NTRES 101 Biological Statistics Lab Salamanders

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NTRES 101Biological Statistics LabSalamanders 

• Topics
• Random Sampling
• Data Visualization
• Summary Statistics
• Statistical Analysis

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Website

• http//www.dnr.cornell.edu/pjs31/quantitativepopul
  ation.htm
• NTRES 101 Salamander Statistics Workshop

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Scientific Method

• Make observations
• Form a hypothesis
• Make predictions
• Test the hypothesis
• Build understanding
• Form judgment
• Take action

Shoals Marine Laboratory
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Statistical Methods

• Provide a logical objective structure for
  addressing questions that are inherently
  uncertain.

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Splus

• A statistical computing environment
• An Introduction to S and Splus
• Spector, 1994
• Modern Applied Statistics with S, 4th Ed
• Venables and Ripley, 2002

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Leaves Data

• leaves.txt
• 132 points, leaf length mm
• 61
• 75
• 79
• 68
• 79
• 66
• 73
• 52
• 72

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Histogram (number of leaves per 10 mm category)
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Population Mean
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Population Variance
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Population Standard Deviation
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Population Parameters

• Mean
• Variance
• Standard deviation

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Normal Distribution
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Normal Curve (Using Population Mean and
Variance)
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A Random Sample

• A subset of the population taken in such a way
  that each sample unit was equally likely to get
  selected
• Population
• All leaves
• Sample unit
• One leaf
• Random Sample
• Set of leaves randomly chosen

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Key Statistics

• Mean
• Variance
• Standard deviation
• Median
• Mode
• Quantiles

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Mean
Population
Sample
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Variance
Population
Sample
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Standard Deviation
Population
Sample
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Population ? Sample

• my.samplelt-sample(leaves,50)
• mean(my.sample)
• 68.78
• stdev(my.sample)
• 13.202
• median(my.sample)
• 70

• mean(leaves)
• 67.977
• stdev(leaves)
• 13.666
• median(leaves)
• 68

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Compare Variances

• var(leaves)
• 1 188.2056
• Population variance
• sum(((leaves-mean(leaves))2))/length(leaves)
• 1 186.7798
• Sample variance
• sum(((leaves-mean(leaves))2))/(length(leaves)-1)
• 1 188.2056

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Properties of Sample

• Sample Mean
• Sample Variance
• Sample Standard Deviation
• Variation of an observation
• Standard Error
• Variation of the mean

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Distribution of Leaf Sample Means
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Normal Distribution
x lt- seq(-3,3,by0.2) y lt- dnorm(x)
plot(x,y,typel)
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Normal Distribution

• Good for characterizing
• Sums
• Averages
• Proportions

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Trout Lengths (mm)
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Two Measures of Variation
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Trout 1
Trout 2
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But is there a difference?