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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

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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. 

R version 4.0.1 (2020-06-06) -- "See Things Now"

Copyright (C) 2020 The R Foundation for Statistical Computing

Platform: x86_64-w64-mingw32/x64 (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.

You are welcome to redistribute it under certain conditions.

Type 'license()' or 'licence()' for distribution details.

 

R is a collaborative project with many contributors.

Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help.

Type 'q()' to quit R.

> 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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