Fundamentals of statistics using R

the hypothesis of McCulloch and Pitts

the Bernoulli distribution

the

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

the probability of accepting some alternate hypothesis

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

central tendency

The

It is

dispersion:

The

the

If the skew is zero, then the distribution is

the

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

called μ and σ

μ , equal to its mean

σ , equal to its variance

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*distributiondbinom(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 testthe 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 valueThe

*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 variablesdispersion:

*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*distributionIt 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()*