The following are data from an experiment to test the ability of a fungal pathog

Question

The following are data from an experiment to test the ability of a fungal pathogen to effect the ability of mosquitoes to transmit malaria. The fungus (Metarhizon anisopliae) can reduce the life span of infected insects. There is also a transgenic strain of the fungus expressing a gene for scorpine, a protein from scorpion venom that is known to inhibit the gamete stage of malaria in vitro. The experimenters compared three groups (treatments) of mosquito: a “control” group that was not infected with the fungus, a “wild type” group that was infected with the untransformed fungus and a “transgenic” group that was infected with the transgenic fungus. All mosquitoes carried malaria.

The data shown are sporozoite (infectious cells of malaria) counts in the salivary glands of individual mosquitoes.

control

transgenic

wild_type

1339

55

270

1636

81

665

1636

200

812

2208

270

1097

2697

60

1808

2697

200

2697

2981

365

2697

3641

403

2981

4024

403

2981

4447

446

3641

4447

493

4447

4915

1097

8103

8955

1808

8955

9897

8103

9897

8955

Graph the data. What do the patterns suggest about the effectiveness of the wild type and transgenic fungus?

Examine the frequency distributions of the data. Would it be appropriate to conduct an ANOVA on the data? Explain.

Identify an appropriate transformation and test for differences between the group means using ANOVA and any additional tests you think appropriate.

What fraction of the variation in the response variable is explained by the treatments?

Are you completely satisfied that the data transformation (or otherwise) that you used was satisfactory? Refer to appropriate plots and the assumptions of ANOVA to justify your answer.

Regardless of the answer to part (e) display the results of your tests as you might for a paper and answer the questions
1        Does the fungus reduce sporozoite count and
2        Does possession of the scorpine gene change efficacy of the fungus in reducing sporozoite count?

control

transgenic

wild_type

1339

55

270

1636

81

665

1636

200

812

2208

270

1097

2697

60

1808

2697

200

2697

2981

365

2697

3641

403

2981

4024

403

2981

4447

446

3641

4447

493

4447

4915

1097

8103

8955

1808

8955

9897

8103

9897

8955

Explanation / Answer

fraction of the variation in the response variable is explained by the treatments is = SS Between/SS Total = 0.323

Anova: Single Factor SUMMARY Groups Count Sum Average Variance control 15 65417 4361.133 8529603 transgenic 13 5881 452.3846 239824.4 wild_type 15 58212 3880.8 9770851 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 123795814 2 61897907 9.556414 0.000405 3.231727 Within Groups 259084243 40 6477106 Total 382880057 42

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