T-tests Flashcards
Estimated Standard Error
the standard error using sample variance versus population variance, since population variance is generally unknown
Estimated Standard Error Formula
sm=sqrt s^2/n=SD/sqrt n
T-Distribution
A sampling distribution derived from the sample variance, not the population variance
DF for t-distribution
n-1, amount in the distro tail decreases with fewer degrees of freedom
T-table
A table of “critical values” for the T-distribution
Z vs T formula
z=M-μ/σm
t=M-μ/SD/√n
Comparison
Tobt is < or > or = Tcritical
One Sample t-Test (Independent) assumptions
Assumptions made:
- data are normally distributed
- data were obtained using random sample
- probabilities of each outcome in study are independent (there is no influence, sampling with replacement etc)
- Degrees of freedom will be used
Confidence Interval (CI)
A scope or range of values that could possibly contain the population parameter we’re inferring
Point Estimate
A sample statistic (usually a single value) given as a probable population parameter
Level of Confidence
The probability that an estimate of interval will contain a particular population parameter
Estimation
A statistical method where a sample statistic is used to estimate an population parameter, which often isn’t known.
Degrees of Freedom
n-1 for the t-distro: the number of sample items that is allowed to vary.
Increases with sample size
Estimated Cohen’s D
The estimate of effect size used with t-tests: sample standard deviation (SD) is used instead of population standard deviation (σ)
estimated standard error
Since, on average, the sample variance is an “unbiased” estimator of population variance, we can substitute it into the standard error formula
Estimated Standard Error formula
SD/√n
t-statistic (Tobs/Tobt)
Inferential stat that helps determine, in t-distro, the number of standard devs that a sample mean deviates from the mean value OR mean difference in the null.
t-distribution
A distribution very similar to the normal, except that the further out you go, the more spread the scores are because of the greater variability of sample variance.
Proportion of Variance
An estimate of how much the difference observed in an experiment caused can be attributed to their treatment
Proportion of variance formula
Prop of var= variability explained/total variability
Eta-Squared (η^2)
A measure of proportion of variance using t-statistic and degrees of freedom
η^2 formula
η^2=t^2/t^2-df
omega squared formula (ω^2)
ω^2=t^2-1/t^2+df
Omega-Squared
A more conservative estimating statistic of proportion of variance, since Eta-Squared tends to run high
treatment
A procedure done to a randomly sampled proportion of a sample to produce a specific variance and test hypotheses
