Lecture 2 replication and pseudoreplication
Download
1 / 32

Lecture 2: Replication and pseudoreplication - PowerPoint PPT Presentation


  • 577 Views
  • Uploaded on

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.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Lecture 2: Replication and pseudoreplication' - hedda


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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Lecture 2 replication and pseudoreplication l.jpg

Lecture 2:Replication and pseudoreplication


This lecture will cover l.jpg
This lecture will cover:

  • Experimental units (replicates)

  • Pseudoreplication

  • Degrees of freedom


Experimental unit l.jpg
Experimental unit

Scale at which independent applications of the same treatment occur

Also called “replicate”, represented by “n” in statistics


Experimental unit4 l.jpg
Experimental unit

Example: Effect of fertilization on caterpillar growth


Experimental unit5 l.jpg
Experimental unit ?

+ F

+ F

- F

- F

n=2


Experimental unit6 l.jpg
Experimental unit ?

+ F

- F

n=1


Pseudoreplication l.jpg
Pseudoreplication

Misidentifying the scale of the experimental unit;

Assuming there are more experimental units (replicates, “n”) than there actually are



Slide9 l.jpg

Example 1.

Hypothesis: Insect abundance is higher in shallow lakes


Slide10 l.jpg

Example 1.

Experiment:

Sample insect abundance every 100 m along the shoreline of a shallow and a deep lake


Slide11 l.jpg

Example 2.

What’s the problem ?

Spatial autocorrelation


Slide12 l.jpg

Example 2.

Hypothesis: Two species of plants have different growth rates


Slide13 l.jpg

  • 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?



Slide15 l.jpg

Example 2.

time


Slide16 l.jpg

Temporal pseudoreplication:

Multiple measurements on SAME individual, treated as independent data points

time

time


Spotting pseudoreplication l.jpg
Spotting pseudoreplication

  • Inspect spatial (temporal) layout of the experiment

  • Examine degrees of freedom in analysis


Degrees of freedom df l.jpg
Degrees of freedom (df)

Number of independent terms used to estimate the parameter

= Total number of datapoints –

number of parameters estimated from data


Slide19 l.jpg

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)


Slide20 l.jpg

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)


Slide21 l.jpg

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


Slide22 l.jpg

Example: Linear regression

Y = mx + b

Therefore 2 parameters estimated simultaneously

(df = n-2)


Slide23 l.jpg

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?


Slide24 l.jpg

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?


Slide25 l.jpg

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


Slide26 l.jpg

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)


Spotting pseudoreplication27 l.jpg
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?


Spotting pseudoreplication28 l.jpg
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


Spotting pseudoreplication29 l.jpg
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?


Spotting pseudoreplication30 l.jpg
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


Why is pseudoreplication a problem l.jpg
Why is pseudoreplicationa problem?

Hint: think about what we use df for!


How prevalent l.jpg
How prevalent?

Hurlbert (1984): 48% of papers

Heffner et al. (1996): 12 to 14% of papers


ad