Abstract: That cuckoo eggs were peculiar to the locality where found was already known in 1892. A study by E.B. Chance in 1940 called The Truth About the Cuckoo demonstrated that cuckoos return year after year to the same territory and lay their eggs in the nests of a particular host species. Further, cuckoos appear to mate only within their territory. Therefore, geographical sub-species are developed, each with a dominant foster-parent species, and natural selection has ensured the survival of cuckoos most fitted to lay eggs that would be adopted by a particular foster-parent species.

Image: Boxplot of Cuckoo Eggs by Other Bird Species

Number of cases: 115

Variable Names:

  1. 1. MDW PIPIT: Meadow Pipit
  2. 2. TREE PIPIT: Tree Pipit
  3. 3. HDGE SPRW: Hedge Sparrow
  4. 4. ROBIN: Robin
  5. 5. PIED WTAIL: Pied Wagtail
  6. 6. WREN: Wren
     

All data are lengths in millimeters (see table on separate page).  For this test, we are comparing average egg lengths among the host species type.

 

 

 

egg

MDW PIPIT

TREE PIPIT

HDGE SPRW

PIED ROBIN

WTAIL

 WREN

1

19.65

21.05

20.85

21.05

21.05

19.85

2

20.05

21.85

21.65

21.85

21.85

20.05

3

20.65

22.05

22.05

22.05

21.85

20.25

4

20.85

22.45

22.85

22.05

21.85

20.85

5

21.65

22.65

23.05

22.05

22.05

20.85

6

21.65

23.25

23.05

22.25

22.45

20.85

7

21.65

23.25

23.05

22.45

22.65

21.05

8

21.85

23.25

23.05

22.45

23.05

21.05

9

21.85

23.45

23.45

22.65

23.05

21.05

10

21.85

23.45

23.85

23.05

23.25

21.25

11

22.05

23.65

23.85

23.05

23.45

21.45

12

22.05

23.85

23.85

23.05

24.05

22.05

13

22.05

24.05

24.05

23.05

24.05

22.05

14

22.05

24.05

25.05

23.05

24.05

22.05

15

22.05

24.05

*

23.25

24.85

22.25

16

22.05

*

*

23.85

*

*

17

22.05

*

*

*

*

*

18

22.05

*

*

*

*

*

19

22.05

*

*

*

*

*

20

22.05

*

*

*

*

*

21

22.25

*

*

*

*

*

22

22.25

*

*

*

*

*

23

22.25

*

*

*

*

*

24

22.25

*

*

*

*

*

25

22.25

*

*

*

*

*

26

22.25

*

*

*

*

*

27

22.25

*

*

*

*

*

28

22.25

*

*

*

*

*

29

22.45

*

*

*

*

*

30

22.45

*

*

*

*

*

31

22.45

*

*

*

*

*

32

22.65

*

*

*

*

*

33

22.65

*

*

*

*

*

34

22.85

*

*

*

*

*

35

22.85

*

*

*

*

*

36

22.85

*

*

*

*

*

37

22.85

*

*

*

*

*

38

23.05

*

*

*

*

*

39

23.25

*

*

*

*

*

40

23.25

*

*

*

*

*

41

23.45

*

*

*

*

*

42

23.65

*

*

*

*

*

43

23.85

*

*

*

*

*

44

24.25

*

*

*

*

*

45

24.45

*

*

*

*

*

Average

22.29888889

23.09

23.12142857

22.575

22.90333333

21.13

SD

0.920627805

0.901427439

1.068736545

0.684592336

1.067618623

0.743735744

Question:

Assuming the samples of cuckoo lengths are independent, perform three two-sample t-tests on the cuckoo egg length data, using two-tailed tests with a 0.05 level of significance.  Choose any samples you wish to compare (later on we will learn how to do Analysis of Variance, in which case all of the samples can be compared at once).  Assume unequal variances, but for one of your tests assume both equal and unequal variances.  What kind of biological inferences might you make based on all of these tests? 

A)    Write the null and alternative hypotheses

B)     Decide on your sampling distribution and find your rejection regions

C)    Calculate your (3) test statistic(s)

In general, H0: mi = mj  ; Ha: mi ¹ mj where i,j = 1,2,…6, i ¹ j, 1 refers to the first sample (first column of data) up through the last column (= 6)

For example, i=1,j=2, then: H0: m1 = m2 ; Ha: m1 ¹ m2

Xbar:1 = 22.30 ; n1 = 45 ; s1 = 0.921

Xbar:2 = 23.09 ; n2 = 15 ; s2 = 0.901

For unequal variances, sxbar1-xbar2 = 0.270; for equal variances sxbar1-xbar2 = 0.239

For unequal variances t = -2.94; for equal variances t = -3.31

t0 = +/-2.145 with 14 df (unequal variances)

t0 =  +/-1.96 with 58 df

 

 

Description: Prices in cents per pound received by fishermen and vessel owners for various species of fish and shellfish in 1970 and 1980

Number of cases: 14

Variable Names:

1.      Type_Fish: Species of fish

2.      Price_1970: Price in cents per pound in 1970

3.      Price_1980: Price in cents per pound in 1980
 

The Data:

Type_Fish

Price_1970

Price_1980

d

d2

COD

13.1

27.3

14.2

201.64

FLOUNDER

15.3

42.4

27.1

734.41

HADDOCK

25.8

38.7

12.9

166.41

MENHADEN

1.8

4.5

2.7

7.29

OCEAN PERCH

4.9

23

18.1

327.61

SALMON, CHINOOK

55.4

166.3

110.9

12298.81

SALMON, COHO

39.3

109.7

70.4

4956.16

TUNA, ALBACORE

26.7

80.1

53.4

2851.56

CLAMS, SOFT-SHELLED

47.5

150.7

103.2

10650.24

CLAMS, BLUE HARD-SHELLED

6.6

20.3

13.7

187.69

LOBSTERS, AMERICAN

94.7

189.7

95

9025

OYSTERS, EASTERN

61.1

131.3

70.2

4928.04

SEA SCALLOPS

135.6

404.2

268.6

72145.96

SHRIMP

47.6

149

101.4

10281.96

 

 

Sum

961.8

128762.78

 
 

 

Question:

Decide which kind of test would be appropriate for these data and perform that test.  Test for significance at the 0.05 level.  What you want to compare is the price of fish in 1970 to the price of fish in 1980.  Test the claim that the price of fish increased between the two times.

A)    Write the null and alternative hypotheses

B)     Decide on your sampling distribution and find your rejection regions

C)    Calculate your (3) test statistic(s)

Do a paired t-test.  Utilize the extra columns above to calculate your d’s and d2’s (see values above) which will help you calculate sd and dbar.

These are the calculated values you need for your test statistic:

dbar = 68.7 ; sd = 69.44 ; sdbar = 18.56

t = 3.70 ; t0 = 2.160 (looking at a = 0.05, 13 df)

Reject the null hypothesis, conclude that the prices have changed for fish in general.