Stats 🤢

requirements for poisson to be suitable

each event is random and independent

there is a constant average rate of events occurring

requirements for Spearman’s rank to be applicable

data is drawn from a random sample

requirements for pmcc

the underlying population data should follow a bivariate normal distribution

the scatter diagram should show an elliptical shape

requirements for binomial

fixed number of trials
each trial must be a success or failure
each trial must be independent
the probability of each trial must be constant

mean of a uniform distribution

The mean/expected value of a symmetric uniform distribution is the midpoint between the minimum value ($a$) and the maximum value ($b$).

$$E(X)=\frac{a + b}{2}$$

variance of a uniform distribution

$$\text{Var}(X) = \frac{(b - a)^2}{12}$$

define randomness

every outcome has an equal chance of occurring and they are all unpredictable

what is a p value

the probability of observed results happening from null hypothesis, compared to significance level

finding outliers in symmetrical data

$\mu \pm 2\sigma$
$\bar{x}

finding outliers in skewed data

$$\text{LQ}-1.5\times\text{IQR}$$

$$\text{UQ}+1.5\times\text{IQR}$$

setting to find regression lines

y = a + bx for y on x

if x on y, SET XVar to List 2 and YVar to List 1

random on random regression lines

Both the independent variable (X) and the dependent variable (Y) are random variables. They are sampled together from a population, and both are subject to natural variation or measurement error.

Error exists in both X and Y

random on non random regression lines

The independent variable (X) is non-random (fixed or controlled by the researcher), while the dependent variable (Y) is a random variable containing measurement error or natural variation.

Error is assumed to exist only in the dependent variable (Y). The values of X are assumed to be measured with perfect accuracy.

sample variance of a DRV

$$s^{2}=\frac{S_{xx}}{n-1}$$

sample standard deviation of a DRV

$$s=\sqrt{\frac{S_{xx}}{n-1}}$$

information in s.d. of normal distribution

1σ ≈ 68%

2σ ≈ 95%

3σ ≈ 99.7%

therefore if a large proportion of the data is outside 3σ, it is likely not normally distributed

normal approximation to binomial

large n
original binomial should be symmetrical, so p should be close to 0.5