Name



|Name | |Lab Section | |

|Pts | | | | |

On your own

PROBLEM #1

You are studying the distribution of a seastar, Pisaster ochraceus, which has two color morphs, Black and ochre. You want to know if color is adaptive and may provide some type of advantage in certain environments. You randomly sample 50 locations and record the color morph, black or not-black, of the first three seastars you encounter. Assume that, if a pattern exists, you will spend time and effort in trying to find out why. If not, you will just move on to a different problem:

1) What is Ho? The observed distribution of black seastars fits a binomial distribution with p=0.593 and K=3

2) What is Ha? The observed distribution of black seastars fits a binomial distribution with p=0.593 and K=3

.

3) What is the measured variable?. Presence or absence of the black seastar for each of 3 seastars

4) Is the sample size fixed? If so, what is the value? The sample size is fixed at 3 (k=3)

5) What is the appropriate theoretical probability distribution for this problem? Binomial

6) What would it mean if the results showed a clumped distribution? That the black seastars are found in clumps and most likely responding to some aspect of that microhabitat.

7) What would it mean if the results showed a uniform distribution? That the black seastars are over dispersed which most likely means that they are defending territories.

8) What would it mean if the observed frequencies were essentially the same as the expected frequencies? The distribution of black seastars is unpredictable (stochastic).

9) Determine statistical error to avoid. Complete Table 1

Table 1: Select the statistical error to avoid for Problem 1 – Pisaster ochraceus color morph frequencies.

|Statistical Decision |Conclusion |Action |What if I’m wrong? |Type of error |

|Accept Ho: Observed fits | | |Lost out on finding |II |

|the expected |No pattern |Find another problem |something interesting. | |

| | | | | |

| | | | | |

|Reject Ho: Observed does | | | |I |

|not fit the expected |Pattern |Try to find out why |Wasted time and energy | |

| | | | | |

| | | | | |

10) Alpha (α) = 0.025

11) Are the parameters Intrinsic or Extrinsic? Intrinsic

Data

Table 2: Data for Problem 1- Color morph frequencies for Pisaster ochraceus.

|# of black morphs per quadrat |Observed Frequency (f) |fY |fY2 |

|(Y) | | | |

|0 |13 |0 |0 |

|1 |7 |7 |7 |

|2 |8 |16 |32 |

|3 |22 |66 |198 |

|TOTAL |50 |89 |237 |

12) How many seastars did you examine? 3*50=150

13) How many of those were black? 89

14) What is the value for p? 89/150 = 0.593

15) What is the value for q? 1-0.593 = 0.407

16) Compute the appropriate Expected Frequency distribution. Complete Table 3

Table 3: Compute expected frequencies for color morphs of Pisaster ochraceus.

|# of black morphs per |Observed Frequency (f)|Probability equations|Probabilities |Expected Frequencies |

|quadrat (Y) | | | | |

|0 |13 |1p0q3 |0.067254 |3.4 |

|1 |7 |3p1q2 |0.294372 |14.7 |

|2 |8 |3p2q1 |0.429494 |21.5 |

|3 |22 |1p3q0 |0.208880 |10.4 |

|TOTAL |50 | | | |

17) For Poisson Only – Lump classes when an Expected Frequency ................
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