1 / 32

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.

hedda
Télécharger la présentation

Lecture 2: Replication and pseudoreplication

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related