Evolution, 4th Edition

SUMMARY

■■A probability distribution describes the frequen-

cies of different events or kinds of things. A

distribution can be either discrete or continuous.

■■Two of the most commonly used descriptive

statistics are the mean, which describes the

average individual in a population, and the vari-

ance, which describes the amount of dispersion

around the mean.

■■A correlation measures the degree to which two

kinds of measurements vary together.

■■A regression predicts the value of one variable

from the value of another. The regression coef-

ficient is the slope of a regression line.

■■When we have two or more measurements on

each individual, principal components are used

to simplify analyses by reducing the size of the

data set.

■■Statistics is used to estimate properties of a pop-

ulation (such as the mean and variance) based on

a sample from it.

■■Statistics can measure our confidence in a null

hypothesis. We reject the null hypothesis if there

is less than a 5 percent probability that the data

would result from it. If we reject the null hypoth-

esis that the means of two populations are equal,

we say that they are significantly different.

■■The likelihood is the probability that the data

would be produced, given a specific assumption

for how the data were produced. Likelihood can

be used to estimate properties of a distribution

such as its mean and variance, to test hypotheses,

and to determine confidence intervals (the range

of plausible values for a property of a popula-

tion, such as its mean).

■■Bayesian inference combines prior informa-

tion about the distribution of a variable with

new data. As with likelihood, it is used to make

estimates, test hypotheses, and so on. A second

use of Bayesian inference is to estimate quantities

when the likelihood function is too complex to

analyze directly.

TERMS AND CONCEPTS

Bayesian inference

confidence interval

continuous

distribution

correlation

covariance

descriptive statistic

discrete distribution

estimate

maximum likelihood

estimate

mean

null hypothesis

population

posterior probability

distribution

principal component

prior probability

distribution

probability

distribution

randomization

regression

sample

standard deviation

statistically

significant

variance

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