Hypothesis testing part 2

Hypothesis testing

formulate null (H₀) and alternative (H₁)

decide level of sig

look up critical value - threshold for rejecting null

calculate statistic and compare to critical value

choose a critical value in terms of probability

can choose a critical value that represents the boundary between what we think as an acceptable observation difference and an unexpectedly large difference

difficulties

not always obvious what specific difference we are looking for

sometimes comparing average is not meaningful e.g. bimodal and unimodal have the same mean

data may not be interval scale

parametric stats

indépendant ransom samples - interval scale data

values of interest are close to known theoretical distribution - testing for normal distribution

non- parametric

distribution free stats

independent random samples - nominal or ordinal data

no assumption is made with regarding the underlying distribution

Chi-squared for difference

no assumptions

observations can be compared to any other empirical or theoretical difference

frequency data

test summarises all differences between samples

comapres frequency data across multiple samples and multiple categories

O = observed

E = expected

difference between observed and expected

observed = frequency data already organised into classes

interval data - need to be put into classes

ordinal data - need to be put into classes

expected = what we would expect if there were no difference in the pops of each class

requirements for chi squared testing

data must be in the form of frequencies

contingency table must have 2 or more categories

expected frequencies should be less than 5 (20% can be more than 5 if table larger than 2×2) but all expected frequencies must be greater than 1

samples unbiased - randomly chosen and independent