Instructions
There is another approach for assessing the validity of ANOVAs. We usually interpret the F-test by looking at the significance level of the test. This significance level is determined by the p-value, which reflects the probability of finding a less likely result under the null hypothesis - i.e. when there is no effect. As opposed to the F-test itself, its corresponding p-value behaves consistently under the null hypothesis. More specifically, for any ANOVA based on any given data set under the null hypothesis, the corresponding p-value has a uniform distribution, an expected value of .50 and requires the p-value to be confidence valid (a p-value of .05 should only occur 5 percent of the time).
What I need to understand:
How to examine the following about the p-value:
- Has an expected value of .50 (why .50 to look at the bias? Which table of the results do I have to use to evaluate the bias, see output )
- Should be confidence valid (Neyman, 1934) in the sense that a p-value of .05 should only occur 5 percent of the time. (how to check this using my results)
Interpretation of the results:
- Expected value of the p-values: text with expected values and table + interpretation
- Proportion E(p<=.05): text + table
- Proportion correct (i.e. how many p-values less than .05 are the same as the population)
- what can I say about the reliability? And the power?
- Why use an intercept only model in the code (model with only the intercept)
Those results can be obtained by using the R script. I added some in the info document.
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> library(mice)
Attaching package: ‘mice’
The following objects are masked from ‘package:base’:
cbind, rbind
> library(miceadds)
* miceadds 3.9-14 (2020-05-09 11:27:27)
> library(magrittr)
> library(dplyr)
Attaching package: ‘dplyr’
The following objects are masked from ‘package:stats’:
filter, lag
The following objects are masked from ‘package:base’:
intersect, setdiff, setequal, union
> library(purrr)
Attaching package: ‘purrr’
The following object is masked from ‘package:magrittr’:
set_names
> library(mvtnorm)
> library(ggplot2)
Need help getting started? Try the R Graphics Cookbok:
https://r-graphics.org
> #install.packages("ggplot2")
> set.seed(123)
>
> # Simulation parameters
> nsim = 1000
> rho = 0 # correlation set to zero to conform to null hypothesis (no effect)
>
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