1 / 34

Spotting pseudoreplication

Spotting pseudoreplication. Inspect spatial (temporal) layout of the experiment Examine degrees of freedom in analysis. Degrees of freedom (df). Number of independent terms used to estimate the parameter = Total number of datapoints – number of parameters estimated from data.

shoshana-benjamin
Download Presentation

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

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

  3. 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)

  4. 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)

  5. 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

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

  7. 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?

  8. 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?

  9. 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

  10. 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)

  11. 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?

  12. 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

  13. 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?

  14. 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

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

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

  17. Statistics review Basic concepts: • Variability measures • Distributions • Hypotheses • Types of error • Common analyses • T-tests • One-way ANOVA • Two-way ANOVA • Randomized block

  18. Variance • Ecological rule # 1: Everything varies • …but how much does it vary?

  19. Variance • S2= Σ (xi – x )2 • n-1 Sum-of-square cake x

  20. Variance • S2= Σ (xi – x )2 • n-1 x

  21. S2= Σ (xi – x )2 • n-1 Variance What is the variance of 4, 3, 3, 2 ? What are the units?

  22. Variance variants 1. Standard deviation (s, or SD) = Square root (variance) Advantage: units

  23. Variance variants 2. Standard error (S.E.) = s n Advantage: indicates precision

  24. How to report • We observed 29.7 (+ 5.3) grizzly bears per month (mean + S.E.). • A mean (+ SD)of 29.7 (+ 7.4) grizzly bears were seen per month + 1SE or SD - 1SE or SD

  25. Distributions Normal • Quantitative data Poisson • Count (frequency) data

  26. Normal distribution 67% of data within 1 SD of mean 95% of data within 2 SD of mean

  27. Poisson distribution mean Mostly, nothing happens (lots of zeros)

  28. Poisson distribution • Frequency data • Lots of zero (or minimum value) data • Variance increases with the mean

  29. What do you do with Poisson data? • Correct for correlation between mean and variance by log-transforming y (but log (0) is undefined!!) • Use non-parametric statistics (but low power) • Use a “generalized linear model” specifying a Poisson distribution

  30. Hypotheses • Null (Ho): no effect of our experimental treatment, “status quo” • Alternative (Ha): there is an effect

  31. Whose null hypothesis? Conditions very strict for rejecting Ho, whereas accepting Ho is easy (just a matter of not finding grounds to reject it). A criminal trial? Exotic plant species? WTO?

  32. Hypotheses Null (Ho) and alternative (Ha): always mutually exclusive So if Ha is treatment>control…

  33. Types of error Reject Ho Accept Ho Ho true Ho false

  34. Types of error • Usually ensure only 5% chance of type 1 error (ie. Alpha =0.05) • Ability to minimize type 2 error: called power

More Related