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## Data in Anatomy and Physiology

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**Anatomy = the structure of living things**• Physiology = the mechanical, physical, and biochemical functions of living things • Data = information (values) belonging to a set of subjects**Types of Data**• Measurement – measurements with a value within a finite or infinite interval • Continuous – infinite number of values between • Discontinuous (meristic) – fixed numeric values • Ordinal – values that are ranked or have a rating scale • Nominal(Categorical) – cannot be measured; qualitative**Descriptive Statistics**Three categories Measures of central tendency Measures of variability Measures of an overall distribution’s characteristics**Central Tendency**• Mean (average) • Median (middle value) • Mode (most common) Variability • Minimum/Maximum • Variance • Standard deviation • Standard error Jaw opening time (ms) of Hawaiian eleotrid piscivorous predator, Eleotrissandwicensis Distribution Characteristics • Skewness (where longest “tail” is) • Kurtosis (shape of distribution) • + leptokurtosis • - platykurtosis**Presenting Data – Tables**• Advantages? • Disadvantages?**Presenting Data - Figures**• Advantages? • Disadvantages? Independent variable? Dependent variable? Y-axis First, some exceptions… X-axis**Pie Chart**Percent contribution of various foods to average American’s salt intake.**Histogram**Frequency distribution of speeds for two groups.**Bar Graph**Average bite force for males and females.**Box Plot**What are the parts of these? Box plot of serum Na+ and serum K + in HS and SD. Box plot of kidney weight in HS and SD.**Line Graph**Percent of maximal activity for + taurocholate and – taurocholate as a function of pH levels. Lactate concentrations after amylin injection.**Scatterplot**Correlation: no cause and effect; variables can be interchanged on axes Mortality per year as a function of cigarette consumption.**Scatterplot**Regression: cause and effect; variables CANNOT be interchanged on axes Allometry = how characteristics of living creatures change with size Wing area as a function of body mass.**Collared Lizards**Males Head width Juveniles Hindlimb length Females Hypothesize what explains these differences in allometry Snout-vent length**Statistics**• Why? • To separate real effects from random variation • Assumptions • Observations are independent • Your sample measurements came from a large group (population) • The population has a normal distribution (parametric statistics); if not use different tests (non-parametric) • P-values • The probability that a test statistic at least as extreme would occur by chance alone • If P < 0.05, the test result is typically considered statistically significant**Student t-test**• To compare the difference between two sample means • One- vs. two-tailed • Assumes you do or don’t know the direction of the differences • Conditions • Groups are independent: if not, paired t-test • Normal distribution • Large sample size • Non-parametric: Mann-Whitney U test**Correlation and Regression**• Relationship between continuous variables • Correlation: to measure the strength of a relationship between variables • Regression: • to analyze a cause-effect relationship • to develop a model to predict untested variables • Correlation coefficient: -1 < r < 1 • Goodness of fit: 0 < R2 < 1 • Don’t assume that a linear model is always the best one**Correlation**No cause and effect; variables can be interchanged on axes**Analysis of Variance (ANOVA)**• To examine the effect of levels of a particular treatment • To compare more than two sample groups • Post-hoc tests, e.g., Tukey-Kramer HSD, LSD • It is NOT appropriate to run multiple t-tests on multiple groups of data • Non-parametric: Kruskal-Wallis test**Let’s Measure!**• Measure and plot some trait as a function of body size for all cats in the lab (each cat is a data point) • Measure and plot same trait as a function of body size for all mammal species available in lab (each SPECIES is a data point) Each point = species average Individual cats Trait X Trait X Body size Body size