a distribution of statistics obtained by selecting all possible samples of a specific size from a population
the power of a test
the probability that the test will correctly reject a false null hypothesis
It will detect a treatment effect if one exists
Power=1–β or1–p(TypeIIerror)
Influences on power
Treatment effect --> more effect more power
Alpha level --> larger alpha more power
Two-tailedvs.one-tailedtest -->one-tailed more power
Sample size -->larger and more power
z test for one sample
Used when the untreated population’s
μ and σ are given
The z statistic equation
Effect size
d= M - μ / σ
t test for one sample
Used when the untreated population’s μ is given but no σ
The t statistic equation
Effect size
̂d=M-μ /s
Steps for t test
1) set hypothesis
2) set criteria
3) calculate statistics
- sample variance
- sample standard deviation
- estimated standard error
- standard error
- t statistic
4) make a decision
5) Assess effect size
6) report results
Effect Sizes
d= 0.2 (small effect)
d= 0.5 (medium effect)
d= 0.8 (large effect)
Independent Samples t-test
Between subjects design
Simple experiment
Simple quasi-experiment
No matched groups!
H0 : μ2 – μ1 ≤ 0
H1: μ2 – μ1 > 0
Assumptions of independent measures t-test
- Groups are independent
- The two populations are normally distributed
- Homogeneity of variances
σ1 squared =σ2 squared
effect size
A measure of this is intended to provide a measurement of the absolute magnitude of a treatment effect, independent of the size of the sample(s) being used.
Power
The probability that the test will correctly reject a false null hypothesis. That is, power is the probability that the test will identify a treatment effect if one really exists.
t distribution
The complete set of t values computed for every possible random sample for a specific sample size (n) or a specific degrees of freedom (df). The t distribution approximates the shape of a normal distribution.
Estimated Cohen's d
The estimate of the effect size when we don’t know the standard deviation of the population (we’ll use S instead)
independent-measures/between-subjects study
- uses a seperate sample to represent each of the populations or treatment conditions being compared