Biometry exams 2

1. Many researchers have attempted to develop molecular clocks. To do this they must calibrate them in such a way that the measured DNA nucleotide divergence between sister species is associated with a known geological event that led to their divergence. One common such event is the onset of the Wisconsin Glaciation of North America which peaked approximately 85,000 years before present. This glacier subdivided many populations into eastern and western allopatric populations.

A recent argument that has been made is that the clock runs more slowly for ectothermic organisms than for endothermic organisms. Evaluate this hypothesis using the information provided concerning nucleotide divergences in sister species that all arose due to the Wisconsin Glacier. Each datum represents divergence in arbitrarily selected DNA regions of equal lengths that researchers sequenced.

Endothermic species: Ectothermic species:

Organism Number of nucleotides Organism Number of nucleotides

pocket mice 35, 20, 47, 5 ischnuran damselflies 5, 11, 6, 15

kingbirds 35, 25, 35, 16 killifish 15, 12, 24, 11

sparrows 15, 27, 29, 22 jumping spiders 22, 15, 17, 39

2. Dragonfly larvae obtain oxygen through gills located in their rectum. To ensure oxygenated water they pump their abdomen thereby expelling water low in oxygen from their rectum and then refill it with oxygenated water. This mimics our breathing.

A researcher was interested to determine if there was a physiological change in dragonflies subjected to predation risk. She individually studied 5 dragonfly larvae and counted number of pumps per minute before and at 5, 10, and 15 minutes post exposure to a fish predator with its mouth sutured shut. Was there a significant effect of predation risk on abdomen pumping in these larvae?

Before 5 min 10 min 15 min

Larvae

1 7 12 8 5

2 8 15 15 11

3 2 6 6 6

4 11 14 6 11

5 9 22 16 17

3. The length of hospital stay for men having their prostrates removed at a local private hospital was determined and associated to their health insurance coverage. The lengths of stay (in days) for 5 randomly chosen patients for each of 4 categories are:

No insurance: 4, 6, 7, 6, 5

Private carrier: 7, 5, 7, 7, 11

Medicare: 5, 6, 6, 7, 6

HMO: 4, 4, 5, 4, 5

A healthcare watchdog committee which admittedly was ant-HMO had commissioned this study to see if HMO hospital stays were significantly less than other non-HMO categories asks you to analyze these data to evaluate their position. Use your bag of tricks to do this.

4. Test the data in question 3 for outliers and homoscedasticity.

5. Dragonfly larvae swim by means of jet propulsion; they expel water out of their rectum using muscular contraction. Larvae of one species are morphologically distinct from those of other species so they may constitute objects with differing drag in water and their musculature and rectal volume may vary. Final instar larvae of four species from two families were stimulated to swim and their burst speeds measured:

Speed (cm/sec)

Family Aeshnidae Libellulidae

Anax junius Aeschna juncea Perithemis tanera Pachydiplax longipenes

7.2 4.1 3.8 4.2

3.7 4.8 2.1 4.5

5.1 3.9 2.9 3.8

4.3 5.0 4.0 3.1

4.2 4.1 1.8 3.9

Is burst swimming speed species dependent? Using unplanned techniques determine whether members of the family Aeschnidae swim faster than individuals of the Libellulidae. Determine if the data are homoscedastic and if there are outliers.

6. Damselfly larvae have 3 lamellae at the terminal end of their abdomen. These lamellae are sacrificed to predators which grab them, thus allowing the larva to escape. They also may serve as paddles to increase the swimming speed of larvae. An experiment was performed with 5 individuals from one species to determine swimming speed of each larva with 3, 2, 1, and 0 lamellae. Is there a significant effect of number of lamellae present on swimming speed? State any assumptions made to perform analysis.

Number of lamellae

Individual 3 2 1 0

1 2.7 2.5 2.1 0.5

2 2.4 2.4 1.8 0.5

3 2.9 1.8 1.9 0.9

4 4.1 3.1 2.1 0.7

5 1.9 2.0 0.9 0.7

7. Damselfly larvae use their caudal lamellae for oxygen uptake. When the oxygen tension is low in aquatic environments larvae disperse to the water surface to take advantage of gaseous oxygen. An experiment was performed where 14 larvae with lamellae and 14 larvae without lamellae were tested at 4 oxygen concentrations. The percentage of larvae at the water surface after 1 hour was established. Analyze this experiment and state those assumptions you made.

Percentage at surface

Oxygen concentration (%) Lamellae No lamellae

70 7.1 7.1

50 7.1 21.3

30 14.2 56.8

10 92.9 100.0

8. To determine whether diet affected cardiac output in people living in a small town, groups of seven people each were randomly selected. People in the control group continued eating normally; people in the second group ate only spaghetti; people in the third group ate only steak and people in the fourth group ate only fruits and nuts. After one month, each person’s cardiac output was measured. The data are tabulated below. Check these data for homoscedasticity and for outliers.

Control Spaghetti Steak Fruit and nuts

4.6 4.5 4.3 4.3

4.7 5.0 4.4 4.4

4.7 5.2 4.9 4.5

4.9 5.2 4.9 4.9

5.1 5.5 5.1 4.9

5.3 5.5 5.3 5.0

5.4 5.6 5.6 5.6

9. Three strains of Drosophila pseudoobscura were bred for resistance to an insecticide. Three concentrations of the insecticide were used. The data, based upon five replicates per treatment combination, expressed as percent mortality over a given period of time are given below. Analyze these data fully using the most logical a priori transformation. It is unnecessary to test assumptions of ANOVA.

Insecticide level 1

Strain A 60, 55, 52, 38, 31

Strain B 58, 53, 50, 35, 30

Strain C 37, 43, 57, 60, 66

Insecticide level 2

Strain A 44, 37, 54, 57, 65

Strain B 63, 59, 54, 38, 38

Strain C 59, 51, 53, 62, 71

Insecticide level 3

Strain A 45, 51, 63, 66, 74

Strain B 63, 44, 46, 66, 71

Strain C 51, 80, 68, 77, 65

10. Four strains of rats were selectively bred for differences in blood pressure in order to determine the possible effect of heredity on blood pressure. Analyze the data for statistical significance among the means. If a statistically significant value is found, then test for statistical significance among all possible mean pairs.

Strain

A B C D

84 87 89 89

82 84 94 86

86 84 92 88

89 92 91 93

85 88 92 85

85 89 91 85

92 92 95 89

80 89 89 90

79 87 87 90

83 88 91 93

11. The progress of wound-healing was compared when 5 different postoperative regimens were employed after abdominal surgery. The 30 patients in the study were randomly assigned. The numbers below are coded data on the duration of the wound-healing period. Are there differences due to regimen? Is regimen C better than regimen B? Also compare B and D!

Postoperative regimen

A B C D E

3 4 2 6 8

5 7 3 3 2

5 6 4 5 4

2 6 3 5 5

4 9 3 2 6

5 7 5 4 6

12. The activity of a certain enzyme in the blood plasma is an indicator of the severity of tissue damage in certain kinds of heart disease. In order to test the general reliability of the enzyme activity determinations, a single plasma sample was subdivided into many portions, which were given code numbers and distributed to two technicians in each of 4 laboratories for routine assay. Each technician received three samples of the standard plasma. Provide an analysis of this procedure which partitions the total variance into its component parts and indicate if they are significant. The data are coded.

Lab A

Technician 1 -2, -4, -4

Technician 2 -1, 0, -1

Lab B

Technician 1 3, 2, 1

Technician 2 0, 2, 1

Lab C

Technician 1 -2, -2, 0

Technician 2 -3, -2, 1

Lab D

Technician 1 4, 5, 4

Technician 2 3, 5, 2

13. Ten male and ten female rats were divided randomly into subgroups to which two different hypnotic drugs were administered. Sleeping times were then measured in minutes. The data were coded and are presented below. Is there a sex effect? A drug effect? An interaction?

Males Females

Drug A -5 +9

-2 +29

+6 +13

-6 +17

-1 +7

Drug B -6 -6

-8 -2

-2 +5

0 0

-4 +6

14. Fascioliasis is a widespread parasitic disease that is produced by Fasciola hepatica, which is a flatworm commonly called the liver fluke. The adult worms live in the bile duct of the host. Investigators have found that the adult worms secrete significant amounts of certain amino acids, especially proline. It has also been established that the host characteristically exhibits an anemia that involves a reduction in circulatory red blood cells.

An experiment was designed to test the following questions:

1. Is the reduction in the number of the host’s red blood cells associated with the secretion of amino acids by the worms?

2. Is the secretion of significant amounts of proline associated with the reduction in the number of red blood cells?

Forty non-infected Wistar rats were selected, keeping such factors as age and weight as constant as possible. They were assigned randomly, ten each, to four different treatments. The treatments are described as follows:

1. group D - 20 millimolar proline in physiological saline solution

2. group E - 2 millimolar proline in physiological saline solution

3. group F - seven amino acids (excluding proline) in physiological saline solution

4. group C - a control with physiological saline solution

The following table shows the data derived from RBC counts on the individual subjects, reported in million per cubic millimeter and rounded to the hundredth place.

Group D Group E Group F Group C

5.61 6.07 5.69 7.35

5.40 5.20 5.54 7.11

5.26 5.69 5.35 6.99

4.99 5.43 5.11 6.72

5.44 5.87 5.94 7.16

5.13 5.55 5.25 6.85

5.21 5.64 6.02 6.94

5.52 5.95 5.64 7.25

4.79 5.20 5.11 6.51

4.97 5.40 5.04 6.65

SX_D = 52.27 SX_E = 56.00 SX_F = 54.69 SX_C = 69.53

S ²_D= 0.073 S ²_E= 0.091 S ²_F= 0.124 S ²_C= 0.074

Xbar_D= 5.23 Xbar_E= 5.60 Xbar_F= 5.47 Xbar_C= 6.95

n_D= 10 n_E= 10 n_F= 10 n_C= 10

SX² = 1372.61 SX = 232.49

Determine if these treatments affect RBC. If there is a treatment effect compare each pair of means using an a priori test. Assume ANOVA assumptions are met.

15. Twenty dogs are tested for lymphocyte count before and after administration of a drug that is supposed to produce a decrease in circulating lymphocytes. Test this claim using the most powerful test you are familiar with and assuming ANOVA assumptions are met. The data are expressed in thousands per cubic millimeter of blood and are presented in the following table.

Animal Before After

1 2.5 2.6

2 1.2 1.5

3 2.9 2.9

4 3.1 2.0

5 3.1 2.3

6 1.1 1.3

7 1.5 1.6

8 4.1 3.1

9 2.1 1.4

10 2.4 2.5

11 1.3 1.4

12 2.8 2.8

13 3.5 2.4

14 3.6 2.1

15 1.1 1.3

16 1.6 1.7

17 4.2 3.2

18 2.2 1.5

19 2.5 2.1

20 1.3 1.1

16. The following data are plasma calcium levels (in mg/100 ml) of birds of both sexes, half of which were treated with a hormone and half of which remained untreated.

No Hormone Treatment Hormone Treatment

Female Male Female Male

16.5 14.5 39.1 32.0

18.4 11.0 26.2 23.8

12.7 10.8 21.3 28.8

14.0 14.3 35.8 25.0

12.8 10.0 40.2 29.3

Test for: Hormone treatment effect

Sex effect

Hormone/sex interaction

Assume ANOVA assumptions are met.

17. Suppose that we have an approximately one-quarter square mile of area of lake that is used as a dump site for dredgings from a nearby harbor. We are interested in whether or not differences in certain chemical and biotic factors exist between the dump area and other parts of the lake where no dumping has taken place. Or, to put it in more practical terms what effects, if any, do the harbor dredgings have on the lake ecosystem? Design and describe an experiment (using a hypothetical variable) that would permit us to test this. (Hint: Remember that one sample may not faithfully describe an area).

18. It has been proposed that ischnuran damselflies which do not guard their females during oviposition fall into two species groups: sperm removers and non sperm removers. Novak studied the accessory genitalia of several of these species to determine if the flagella (the primary structure involved with sperm removal) length differed between these groups. The data she obtained is presented below. Can she conclude that sperm removers have longer flagella?

Flagella length

Sperm removers Non sperm removers

I. ramburi I. elegans I. posita I. aurora

480 530 185 270

505 530 200 310

520 530 140 350

482 495 190 305

450 560 159 269

19. Suppose the data from the first problem violated the normality assumption of ANOVA and no transformation could be found to correct this problem. Analyze the data to demonstrate whether there is a significant effect of species (not the contrast done in the original problem) on flagella length.

20. It has been proposed that vertebrates are better able to learn the location of food sources and how to exploit them than insects. To test this hypothesis (assume no within day learning occurs) data were obtained on the percentage of nectar removed from an array of artificial flowers in an insectary by bees and in an aviary of hummingbirds. Each day the amount of nectar supplied to these flowers was initialized at identical amounts for each trial. The number of hummingbirds and bees used were adjusted so that they had similar energetic demands. Multiple groups of hummingbirds and bees were used and each group was tested on each of two consecutive days. How would you analyze this and what would be your criterion for evaluating the hypothesis. Analyze the following data which which were unfortunately not matched during collection.

% Nectar Removed

Day 1 Day 2

Hummingbirds Bees Hummingbirds Bees

35 31 70 48

47 44 65 50

40 43 72 35

72 57 55 42

12 51 77 47

21. Three traps, baited for fruit flies, were exposed to each of 7 sites, the types of bait being allocated at random to the 3 positions at each site. The data in the table below are numbers of flies caught in a fixed time interval. Does bait type influence trapping success? Is bait A better than bait B or C? Is B better than C? Show work and state all assumptions.

Bait

Site A B C

I 75 41 47

II 52 30 29

III 58 38 25

IV 19 20 10

V 34 28 13

VI 33 26 17

VII 25 15 12

22. Three clinical methods of determination of hemoglobin content were tested for significant difference in results. Six subjects were used and exposed to each method. Analyze the experiment.

Subject

Method A B C D E F

1 14 12 16 15 10 11

2 18 16 17 19 12 13

3 15 14 12 14 12 9

23. A sample was collected from each of the three geographically isolated populations of a certain species of bird. The bill length of each specimen was measured to the nearest tenth of a millimeter, yielding the data in table 8.12. Analyze the data for statistically significant differences among the populations. Use both most and least powerful a posteriori tests.

Population

A B C

4.2 3.8 3.0

3.3 4.1 3.5

2.8 5.0 4.5

4.3 4.6 4.4

3.7 5.1

4.5

3.6

24. Assume the presence of multiplicative effects in the three sets of treatment data given below. Compute the mean and variance of each set of raw data; then apply the most logical transformation and reanalyze the data. Test the variances of both raw and transformed data sets for homogeneity.

I II III

12 16 31

15 29 26

9 23 20

11 22 36

13 23 28

25. Five treatments for fever blisters, including a placebo, were randomly assigned to 30 patients. The following data give for each treatment the number of days from initial appearance of the blisters until healing is complete.

Treatment Number of days

Placebo 1 5, 8, 7, 7, 10, 8

2 4, 6, 6, 3, 5, 6

3 6, 4, 4, 5, 4, 3

4 7, 4, 6, 6, 3, 5

5 9, 3, 5, 7, 7, 6

Are there significant differences among the effects of the five treatments with regard to the healing of fever blisters? Is there a significant difference between the Placebo and the other 4 treatments combined?

26. The diameters of three species of pine trees were compared at each of four randomly chosen locations using samples of five trees per species at each location. The data are given below.

Location

Species 1 2 3 4

A 23 25 21 14

15 20 17 17

26 21 16 19

13 16 14 20

21 18 27 24

B 28 30 19 17

22 26 24 21

25 26 19 18

19 20 25 26

26 28 29 23

C 18 15 23 18

10 21 25 12

12 22 19 23

22 14 13 22

13 12 22 19

Comment on whether each factor is fixed or random. Analyze the data.

27. In a pediatric clinic a study is carried out to see how effective aspirin is in reducing temperature. Twelve 5 year old girls suffering from influenza had their temperatures taken immediately before and after administration of aspirin. The results are given below.

Patient Before After

1 102.4 99.6

2 103.2 100.1

3 101.9 100.2

4 103.0 101.1

5 101.2 99.8

6 100.7 100.2

7 102.5 101.0

8 103.1 100.1

9 102.8 100.7

10 102.3 101.1

11 101.9 101.3

12 101.4 100.2

Analyze this experiment.

28. Using the data from problem 1, check for homoscedasticity and outliers.

29. The weaning weights of beef calves sired by three Charolais sires and by three Angus sires are shown below. Carry out an analysis of variance for this set of data showing a test of significance between the two breeds of sires and a test among the sires within the breeds.

Charolais Angus

Sire 1 Sire 2 Sire 3 Sire 1 Sire 2 Sire 3

480 430 473 354 410 423

440 420 438 341 413 414

465 461 451 362 390 398

450 433 432 379 401 407

30. Water mites attach to adult Ischnura posita damselflies. Five male and five female damselflies were collected and the number of mites on each were counted. Is there evidence of mite abundance being influenced by the sex of the host.

# of mites

male female

13 7

7 1

21 3

18 14

2 21

31. A random sample of the records of single births was selected from each of four populations. The weights (grams) of the babies at birth were as follows.

Sample

A B C D

2946 3186 2300 2286

2913 2857 2903 2938

2280 3099 2572 2952

3685 2761 2584 2348

2310 3290 2675 2691

2582 2937 2571 2858

3002 3347 2414

2408 2008

2850

2762

Test for a significant difference between all possible pairs of means.

32. Test the data in problem 3 for homoscedasticity. Is the data point 3685 in sample A an outlier.

33. Adult I. posita damselflies were collected, sexed, and weighed on three separate dates (early spring, midsummer, and late summer). Is this species sexually dimorphic for size? Is the degree of dimorphism dependent on season? Does the size of individuals change through the year.

Sex

Season Male Female

Early Spring 7.3 17.0

8.9 16.1

7.8 21.1

10.1 18.0

11.0 17.9

Mid Summer 6.8 9.3

5.2 8.8

5.7 8.5

5.1 9.1

4.1 7.9

Late Summer 5.7 10.0

5.9 8.7

6.3 7.5

4.9 8.5

5.1 9.0

34. A researcher was interested in establishing the indirect effect of the presence of dragonfly predators on agonistic behavior of damselfly larvae. When damselflies aggressively interact they often remove their opponents caudal lamellae. The level of agonistic behavior can then be assessed in contests by determining how many individuals have had their lamellae removed.

She ran a series of 5 trials for each of 4 different dragonfly predators (Anax junius, Tramea lacerata, Erythemis simplicolis, and Pachydiplax longipenis). In each trial 10 damselfly larvae with complete sets of lamellae were placed in an aquarium, left for 24 hours, then examined for missing lamellae. The percentage of damselflies with missing lamellae are provided below. Show with 95% statistical assurity the effects of each of these species versus all other individual species.

Anax: 0, 10, 0, 10, 20 Erythemis: 20, 30, 20, 30, 30

Pachydiplax: 10, 30, 0, 10, 10 Tramea: 10, 20, 0, 10, 10

35. Our stalwart researcher attempted to publish her results and was confronted by a reviewer’s comment that she had not demonstrated that lamellae removal was due to damselfly-damselfly interactions; it might be the result of the dragonflies removing the lamellae themselves. She then repeated her experiment, but this time glued the labia of the dragonflies such that they behaved like normal dragonflies but they could not remove lamellae. Her analogous results are provided below. Combine these data with those from problem 1 to determine if dragonflies remove lamellae, analyze them appropriately and respond to the reviewer’s comments.

RESULTS WITH LAMELLAE GLUED:

Anax: 10, 20, 0, 0, 0

Tramea: 20, 20, 0, 10, 10

Erythemis: 40, 0, 20, 10, 20

Pachydiplax: 10, 20, 10, 60, 20

36. Following remission of the manuscript, the reviewer stated that the reanalysis was fine and dandy but it looked like there might be problems with heteroscedasticity in the data presented in problem 2. Evaluate this comment (for data from 2 only) and then decide if the fourth replicate for Pachydiplax qualifies as an outlier.

37. The question arose as to whether the middle lamellae is more valuable to a larvae than a lateral one. Since larvae regenerate these lamellae through time, a test was performed using 5 larvae. Each individual had a middle and lateral lamella removed and was allowed to go through 2 molts following which he regenerated lamellae were removed. Each time the lamellae were dried and weighed to the nearest microgram. Is there any statistically significant evidence that the percentage regeneration differs between the 2 lamellae types?

Middle Lamella Lateral Lamella

Individual Unregenerated Regenerated Unregenerated Regenerated

1 25 15 23 14

2 27 15 24 13

3 26 15 24 15

4 23 12 21 10

5 26 16 23 14

38. Anisopteran dragonfly larvae swim using jet propulsion. A researcher is interested in determining whether their swimming speed varies as a function of time since molting. She collects five individuals of Anax junius and measures their swimming speed performance 1, 3, 5, and 10 days post molting. Is there an effect of time post molting on swimming speed?

SWIMMING SPEED (cm/sec)

INDIVIDUAL DAY 1 DAY 3 DAY 5 DAY 10

1 1.2 1.7 2.0 0.8

2 8.5 9.0 10.0 8.1

3 5.7 8.0 9.2 2.7

4 6.1 7.1 8.0 5.7

5 4.3 5.0 6.0 3.1

39. Damselflies of the species Ischnua ramburii have females of two different color morphs: andromorphs and heteromorphs. A researcher hypothesizes that andromorphs have lower survivorship and therefore the proportion of andromorphs should be lower at the end of summer than at the beginning. He requests that colleagues establish the proportion of andromorphs in populations near where they live. Each colleague does this in his home town and does it on three separate dates. Yet three colleagues collect only at the beginning of the summer and the other three at the end of the summer. Is there any statistical support from this data for his hypothesis? The proportions of andromorphs are:

EARLY SUMMER Houston: 0.21, 0.32, 0.25

Arlington: 0.40, 0.35, 0.25

Austin: 0.17, 0.25, 0.27

LATE SUMMER Waco: 0.21, 0.17, 0.20

San Antonio: 0.18, 0.19, 0.19

Denton: 0.21, 0.21, 0.15

40. A population of Drosophila melanogaster has been maintained in a university laboratory for over 20 years at a temperature of 20 degrees C. A researcher suggested that this population should have evolved such that female fecundity was higher at 20 degrees C than at other temperatures. She crossed a pair of flies from this population and as adults emerged she randomly assigned individual females such that 5 were maintained at 15 degrees, 5 at 20 degrees, and 5 at 25 degrees. Each was crossed with a wild type male and the total number of eggs produced were determined. Is there an effect of temperature on fecundity? Do not transform data.

Temperature

15 20 25

257 410 610

300 550 715

355 525 650

275 500 638

410 485 490

After looking at these results, she decided that fecundity appeared highest at 25 degrees C. Is there statistical support that fecundity at 25 degrees C is higher than the fecundity in the other two categories combined?

41. Test the data from problem 3 for homoscedasticity and outliers.

42. As a preliminary experiment to evaluate the influence of buffer on the efficiency of a virucidal active ingredient, a test was performed using 5 different buffers and the same active ingredient. The logarithmic reduction in viral titer after a 10 minute exposure to the ingredient in each buffer was determined on two separate occasions for each buffer combination. The data follow:

Buffer A B C D E

Test I 4.57 5.17 5.0 5.17 4.17

Test II 5.0 5.0 5.27 5.0 4.5

Is there a significant (a = .05) effect of buffer? After obtaining these results the researchers wanted to know if buffer E was significantly inferior (i.e. different) than the other 4 buffers as a group. Please provide me with the answer.

43. Paired cages were established in a Texas reservoir, one cage was open to fish predators the other was closed to prevent predator access. Two Ekman Grab samples were taken from each cage. Six of these paired cages were established at different sites within the reservoir. Analyze the data from the experiment for significance of predation, site and interaction (a = .05). Perform the most logical transformation but do not test for agreement with assumptions.

Site Open Closed

1 0, 0 4, 3

2 0, 0 1, 1

3 0, 0 17, 21

4 0, 2 0, 2

5 1, 2 79, 63

6 2, 0 380, 113

44. Dragonfly larvae have rectal gills, which augment their gas exchange capacity. One can visually observe the rate at which they pump water in and out of their rectum by the cyclical swelling and contraction of their abdomen. To determine if these organisms respond to fish predators in such a way that it would be detectable at this level, 6 individuals were observed for 5 minutes prior to a fish being introduced and for 5 minutes immediately after the introduction. The number of contractions are listed below. Analyze at 95%

Individual Before After

1 105 101

2 97 85

3 70 63

4 111 104

5 89 79

6 107 99

45. Analyze the data on page 223 of your text for homoscedasticity and for outliers.

46. A struggling Odonatologist was trying to estimate egg mass in a damselfly species. To do this he dissected 3 eggs from each of 3 individuals as part of a preliminary experiment. Since these eggs are very small he had to use a very sensitive electronic balance to weigh the eggs. The balance had an automatic loading and unloading unit which mechanically adds and removes the load to be weighed on/off the balance. This will be referred to as "automatic" variance. Individual eggs must still be loaded manually on the automatic loader. This will be referred to as "manual" variance. Each time he manually loaded an egg he automatically loaded it 2 times. Each egg was manually loaded 2 times. Analyze the data and advise this researcher concerning the effect of eliminating the replication of manual loading for each egg. The data follow (Data in micrograms)

Individual 1

Egg 1

Manual Load 1 12.5, 12.6

Manual Load 2 12.8, 12.9

Egg 2

Manual Load 1 11.7, 11.9

Manual Load 2 11.5, 11.3

Egg 3

Manual Load 1 12.1, 12.0

Manual Load 2 12.1, 12.1

Individual 2

Egg 1

Manual Load 1 13.0, 12.8

Manual Load 2 12.5, 12.7

Egg 2

Manual Load 1 12.7, 12.8

Manual Load 2 12.8, 12.8

Egg 3

Manual Load 1 12.8, 12.6

Manual Load 2 12.7, 12.7

Individual 3

Egg 1

Manual Load 1 12.0, 12.2

Manual Load 2 11.9, 11.8

Egg 2

Manual Load 1 12.4, 12.5

Manual Load 2 12.6, 12.6

Egg 3

Manual Load 1 12.9, 12.7

Manual Load 2 12.8, 12.9

47. A series of swimming trails were made between dragonfly larvae belonging to 4 species, These individuals were initially screened to ensure they were of equal weight therefore size differences did not effect the outcome. From the results of this experiment I would like to be able to compare any 2 species and comment on whether their comparative speeds are significantly different. Data are in cm/sec and were obtained at 20 C.

A. junius	P. tenera	P. lydia	L. lucuosa
14	7.5	8.9	4.5
12.7	8	7.5	5.1
12.9	9.7	8.8	3.7
14.2	10.1	8.5	5.2
13.4