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