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
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© 2004 Prof. LaFrance, Ancilla College