R day 6

Fundamentals of statistics using R

the hypothesis of McCulloch and Pitts

We shall not often be astray if we draw a conventional line at .05 , and consider that higher values of [the test statistic] indicate a real discrepancy.


the Bernoulli distribution

the binomial distribution

dbinom(x, size, prob, log = FALSE)
dbinom はパラメータ size と prob の二項分布の確率関数


s <- 0:527135
d <- dbinom(s, 527135, 0.2)


the Neyman-Pearson paradigm
the power of a statistical test
the probability of accepting some alternate hypothesis

cumulative distribution function
probability mass function

pbinom()
pbinom(q, size, prob, lower.tail = TRUE, log.p = FALSE)



central tendency

mode: the most common value
The arithmetic mean, or simply the mean, also called the expected value
It is not meaningful for nominal variables or for ordinal variables, that is, for numerical variables

dispersion: how spread out are the likely outcomes

quartiles
The inter-quartile range (IQR)

the variance


skewness
right-skew
positive skew

left-skew or has negative skew
If the skew is zero, then the distribution is symmetric

log()
exp()
hist()

mean(), var(), or sd()



the normal or Gaussian distribution

It is a continuous distribution, unlike the binomial distribution
It is a symmetric distribution.
it has skewness zero
its mean is equal to its median
It has two parameters.
called μ and σ
μ , equal to its mean
σ , equal to its variance

rnorm(): the relevant normal distribution

pnorm(): to calculate an exact p -value

seq()