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Lecture 2: Replication and pseudoreplication

Lecture 2: Replication and pseudoreplication. This lecture will cover:. Experimental units (replicates) Pseudoreplication Degrees of freedom. Experimental unit. Scale at which independent applications of the same treatment occur Also called “replicate”, represented by “n” in statistics.

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Lecture 2: Replication and pseudoreplication

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  1. Lecture 2:Replication and pseudoreplication

  2. This lecture will cover: • Experimental units (replicates) • Pseudoreplication • Degrees of freedom

  3. Experimental unit Scale at which independent applications of the same treatment occur Also called “replicate”, represented by “n” in statistics

  4. Experimental unit Example: Effect of fertilization on caterpillar growth

  5. Experimental unit ? + F + F - F - F n=2

  6. Experimental unit ? + F - F n=1

  7. Pseudoreplication Misidentifying the scale of the experimental unit; Assuming there are more experimental units (replicates, “n”) than there actually are

  8. When is this a pseudoreplicated design? + F - F

  9. Example 1. Hypothesis: Insect abundance is higher in shallow lakes

  10. Example 1. Experiment: Sample insect abundance every 100 m along the shoreline of a shallow and a deep lake

  11. Example 2. What’s the problem ? Spatial autocorrelation

  12. Example 2. Hypothesis: Two species of plants have different growth rates

  13. Example 2. • Experiment: • Mark 10 individuals of sp. A and 10 of sp. B in a field. • Follow growth rate • over time If the researcher declares n=10, could this still be pseudoreplicated?

  14. Example 2.

  15. Example 2. time

  16. Temporal pseudoreplication: Multiple measurements on SAME individual, treated as independent data points time time

  17. Spotting pseudoreplication • Inspect spatial (temporal) layout of the experiment • Examine degrees of freedom in analysis

  18. Degrees of freedom (df) Number of independent terms used to estimate the parameter = Total number of datapoints – number of parameters estimated from data

  19. Example: Variance If we have 3 data points with a mean value of 10, what’s the df for the variance estimate? Independent term method: Can the first data point be any number? Yes, say 8 Can the second data point be any number? Yes, say 12 Can the third data point be any number? No – as mean is fixed ! Variance is  (y – mean)2 / (n-1)

  20. Example: Variance If we have 3 data points with a mean value of 10, what’s the df for the variance estimate? Independent term method: Therefore 2 independent terms (df = 2)

  21. Example: Variance If we have 3 data points with a mean value of 10, what’s the df for the variance estimate? Subtraction method Total number of data points? 3 Number of estimates from the data? 1 df= 3-1 = 2

  22. Example: Linear regression Y = mx + b Therefore 2 parameters estimated simultaneously (df = n-2)

  23. Example: Analysis of variance (ANOVA) A B C a1 b1 c1 a2 b2 c2 a3 b3 c3 a4 b4 c4 What is n for each level?

  24. Example: Analysis of variance (ANOVA) A B C a1 b1 c1 a2 b2 c2 a3 b3 c3 a4 b4 c4 df = 3 df = 3 df = 3 n = 4 How many df for each variance estimate?

  25. Example: Analysis of variance (ANOVA) A B C a1 b1 c1 a2 b2 c2 a3 b3 c3 a4 b4 c4 df = 3 df = 3 df = 3 What’s the within-treatment df for an ANOVA? Within-treatment df = 3 + 3 + 3 = 9

  26. Example: Analysis of variance (ANOVA) A B C a1 b1 c1 a2 b2 c2 a3 b3 c3 a4 b4 c4 If an ANOVA has k levels and n data points per level, what’s a simple formula for within-treatment df? df = k(n-1)

  27. Spotting pseudoreplication An experiment has 10 fertilized and 10 unfertilized plots, with 5 plants per plot. The researcher reports df=98 for the ANOVA (within-treatment MS). Is there pseudoreplication?

  28. Spotting pseudoreplication An experiment has 10 fertilized and 10 unfertilized plots, with 5 plants per plot. The researcher reports df=98 for the ANOVA. Yes! As k=2, n=10, then df = 2(10-1) = 18

  29. Spotting pseudoreplication An experiment has 10 fertilized and 10 unfertilized plots, with 5 plants per plot. The researcher reports df=98 for the ANOVA. What mistake did the researcher make?

  30. Spotting pseudoreplication An experiment has 10 fertilized and 10 unfertilized plots, with 5 plants per plot. The researcher reports df=98 for the ANOVA. Assumed n=50: 2(50-1)=98

  31. Why is pseudoreplicationa problem? Hint: think about what we use df for!

  32. How prevalent? Hurlbert (1984): 48% of papers Heffner et al. (1996): 12 to 14% of papers

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