Lecture 3: Experimental design: randomization,

replication and design control

This lecture will cover

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

Good options for increasing sample size:

• More replicates

• More blocks

False options for increasing sample size:

• More “repeated measurements”

• Pseudoreplication

Ecological rule #1: the world is not uniform!

Good patch Medium patch Poor patch

3 options in assigning treatments:

1. Randomly assign2. Systematic3. Randomized block

Good patch Medium patch Poor patch

1. Randomly assign

Good patch Medium patch Poor patch

Pros?

Cons?

Statistically robust

With small n, chance of all in a bad patch

1. Randomly assign

Good patch Medium patch Poor patch

Pros?

Cons?

What’s the chance of total spatial segregation of treatments?

2. Systematic

Good patch Medium patch Poor patch

Pros?

Cons?

No clumping possible

Violates random assumption of statistics…but is this so bad?

3. Randomized block

Good patch Medium patch Poor patchBLOCK A BLOCK B BLOCK C

3. Randomized block

BLOCK A BLOCK B BLOCK CNote:1. Do not have to know if patches

differ in quality2. Must have all treatment

combinations represented in each block

3. If WANT to test treatment x block interaction, need replication within blocks

Good options for increasing sample size:

• More replicates

• More blocks

False options for increasing sample size:

• More “repeated measurements”

• Pseudoreplication

Experimental unit

Scale at which independent applications of the same treatment occur

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

Experimental unit

Example: Effect of fertilization on caterpillar growth

Experimental unit ?

+ F - F + F - F

n=2

Experimental unit ?

- F

+ F

n=1

Pseudoreplication

Misidentifying the scale of the experimental unit;

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

When is this a pseudoreplicated design?

- F

+ F

Example 1.

Hypothesis: Insect abundance is higher in shallow lakes

Example 1.

Experiment:

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

Example 1.

What’s the problem ?

Spatial autocorrelation

Example 2.

Hypothesis: Two species of plants have different growth rates

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?

Example 2.

Example 2.

time

Temporal pseudoreplication:

Multiple measurements on SAME individual, treated as independent data points

time

time

Spotting pseudoreplication

1. Inspect spatial (temporal) layout of the experiment

2. 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

Example: VarianceIf 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?

Can the second data point be any number?

Can the third data point be any number?

Yes, say 8

Yes, say 12

No – as mean is fixed !

Variance is Σ

(y – mean)2 / (n-1)

Example: VarianceIf 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)

Example: VarianceIf we have 3 data points with a mean value of 10, what’s the df for the variance estimate?

Subtraction methodTotal number of data points?

Number of estimates from the data?

df= 3-1 = 2

3

1

Example: Analysis of variance (ANOVA)

A B C a1 b1 c1a2 b2 c2a3 b3 c3a4 b4 c4

What is n for each level?

Example: Analysis of variance (ANOVA)

A B C a1 b1 c1a2 b2 c2a3 b3 c3a4 b4 c4

n = 4

How many df for each variance estimate?

df = 3 df = 3 df = 3

Example: Analysis of variance (ANOVA)

A B C a1 b1 c1a2 b2 c2a3 b3 c3a4 b4 c4

What’s the within-treatment df for an ANOVA?

Within-treatment df = 3 + 3 + 3 = 9

df = 3 df = 3 df = 3

Example: Analysis of variance (ANOVA)

A B C a1 b1 c1a2 b2 c2a3 b3 c3a4 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 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 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 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 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

Use of a Control – every ecological field experiment must have a control

Control: experimental unit in the experiment without the treatment

Severs as the baseline to compare the effect/s of the treatment against temporal changes and procedural effects

Before(After Green 1979, in Krebs 1999)

After

Control

Impact

Exposure and head bumps (F2, 196 = 63.21 p<0.001)

control

sham

Treatment Experimental Chamber

Camera

Senevirantne & Jones 2009 Animal Behaviour (in press)

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

1. Basic stats> Oneway.2. Add response variable, treatment

(“grouping”) and block.3. Click OK

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

1. Open fit model tab. Enter y-variable.2. Add treatment, block and –if desired-

treatment x block to “effects”.3. Click on block in effects box and

change attributes to random.4. Change Method option to EMS (not

REML)