Statistics for animal breeding

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Statistics for animal breeding

• Data collection
• Continuous distributions for economic traits.
• Population description in terms of average,
  variance, heritability, correlation, covariance
  between traits

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Sample versus population

• Usually evaluate portion of population.
• Calculate stats on sample.
• Sample stats are estimates of population stats.

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Differences between sample and population
statistics

• Sampling Error
• -Due sample not reflecting population (biase)
• -Due sample size (small samples bigger dif.)
• Non Sampling Error
• -Measurement error

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Differences between sample and population
statistics
A sample representing the population
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Common statistics

• Statistic Population Sample
• mean (avg) ?
• variance ?2 s2
• standard deviation ? s
• coefficient
• of variation C.V C.V.
• regression coef. ? b
• correlation coef. ? r

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What fraction of a data set would you expect to
fall within 1, 2 and 3 standard deviation from
the mean?
From the Normal distribution we expect 68 on the
small interval, 95 in the middle interval and
99 in the large interval.
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Example, 3 pigs

• Pig Backfat (inches)
• 1 .9
• 2 .8
• 3 .7
• mean (.9 .8 .7) / 3 .8 inches

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Variance
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Standard deviation
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Coefficient of Variation
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2nd Sample, 3 pigs

• Pig Backfat (inches)
• 1 1,2
• 2 .8
• 3 .4
• mean (1.2 .8 .4) / 3 .8 inches

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• Sample 1
• (data .9, .8, .7 in)
• mean .8 in
• s2 .01 in2
• s .1 in
• C.V. 12.5

• Sample 2
• (data 1.2, .8, .4 in)
• mean .8
• s2 .16 in2
• s .4 in
• C.V. 50

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Co-variance
Positive

• A description of how two traits vary together in
  a population.
• Three types of variation
• -Positive
• -Negative or
• -No co-variation

Negative
No Co-variation
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Positive () or Negative (-)
Correlation
Regression
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Covariance is a measure of co-variation Cov(X,Y)
or SXY
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Correlation coefficient (r)
Co-variance
X and Y variances
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Correlation coefficient (r)

• A standardized measure of the strength/degree of
  relationship between 2 variables (x and y).
• Ranges in value from -1 to 1. No units.
• negative r -1 to 0. High values of x tend to
  occur with high values of y and vice versa.
• positive r 0 to 1. Higher values of x tend to
  occur with lower values of y and vice versa.

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Correlation coefficient (r)
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Correlation coefficient (r)

• Positive correlations
• Study time and test score
• Mature cow wt with hip height
• Calf birth wt with yearling wt
• Milk yield with feed intake
• Negative correlations
• Swine backfat with Lean RibEye Area
• ADG with F/G (feed Efficiency)
• Note negative does not imply unfavorable.

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Correlation coefficient (r)
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Correlation coefficient (r)

• Caution. r can be misleading.
• Does not necessarily imply cause-and-effect.

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Regression coefficient (b)

• Predicts y from x.
• b change in y per 1-unit increase in x.
• Equals slope of a straight line.

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Regression coefficient (b)
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Correlation (r)Regression coefficient (b)