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Measuring Variation Patterns of distribution. Normal distributions Most common type to describe individuals w/in populations Bell shaped More are closer to the average than to the extremes Based on continuous variables Binomial distributions
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Measuring VariationPatterns of distribution • Normal distributions • Most common type to describe individuals w/in populations • Bell shaped • More are closer to the average than to the extremes • Based on continuous variables • Binomial distributions • Good for gene/allele distributions w/in a population • Uniform and predictable, • Binomial (polynomial) equations, (p+q)2 • Pascal’s triangle used to calculate coefficients • Based on discrete variables • Poisson distributions • Few populations, good for spatial or temporal patterns in ecology • Usually Skewed, not uniform • More are close to one extreme than the other • Based on discrete variables; # indiv. in area
Measuring VariationDescriptive Statistics of a Population Central Tendencies of data in a population • Mean, Avg. ( x ) • Calculated value as the average of observations • Continuous variables or counts Ex. Body wt.(g): 125, 134, 139, 142, 147, 147, 156, x= 141.4g • Median, M, used for averages of ranked data, (percentiles, quartiles) • the middle value, if odd Ex. Body wt.(g): 125, 134, 139, 142, 147, 147, 156, M= 142g • the average of two central values, if even Ex. Body wt.(g): 125, 134, 139, 142, 147, 156, M= 140.5g • Mode • Observed value that most frequently occurs Ex. Body wt.(g): 125, 134, 139, 142, 147, 147, 156 = 147g
x s2 Measuring VariationDescriptive Statistics of a Population Distribution of data in a population • Range, observed dispersion of data • max and min values • Variance, s2 • estimates the width of dispersion of a measurable parameter in a population about its mean ( x ); • Normal or bell shaped distributions • Mean, median, & mode are equal
mean variance 1sd 2sd 3sd Measuring VariationDescriptive Statistics of a Population Degree of Variation of a measurable parameter • Standard deviation, s or sd • Sq. rootof Variance, s2 • 1 sd unit ± the mean = 68% pop. • 2 sd units ± the mean = 95% pop. • (± 1.96 sd units min. for significance) • 3 sd units ± the mean = 99% pop
Measuring VariationWhisker-Box Plot Comparisons can be visualized using a whisker-box plot. Often means separated by at least 2 sd units are likely to be significantly different and should be subjected to statistical testing. Range = whisker Mean = whisker Dependent variable sd = box 1 sd 1 sd Species 1 Species 2
Measuring VariationDescriptive Statistics of a Population Comparing means for significance using a whiskers-box plot. Means are expected to be significantly different because they are separated by more than 2 sd. 1 sd 1 sd 1 sd
Measuring VariationDescriptive Statistics of a Population Comparing means for significance using a whiskers-box plot. Means are NOT significantly different because they are separated by less than 2 sd. 1 sd 1 sd