Lecture%202:%20Blocks%20and%20pseudoreplication

1
Lecture 2Blocks and pseudoreplication
2
This lecture will cover

• Blocks
• Experimental units (replicates)
• Pseudoreplication
• Degrees of freedom

3

• Good options for increasing sample size
• More replicates
• More blocks
• False options for increasing sample size
• More repeated measurements
• Pseudoreplication

4
Ecological rule 1 the world is not uniform!
Medium patch
Poor patch
Good patch
5

• 3 options in assigning treatments
• Randomly assign
• Systematic
• Randomized block

Medium patch
Poor patch
Good patch
6
1. Randomly assign
Medium patch
Poor patch
Good patch
Statistically robust
Pros? Cons?
With small n, chance of all in a bad patch
7
1. Randomly assign
Medium patch
Poor patch
Good patch
Whats the chance of total spatial segregation of
treatments?
Pros? Cons?
8
2. Systematic
Medium patch
Poor patch
Good patch
No clumping possible
Pros? Cons?
Violates random assumption of statisticsbut is
this so bad?
9
3. Randomized block
Medium patch
Poor patch
Good patch
BLOCK A
BLOCK B
BLOCK C
10
3. Randomized block
BLOCK A
BLOCK B
BLOCK C

• Note
• Do not have to know if patches differ in quality
• Must have all treatment combinations represented
  in each block
• If WANT to test treatment x block interaction,
  need replication within blocks

11
How to analyze a blocked design in JMP (Method 1)

1. Basic statsgt Oneway.
2. Add response variable, treatment (grouping) and
   block.
3. Click OK

12
How to analyze a blocked design in JMP (Method 2)

• Open fit model tab. Enter y-variable.
• Add treatment, block and if desired- treatment x
  block to effects.
• Click on block in effects box and change
  attributes to random.
• 4. Change Method option to EMS (not REML)

13

• Good options for increasing sample size
• More replicates
• More blocks
• False options for increasing sample size
• More repeated measurements
• Pseudoreplication

14
Experimental unit
Scale at which independent applications of the
same treatment occur Also called replicate,
represented by n in statistics
15
Experimental unit
Example Effect of fertilization on caterpillar
growth
16
Experimental unit ?
F
F
- F
- F
n2
17
Experimental unit ?
F
- F
n1
18
Pseudoreplication
Misidentifying the scale of the experimental
unit Assuming there are more experimental
units (replicates, n) than there actually are
19
When is this a pseudoreplicated design?
F
- F
20
Example 1. Hypothesis Insect abundance is
higher in shallow lakes
21
Example 1. Experiment Sample insect abundance
every 100 m along the shoreline of a shallow and
a deep lake
22
Example 2. Whats the problem ?
Spatial autocorrelation
23
Example 2. Hypothesis Two species of plants
have different growth rates
24

• 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 n10, could this still
be pseudoreplicated?
25
Example 2.
26
Example 2.
time
27
Temporal pseudoreplication Multiple
measurements on SAME individual, treated as
independent data points
time
time
28
Spotting pseudoreplication

1. Inspect spatial (temporal) layout of the
   experiment
2. Examine degrees of freedom in analysis

29
Degrees of freedom (df)
Number of independent terms used to estimate the
parameter Total number of datapoints number
of parameters estimated from data
30
Example Variance If we have 3 data points with a
mean value of 10, whats 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)
31
Example Variance If we have 3 data points with a
mean value of 10, whats the df for the variance
estimate? Independent term method
Therefore 2 independent terms (df 2)
32
Example Variance If we have 3 data points with a
mean value of 10, whats 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
33
Example Linear regression Y mx b
Therefore 2 parameters estimated simultaneously
(df n-2)
34
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?
35
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?
36
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
Whats the within-treatment df for an ANOVA?
Within-treatment df 3 3 3 9
37
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, whats a simple formula for
within-treatment df?
df k(n-1)
38
Spotting pseudoreplication
An experiment has 10 fertilized and 10
unfertilized plots, with 5 plants per plot. The
researcher reports df98 for the ANOVA
(within-treatment MS). Is there
pseudoreplication?
39
Spotting pseudoreplication
An experiment has 10 fertilized and 10
unfertilized plots, with 5 plants per plot. The
researcher reports df98 for the ANOVA. Yes! As
k2, n10, then df 2(10-1) 18
40
Spotting pseudoreplication
An experiment has 10 fertilized and 10
unfertilized plots, with 5 plants per plot. The
researcher reports df98 for the ANOVA. What
mistake did the researcher make?
41
Spotting pseudoreplication
An experiment has 10 fertilized and 10
unfertilized plots, with 5 plants per plot. The
researcher reports df98 for the ANOVA. Assumed
n50 2(50-1)98
42
Why is pseudoreplicationa problem?
Hint think about what we use df for!
43
How prevalent?
Hurlbert (1984) 48 of papers Heffner et al.
(1996) 12 to 14 of papers