You wished to test whether a potentially pathogenic fungus affects growth of pyr
ID: 3253332 • Letter: Y
Question
You wished to test whether a potentially pathogenic fungus affects growth of pyrethrum plants. You conducted a glasshouse experiment in which you grew 20 plants, one plant per pot, randomly chose 10 of the plants and inoculated them using an aqueous suspension of fungal spores poured into the soil in the pot. The other 10 plants received the same soil drenching as the inoculated plants but without any spores in the aqueous mix. All plants were then placed in random positions on a glasshouse bench, grown for three months and plant dry weight measured.
(a) Is this a valid experiment? Do you think you could improve it given you are limited by space and the number of plants you can test? Explain and justify your answer.
(b) Name the experimental design in (a), give the form of the ANOVA table (i.e. list the sources of variation and the degrees of freedom for each).
(c) Explicitly state what null and alternative hypotheses you might validly test by ANOVA. Are these one-tailed or two-tailed and is that distinction important?
(d) You conducted the ANOVA on the untransformed dry weight data and found a significant difference between inoculated and uninoculated plants. Your friend then said “I have read that weight data should be log transformed”. You repeated the analysis on log(dry weight) but this time found no significant difference. Which result (if either) is right? Explain how you would make that decision?
(e) A second friend then told you to do a t-test rather than an ANOVA. Would that really be more appropriate? Explain which is better in this situation, ANOVA or t-test.
Explanation / Answer
(a) Of course this is a valid experiment. Actually, I don't know that pyrethrum plant is of several types or not. If so, then the experiment can be improved by taking the several types of pyrethrum plant among the 20 grown plants.... because two way ANOVA is more preferable than one way ANOVA.
(b) The considered design is called C.R.D. ( ie.. Completely Randomised Design).
(c) H0 : potentially pathogenic fungus affects growth of pyrethrum plants.
against H1: potentially pathogenic fungus does not affect growth of pyrethrum plants.
It is a two-tailed test and the distinction is important.
(d) This is the problem of Linear model ... so if data is of logarithmic form then this model or design will not be valid.
If the friend's word is correct then ... We have to fit the logarithmic model and the conclusion will be different..
ANOVA table Source of variation Sum of Squares degrees of freedom Mean Squares Variance ratio Due to pathogenic fungus (T) SST (2-1) MST=SST/(1) F= MST/MSE Error SSE (20-2) MSE=SSE/(18) Total Total SS (20-1)Related Questions
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