.0 (Armonk, NY: IBM Corp) and descriptive statistics presented as mean ± SD, and 95% confidence intervals (95% CI). One-way analysis of variance (ANOVA) compared baseline differences between conditions, including IPAQ responses and daily macronutrients. Analysis of covariance (ANCOVA), analysed between-condition differences, using baseline data as a covariate. Within-condition changes were analysed with Bonferroni corrected paired t-tests. Ancillary ANCOVA analyses were performed to compare the impact of movement velocity only [HVLL (n = 20) vs. LVHL (n = 20) vs. CON (n = 10)] or frequency of exercise only [Once (n = 20) vs. twice-weekly (n = 20) vs. CON (n = 10)]. These data are available as online supplementary material and are only reported when significant. All significance tests were two-tailed with an alpha level of 0.05 required for significance. All p-values are reported as exact values unless p < .001. Partial eta squared () was used to quantify the meaningfulness of any differences, and defined as trivial (< 0.1), small (0.1–0.29), moderate (0.3–0.49) or large (≥ 0.5) (Hopkins, Marshall, Batterham, & Hanin, 2009). Hedges’ g effect size estimates were also applied as they allow correction for smaller sample sizes, and were calculated using the adjusted means and pooled SD. The interpretation of Hedges’ g is similar to Cohens d e.g. small (0.2–0.49), moderate (0.5–0.79), and large (≥ 0.8).