What is a t distribution?
A distribution for a small sample size.
All t-distributions resemble normal distributions in that they are unimodal with the mean centered.
t-distributions have somewhat “fatter” tails than normal distributions.
How do you calculate degrees of freedom?
n-1
where n is the sample size
What is the use of t tests?
Providing CI’s around the mean
What is the alpha number?
The 1-CI
e.g. 95% CI has an alpha number of 0.05
How is this interpreted:
95%CI = 63.36 ± (2.228)(3.41) = 60.36 ± 7.60 = 52.76, 67.96
?
We are 95% confident that the mean is between 52.76 and 67.96
What assumptions must be made to do a t-test?
- The sample is random or unbiased.
- All observations are independent
- We are sampling from a normal population.
When can you not use pooled variance?
If the difference in variance (SD) is different by a factor of 2, you should use separate variances rather than pooled variances.
Based on CI, how can you tell if two means are significantly different?
If the CI of the difference between the two does not include zero.
How do you calculate df for pooled (equal) variance?
n1 + n2 -2
What determines df?
ALWAYS SAMPLE SIZE!
What is a shortcut for calculating df for unequal variances?
df = n-1
using n of the SMALLER of the two sample sizes
What is true of repeated measures on the same individual?
They can never be independent! Must first find the difference between the paired measurements and look at the variance in THAT (basic t test).
What test in stata do you use to test for equal variances?
Robust-equal variance test. aka as Levene’s test
What is the null hypothesis for Levene’s test?
That the variances are equal
Does a p value tell you anything about the magnitude of the difference between values?
Nope
What test would you use for a simple hypothesis test?
A one-sample t test. Compares your sample to a theoretical value.
What is Ho and Ha?
Ho = null hypothesis Ha = alternative hypothesis
What is the difference between z scores and t scores?
The z-test (resulting in a z-score) can be used to test a hypothesis when researchers know, or can closely estimate, population parameters like μ and σ. The z-score is based on a standard normal distribution.
What does it mean for a test to be ‘robust’?
It can withstand significant derivation from normality and still be functional.
Is a one-sided or two-sided test more conservative (harder to reject the null).
two-sided
Why is a two-sided test more conservative?
Your alpha (usually 0.05) is divided by two. 1/2 below and 1/2 above, leading to a wider acceptance area/narrower rejection area
