Statistical Sciences 2244A/B Lecture Notes - Lecture 16: Simple Random Sample, Null Hypothesis, Species Richness
22 May 2018
School
Department
Professor
Stats 2244
One-factor ANOVA
Introducing the model and assumptions
Scenario
- To investigate the influence of herbivory on plant species richness, 60 experimental plant
communities (initially containing 15 species) were randomly assigned to one of three levels of
defoliation (to simulate the effects of herbivory). The number of species remaining at the end of
one year was measured for each community
- Species richness = # of different species in a defined region
- Defoliation = removal of plant tissue (leafs)
- is just a sample means species richness for the no defoliation group
o so up until now, we used x bar for the sample means, but we can use whatever
- we are going to end up with 3 diff sample means and we are going to compare those 3 sample
means
- note: this is a balanced design
o # of replicates in the treatment groups are equal (20)
o this is not a requirement – you don’t have to have balanced design but ANOVA tends to
be more powerful when you have a balanced design
One-factor ANOVA
- null hypotheses says that all the population means are the same
- conditions:
o samples are independent
▪ there are all sorts of diff ANOVAs out there but in this class we do independent
o all SRSs (or randomized design)
▪ need the samples to be SRSs
▪ this is so we know how the sampling distributions behave and we can
characterize them
▪ when we use ANOVA, we use it on artificially constructed objects (in which case
we would never have a simple random sample)
▪ so you can get around the SRS assumption if you are using a completely
randomized design
o population distributions are approx. normal
▪ the Y values must be normally distributed for each population (each value of our
explanatory variable)
o constant variance across populations
find more resources at oneclass.com
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Clicker Question
- ANSWER: C
o The 60 plant communities are the sample
o We take them and randomly assign them to 1 of 3 treatment groups
o The 60 communities are like a population that we are taking 3 samples from
Model: Describing Y
- We have a n equation that tries to explain the relationship bw x and y
- We can describe how diff a particular group or population mean is from the overall mean using
alpha
- Alphai is the affect of one of the populations (Ex:population i) on mu
- What would alpha (the effect) be if all the means were the same? 0
o If all the means are the same, the 3 distributions would sit on eachother and their means
would be equal to the mu
o So the effects would be 0
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
To investigate the influence of herbivory on plant species richness, 60 experimental plant communities (initially containing 15 species) were randomly assigned to one of three levels of defoliation (to simulate the effects of herbivory). The number of species remaining at the end of one year was measured for each community. Species richness = # of different species in a defined region. Defoliation = removal of plant tissue (leafs) is just a sample means species richness for the no defoliation group: so up until now, we used x bar for the sample means, but we can use whatever. We are going to end up with 3 diff sample means and we are going to compare those 3 sample means. Answer: c: the 60 plant communities are the sample, we take them and randomly assign them to 1 of 3 treatment groups, the 60 communities are like a population that we are taking 3 samples from.
