# Presentation: 340026

## Analysis of Data From Channel Islands National Park

- Paul Geissler, U.S. Geological Survey
-  **Red Urchins**
-  Within-Subject Functions Approach
-  Analysis of Variance Approach – Period Comparison
-  Analysis of Variance Approach – Slope
-  Looking At The Population Trajectory
-  **Orange-Crowned Warblers**
-  Within-Subject Functions Approach
-  Analysis of Variance Approach – Period Comparison
-  Analysis of Variance Approach – Slope
-  Looking At The Population Trajectory
-  Discussion

## Slide 2

## Slide 3

## Slide 4

## Slide 5

## Slide 6

## Slide 7

## Slide 8

## Within-Subject Functions Approach Analysis of Variance

|  |  | Log Differences |  | Log Slope |  |
| --- | --- | --- | --- | --- | --- |
| Source
 | df | Mean Square | P | Mean Square | P |
| Island | 4 | 0.711 | 0.030 | 0.00365 | 0.130 |
| Error | 11 | 0.177 |   | 0.00162 |   |

## Summary Statistics For Site Functions

|  | Diff | Slope | Log Diff | L Slope |
| --- | --- | --- | --- | --- |
| N | 16 | 16 | 16 | 16 |
| Mean | 0.883 | 0.122 | 0.011 | 0.016 |
| 95% CL | 1.912 | 0.227 | 0.312 | 0.04 |
| 95% CL | -0.145 | 0.017 | -0.291 | -0.009 |
| Std.Dev. | 0.483 | 0.049 | 0.141 | 0.012 |
| Std.Error | 1.93 | 0.196 | 0.565 | 0.047 |
| t | 1.828 | 2.490 | 0.078 | 1.333 |
| P | 0.087 | 0.025 | 0.939 | 0.202 |

- Mean count is 4.1 urchins.

## Mean count is 4.1 urchins.

## Mean count is 4.1 urchins, with 20 years of data

## Analysis of Variance ApproachPeriod Comparison 

| Source | d.f. | Expected Mean Square | F  |
| --- | --- | --- | --- |
| I: Islands | i-1 | spyI2 + pyS2 + SY2 | I/S |
| S: Sites (Island)  | i(s-1) | pyS2 + SY2 |   |
| P: Periods | p-1 | isyP2 + isY2 + SY2 | P/Y |
| Y: Years (Period) | p(y-1) | isY2 + SY2 |   |
| IP: I x P | (a-1)(p-1) | syIP2 + SY2 | IP/SY |
| SY: S x Y (I, P) | ip(s-1)(y-1) | SY2 |   |

## Analysis of Variance

|  |  |  | Untransformed |  | Transformed |  |
| --- | --- | --- | --- | --- | --- | --- |
| Source | Model | d.f. | Mean Square | P | Mean Square | P |
| I: Islands | M1 | 4 | 60.943 | 0.715 | 4.345 | 0.727 |
| S: Sites (Island)  | M1 | 13 | 114.822 |   | 8.449 |   |
| P: Periods | M1 | 1 | 51.457 | 0.203 | 0.005 | 0.966 |
| Y: Years (Period) | M1 | 18 | 29.426 |   | 2.610 |   |
| IP: I x P | M2 | 4 | 31.308 | 0.000 | 3.106 | 0.000 |
| SY: S x Y (I, P) | M3-M2 | 231 | 3.263 |   | 0.283 |   |

**Analysis of Variance**

- M1: count = constant + island + site(island) + period + year(period)
- M2: count = constant + island + site(island) + period + year(period) + island*period
- M3: count = constant + island + site(island) + period + year(period) + island*period + site(island)*year(period)

## Within-Subject Functions

- se = 0.48, df = 15

- Analysis of Variance
- rmse = 5.42, df = 18

## Analysis of Variance Approach – Slope

- M1: count = constant + island + site (island) 	+ categorical year
- M2: count = constant + island + site (island) 	+ numerical year
- M3: count = constant + island + site (island) 	+ categorical year 	+ categorical year * island
- M4: count = constant + island + site (island) 	+ numerical year + numerical year * island

## Analysis of Variance Approach – Slope 

|  |  |  | Untransformed |  | Transformed |  |
| --- | --- | --- | --- | --- | --- | --- |
| Source | Model | df | Mean Square | P | Mean Square | P |
| Islands | M1 | 4 | 60.943 |   | 4.345 |   |
| Sites (Island) | M1 | 13 | 114.822 |   | 8.449 |   |
| Years | M1 | 19 | 30.770 |   | 2.473 |   |
| - Slope | M2 | 1 | 118.698 | 0.046 | 1.384 | 0.469 |
| - Residual  | M2-M1 | 18 | 25.885 |   | 2.533 |   |
| Islands * Years | M3 | 76 | 6.055 |   | 6.055 |   |
| - Slopes | M4 | 4 | 24.632 | 0.001 | 24.632 | 0.000 |
| - Residual  | M4-M3 | 72 | 5.023 |   | 0.537 |   |

## Within-Subject Functions

- se = 0.05, df = 15

- Analysis of Variance
- rmse = 5.09, df = 18

## Counts of Red Urchins

## Standardized Counts of Red Urchins

## Orange-Crowned Warblers

| Observer | Years | Detectability | CV |
| --- | --- | --- | --- |
| TJC | 94, 95 | 0.047 | 21.6% |
| GSA | 96, 97, 98 | 0.309 | 18.5% |
| LCD |  00 | 0.110 | 24.4% |

- Detectability was estimated by John Sauer.

## Slide 22

## Within-Subject Functions Approach

|  | Slope |  | Difference |
| --- | --- | --- | --- |
|  | Unadj. | Adj. | Unadj. |
| N of cases | 42 | 52 | 52 |
| Mean | -0.205 | -0.303 | -0.765 |
| 95% CI Upper | 0.000 | 0.447 | 1.411 |
| 95% CI Lower | -0.410 | -1.054 | -2.941 |
| Std. Error | 0.102 | 0.374 | 1.084 |
| Standard Dev | 0.658 | 2.697 | 7.816 |
| t | 2.010 | 0.810 | 0.706 |
| P | 0.051 | 0.422 | 0.484 |

## Means

- Unadjusted 0.50
- Adjusted     4.59
- 0.8/7.3 = 0.50/4.59

## Analysis of Variance Approach – Period Comparison

| Source | df | Mean Square | P |
| --- | --- | --- | --- |
| Habitat | 4 | 208.63 | 0.013 |
| Site(Habitat) | 47 | 58.28 |   |
| Period | 1 | 80.65 | 0.745 |
| Year(Period) | 4 | 665.59 |   |
| Habitat*Period | 4 | 184.87 | 0.060 |
| Site(Habitat)*Year(Period) | 100 | 78.90 |  |

## Within-Subject Functions

- se = 1.1, df = 51

- Analysis of Variance
- rmse = 25.8, df = 4

## Analysis of Variance Approach – Unadjusted Slope

| Source | df | Mean Square | P |
| --- | --- | --- | --- |
| Observers | 2 | 0.936 |   |
| Habitats | 4 | 0.549 |   |
| Sites (Habitat) | 47 | 0.397 |   |
| Years | 3 | 0.524 |   |
| - slope | 1 | 0.721 | 0.323 |
| - residual  | 2 | 0.426 |   |
| Islands * Years | 8 | 0.352 |   |
| - slope | 4 | 0.501 | 0.202 |
| - residual  | 4 | 0.203 |   |

## Analysis of Variance Approach – Adjusted Slope

| Source | df | Mean Square | P |
| --- | --- | --- | --- |
| Observers | 4 | 208.627 |   |
| Habitats | 47 | 58.280 |   |
| Sites (Habitat) | 5 | 550.011 |   |
| Years | 1 | 338.312 | 0.495 |
| - slope | 4 | 602.937 |   |
| - residual  | 10 | 320.773 |   |
| Islands * Years | 4 | 166.923 | 0.807 |
| - slope | 6 | 423.340 |   |
| - residual  | 4 | 208.627 |   |

## Within-Subject Functions

- se = 0.10 , df = 41

- Analysis of Variance
- rmse = 0.65, df = 2

## Within-Subject Functions

- se = 0.4 , df = 51

- Analysis of Variance
- rmse = 25.6, df = 4

## Discussion - Approaches

|  | Within-Subject | ANOVA |
| --- | --- | --- |
| Error | Sites | Years |
| Tests | Consistency | Fit of line/period |
| Driver | Habitat changes | Weather, etc. |
| df | more | less |
|  | Simple | Complex |
|  |  | Annual pop not independent |

## Discussion – Power

-  Concerns about misuse
-  Conf. int. and power are properties of a test.
-  Use confidence intervals for location.
-  Use test when need to make a decision.
-  Power evaluates effectiveness of monitoring.
-  If you have data, use it to estimate power of your specific test.
-  Simulation approach is useful where data are not available.

## Discussion – Detectability

-  Importance of estimating
-  Needed to compare counts by different observers
-  Estimated with substantial uncertainty
-  Counts are no longer independent after adjustment
-  I do not know how to include detectability standard errors in an ANOVA or other analysis.