Jon Lefcheck

February 7, 2014

- What is the hypothesis?
- What are the treatments?
- Control
- Randomization
- Replication
- Blocking
- Independence

A **hypothesis** is a question (or questions) that you hope to answer through experimentation.

Hypotheses should ideally be developed *before* data are collected.

Hypotheses should be developed to address the range of possible outcomes, not just “it worked” or “it didn't.”

An **experimental treatment** is a manipulation or procedure that is administered to experimental replicates.

Treatments should be selected to directly address your hypotheses.

A **control** represents unmanipulated replicates against which treatment replicates are compared.

Example: Andrew & Underwood 1993

Do the effects of sea urchin grazing on filamentous algae depend on urchin density (100?

Densities = 100% (natural), 66%, 33%, 0%

```
TREAT PATCH QUAD ALGAE
1 0% 1 1 46
2 0% 1 2 44
3 0% 1 3 41
4 0% 1 4 29
5 0% 1 5 11
6 0% 2 1 65
```

Df | Sum Sq | Mean Sq | F value | Pr(>F) | |
---|---|---|---|---|---|

TREAT | 3 | 4526.42 | 1508.81 | 2.84 | 0.0434 |

TREAT: C vs 66 | 1 | 1109.47 | 1109.47 | 2.09 | 0.1524 |

TREAT: C vs 33 | 1 | 605.49 | 605.49 | 1.14 | 0.2889 |

TREAT: C vs 0 | 1 | 2811.45 | 2811.45 | 5.30 | 0.0241 |

Residuals | 75 | 39811.79 | 530.82 |

Df | Sum Sq | Mean Sq | F value | Pr(>F) | |
---|---|---|---|---|---|

TREAT | 2 | 3521.62 | 1760.81 | 2.50 | 0.0915 |

TREAT: 66 vs 33 | 1 | 1725.21 | 1725.21 | 2.45 | 0.1235 |

TREAT: 66 vs 0 | 1 | 1796.41 | 1796.41 | 2.55 | 0.1161 |

Residuals | 56 | 39500.07 | 705.36 |

What does it mean, going from 66% to 33% natural density when natural density is not included? How would you interpret this?

**Randomization** refers to the idea that replicates are not assigned to treatments with any bias.

Bad randomization: all replicates in location A recieve Treatment A, all replicates in location B recieve Treatment B.

Example: Quinn 1988

Does limpet density (8, 15, 30, and 45 individuals) and season (spring vs summer) influence egg production?

```
DENSITY SEASON EGGS
1 8 spring 2.875
2 8 spring 2.625
3 8 spring 1.750
4 8 summer 2.125
5 8 summer 1.500
6 8 summer 1.875
7 15 spring 2.600
8 15 spring 1.866
9 15 spring 2.066
10 15 summer 0.867
```

Df | Sum Sq | Mean Sq | F value | Pr(>F) | |
---|---|---|---|---|---|

DENSITY | 3 | 5.28 | 1.76 | 9.67 | 0.0007 |

SEASON | 1 | 3.25 | 3.25 | 17.84 | 0.0006 |

DENSITY:SEASON | 3 | 0.16 | 0.05 | 0.30 | 0.8240 |

Residuals | 16 | 2.91 | 0.18 |

A strong effect of both density and season, but the effects are not interactive!

Let's put all small densities in spring and all large densities in summer.

```
DENSITY SEASON EGGS DENS
1 8 spring 2.875 8
2 8 spring 2.625 8
3 8 spring 1.750 8
4 8 spring 2.125 8
5 8 spring 1.500 8
6 8 spring 1.875 8
7 15 spring 2.600 15
8 15 spring 1.866 15
9 15 spring 2.066 15
10 15 spring 0.867 15
```

As we planned, small densities are in spring and large densities are in summer.

Df | Sum Sq | Mean Sq | F value | Pr(>F) | |
---|---|---|---|---|---|

DENSITY | 3 | 5.28 | 1.76 | 5.57 | 0.0061 |

Residuals | 20 | 6.33 | 0.32 |

Uh-oh, we can no longer estimate an effect of season because we lack proper replication for all density treatments across spring and summer!

**Replication** is the act of duplicating measurements of experimental treatments.

Replication increases the power, and therefore accuracy, of your experimental results.

Example: Andrew & Underwood 1993

Do the effects of sea urchin grazing on filamentous algae depend on urchin density?

Df | Sum Sq | Mean Sq | F value | Pr(>F) | |
---|---|---|---|---|---|

TREAT | 3 | 4526.42 | 1508.81 | 2.84 | 0.0434 |

Residuals | 75 | 39811.79 | 530.82 |

What happens when we halve the number of replicates?

Df | Sum Sq | Mean Sq | F value | Pr(>F) | |
---|---|---|---|---|---|

TREAT | 3 | 3687.97 | 1229.32 | 1.87 | 0.1519 |

Residuals | 35 | 22953.46 | 655.81 |

If we repeat this procedure 100 times, how many times is TREATMENT significant?

significant | |
---|---|

FALSE | 93 |

TRUE | 7 |

Not very many, which would lead us to conclude that limpet density does not have any effect on algal cover.

But what if we double the number of replicates, and repeat 100 times again?

significant | |
---|---|

FALSE | 6 |

TRUE | 94 |

Increasing replication (and thus power) has shown us that algal cover is indeed related to limpet density, it is just so variable we couldn't detect it with only a few samples!

**Blocking** is the act of grouping replicates into discrete spatial or temporal units.

Blocking helps account for any error associated with being in a particular place or time.

**Randomized block design**: each block receives at least 1 replicate of each treatment

Example: Caffrey 1982

How do different substrate types (granite, slate & cement) influence barnacle settlement?

```
substrate patch abundance
1 granite 1 8
2 slate 1 2
3 cement 1 3
4 granite 2 14
5 slate 2 11
6 cement 2 8
```

Some patches are more variable than others!

Df | Sum Sq | Mean Sq | F value | Pr(>F) | |
---|---|---|---|---|---|

substrate | 2 | 117.60 | 58.80 | 4.01 | 0.0362 |

Residuals | 18 | 263.73 | 14.65 |

Df | Sum Sq | Mean Sq | F value | Pr(>F) | |
---|---|---|---|---|---|

substrate | 2 | 117.60 | 58.80 | 2.90 | 0.0724 |

Residuals | 27 | 547.90 | 20.29 |

Removing the blocking term eliminates the relationship between abundance and substrate type!

**Independence** is the idea that replicates are completely isolated from one another.

Non-independence arises when replicates are close together in space and/or time, and could influence one another non-randomly.

Non-independence also arises when subreplicates are taken from the same replicate and treated as independent, a condition known as **pseudoreplication**.

Example: Driscoll & Roberts 1997

Investigated the impact of fuel-reduction burning on the number of individual male frogs calling.

Measured the difference in the number of calls between matched burned and unburned sites across three years: 1992 pre-burn, 1993 post-burn, and 1994 post-burn.

**Non-independence**: Two post-burn years are more closely related than either is to the pre-burn year.

```
BLOCK BLCK YEAR CALLS
1 logging 1 1 4
2 angove 2 1 -10
3 newpipe 3 1 -15
4 oldquinE 4 1 -14
5 newquinW 5 1 -4
6 newquinE 6 1 0
```

Accounted for closer relationship between 1993 and 1994.

numDF | denDF | F-value | p-value | |
---|---|---|---|---|

(Intercept) | 1 | 28.00 | 0.92 | 0.34 |

YEAR | 2 | 28.00 | 4.47 | 0.02 |

Df | Sum Sq | Mean Sq | F value | Pr(>F) | |
---|---|---|---|---|---|

YEAR | 2 | 287.17 | 143.58 | 2.43 | 0.1068 |

Residuals | 28 | 1657.50 | 59.20 |

Year is no longer significant!

Before conducting an experiment, consider:

- What is my question?
- Do my treatments address this question?
- Do I have a baseline against which to test treatment effets?
- What are my replicates?
- Are replicates random and independent?
- Are there any additional sources of error?