Comparing two management options

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Comparing two management options

• ESM 206A
• Nov 28 2006

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Environmental challenge

• The problem There is a great deal of controversy
  about how to manage California grasslands for
  biodiversity values. In particular, there is
  debate about whether grazing by cattle is
  promotes or is deleterious to plant diversity
• Data on plant diversity and relative abundance
  have been collected from plots at Sedgwick
  Reserve where grazing has been either allowed or
  excluded.
• Your job Using these data, determine whether
  grazing increases or decreases plant diversity.

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Diversity in Sedgwick grassland plots
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2-sample t-test
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Paired t-test
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2-sample vs paired t-test

• TWO SAMPLE t-TEST
• Difference of means
• Use when observations are independent between
  groups
• Assumes each population is normally distributed

• PAIRED t-TEST
• Mean of differences
• Use when observations are naturally paired
• Assumes population of differences is normally
  distributed

• Both will estimate same mean difference
• If there is variation among pairs (e.g., due to
  location, soil type, habitat), then paired test
  will have more power to reject null hypothesis

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More on two-sample tests

• Null hypothesis for two-sample t-test actually
  assumes that the two datasets are samples from
  the same statistical populations
• H0 mx my, sx sy, both normal
• If population variances differ, P-values are not
  correct
• Solution Heteroskedastic t-test (also known as
  Satterthwaites approximate test)
• Calculate t statistic in same way
• Complex formula for df

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Bootstrapping (for non-normal populations)

• Paired test Calculate differences, di xi - yi,
  and treat like one-sample test
• H0 md 0
• Two sample test the permutation test
• H0 X and Y are from identical populations
• Pool the observations from x and y
• Randomly assign the observations to the two
  groups, ensuring that nx and ny are the same as
  in the data this is the bootstrap sample
• Calculate t-statistic for the bootstrap sample in
  same way as for data
• Repeat many times compare data t-statistic with
  distribution from bootstrap samples