Topic 1: Statistical Inference Flashcards
parameter
a property or number descriptive of the population
statistic
- a property or number descriptive of a sample
- often used to estimate an unknown -parameter
nominal
classifies/identifies objects
ordinal
ranking data (distances are not the same)
interval
rating data (equal distances)
ratio
a special kind of interval with a meaningful zero point
univariate
- one DV, can have multiple IVs
- linear regression
multivariate
multiple DVs, regardless of the # of IVs
z-scores
transforms any normal distribution into the standard normal distribution where mean = 0 & standard deviation = 1
statistical inference
a process to conclude a population from data on selected individuals
two types of statistical inference
tests of significance & CIs
central limit theorem (CLT)
as n increases, the distribution of the sample mean becomes closer to a normal distribution
NHST
- state the null & alternative hypotheses
- calculate the value of an appropriate test statistic
- find the p-value of the observed data
- state a conclusion
small effect
r2 = 0.01, r = 0.1, d = 0.25
medium effect
r2 = 0.06, r = 0.3, d = 0.5
large effect
r2 = 0.15, r = 0.5, d = 0.8
type l error
reject H0 when it’s true (false +)
type ll error
retain H0 when it’s false (false -)
a
probability of committing a type l error
b
probability of committing a type ll error
1-b
power: the probability of correctly rejecting a false H0
purpose of z-test
to test whether a sample mean differs from a population mean
assumptions of z-test
- the population is normally distributed
- the population standard deviation must be known
- independence of observation (simple random sample of the population)
limitation of z-test
we rarely know the population standard deviation
purpose of t-test
to test whether a sample mean differs from a population mean
assumptions of t-test
- the population is normally distributed
- independence of observation (simple random sample of the population)
t-distribution
varies in shape according to df = n01
p-value
assuming H0 is true, the probability of obtaining a test statistic equal to or more extreme than what was observed from a given sample
sampling distribution
the distribution of values taken by the statistic in all possible samples of size N from the same population
the shape of the sampling distribution
The shape of the distribution of the sample mean depends on the shape of the population.
effect size
a standardized measure of the magnitude of a treatment effect
common types of effect size measures
- Pearson’s correlation coefficient (r) or correlation ratio squared (r²)
- Cohen’s d
- Omega (ω) or omega squared (ω²)
