statistics

normal distribution

can be transformed into standard distribution where:

• mean = 0

• sd = 1

negatively skewed distribution

tail on the left side, mean is lower than median

positively skewed distribution

tail on the right, mean is higher than median

bimodal

distribution w/ two peaks and a valley in b/w; if one peak is higher than the other → mode

outlier

any value that falls 1.5x above or below the IQR

standard deviation (sd)

calculated relative to the mean; outlier if the data falls > than 3 sd from mean

causes of outliers

• statistical anomaly

• measurement error

• distribution that is not approximated by the normal

independent events

no effect on one another

dependent events

have an impact on e/o, such that the order changes probability

mutually exclusive events

cannot occur at the same time

exhaustive outcomes

there are no other possible outcomes

null hypothesis

two populations are equal; single population can be described by a parameter equal to a given value

alternative hypothesis

nondirectional/directional; the populations are not equal

p-value > significance level

accept the null hypothesis; no statistical significant difference b/w the two populations

p-value < significance level

reject null hypothesis; statistically significant difference b/w the groupst

type I error

likelihood to report a difference b/w two populations when one does not actually exist

type II error

incorrectly fail to reject null hypothesis; we report no difference b/w 2 groups when one actually exists

confidence interval

determine a range of values from sample mean and sd; reverse of hypothesis testing

semilog graphs

change in the axis ratio making logarithmic data linear

• x axis → maintains traditional unit spacing

• y → spacing based on a ratio, usually multiples of 10

correlation

connection b/w the data

• positive: two variables trend together (+1)

• negative: trend in opposite directions (-1)

• zero: no relationship