Inferential Stats

BIOL 2913

Null Hypothesis

statement being tested; states no change or significant difference

alternate hypothesis

the working hypothesis; can cover all possible outcomes not specified in the null hypothesis

one sided hypothesis

includes values only on one side of the parameter value specified by the null hypothesis

null distribution (for a given statistical test)

the probability distribution for the test stat assuming the null hypothesis is true

p-level

the probability that the measured data was obtained under the conditions specified by the null

critical/significance value (alpha)

0.05 (there is a 5 percent chance we have a false positive)

conditions to reject the null

p < 0.05

type I (alpha) error (false positive)

rejecting the null when the null is actually true

type II (beta) error (false negative)

not rejecting the null when the alternate is actually true

power level (power=1-beta)

the probability that you will NOT commit type II error

which type of error (I or II) has more serious consequences

type II error

chi square (x^2) distribution (two categorical variables)

continuous distribution with k degrees of freedom

chi squared goodness of fit test

tests if sample data fits distribution from a certain population (calculates how far the observed data is from the expected)

degrees of freedom (df) formula

df = number of groups - 1

chi squared contingency test

tests for association between two categorical variables

assumptions of chi squared test

categorical data
independence
the expected value of a cell should be 5 or more in at least 80 percent of the cells
no cells should have an expected value of less than 1

student t-test

used to compare numerical means

t distribution

similar to normal distribution with wider tails (more area under the curve)
low df: wider tails
higher df: narrower tails

standard normal distribution (Z)

mean = 0
standard deviation = 1

one sample t-test

compares the mean of a random sample from a normal population to a population mean specified by the null (ex: predicted ice thickness for whole lake = 14 inches)

assumptions of one sample t-test

data is randomly sampled (scores are independent)
data is normally distributed

two sample t-test

compares how similar INDEPENDENT samples from two different populations are (null: there is no difference between the means of pops)

paired samples t-test

compares means from non-independent samples

assumptions of paired samples t-test

samples are random
subjects are independent
differences of data are normally distributed

analysis of variance (ANOVA) (F)

compares means of multiple groups simultaneously

grand mean

the average of the different groups' means

F value

ratio of variance between groups and variance within groups (larger than 1: significant F, reject null)

F ratio

mean squares between/mean squares within
cannot be less than 0

assumptions of ANOVA test

random sampling
dependent variable is normally distributed
homogeneity of variance

homogeneity of variance

variance is similar in each population

one way ANOVA test

has one independent variable

two way ANOVA

has two independent variables

post-hoc test

tells you specifically which mean is different

Tukey-Kramer test

post hoc test that works like a two-sample t-test, but uses a larger critical value with the same df

planned comparison

small number of specific comparisons defined at the beginning of the experiment based on prior knowledge (contrast analysis in SPSS)

unplanned comparison

multiple comparisons with no prior knowledge

parametric tests

assumes data you have is normally distributed and has homogeneity of variance (t-test and ANOVA)

nonparametric tests

does not assume normality and equal variance (chi squared)

ignore violations to assumptions when

two data sets have similar skew and have a sample size of 30 or more

do not run parametric analyses when

skew of distributions are OPPOSITE or if there are OUTLIERS

data transformations

changes data to help improve fit of data to normal distribution and establish equal variances

log transformation (Y'=logY)

used when data is skewed to the right or there is a large difference in magnitude between groups
(if there are zeroes use Y'=log(Y+1))

square root transformation (Y'=sqrt(Y))

used for skewed distributions and equalize standard deviations

arcsine (p'-arcsin(sqrt(p)))

used only for proportions