﻿ Genetics Statistical

# The Statistical Explanation

All numeric data are estimates of the actual number

• precision = estimate of repeatability
• accuracy = estimate of closeness to Reality

Observable natural variation, sT2, in organisms

• sT2 = sG2 + sE2 + sR2
. . - sG2 = explained by genes
. . - sE2 = explained by environment
. . - sR2 = unexplained, or "residual"

distribution of continuous traits and meristic (integer values only) traits

• usually grouped into classes
. . - in Genetics, classes are usually expressions of traits
. . - divide range (largest - smallest value) by number of classes = class width
. . - label midpoints (half way between bottom and top of class)
. . - display as histogram (bar graph)
• consider:
. . - If one observation is in the wrong class
. . - How does the distribution change?
. . - What is the error in estimating frequency of class?
. . - Could more than zero and less than one observation be incorrect?

• distributions can be summarized
. . - mean = total of observed values / number of values
. . - estimates center of distribution
. . - variance = sum of squared deviates / (number of values - 1)
. . - estimates spread of distribution
. . - deviate = observed value - mean
. . - standard deviation = square root of variance
. . . - approx 68% of values within 1 standard deviate
. . . - approx 95% of values within 2 standard deviates
. . . - approx 99.7% of values within 3 standard deviates

Statistical tests exist to estimate probability that observed data match expected results
• most common in Genetics is Chi-square
• ANOVA (analysis of variance) is also applicable