2: T-TEST Flashcards
the t-test
- used when we have 1 IV with 2 levels
- estimates whether the population means under the 2 levels of the IV are different (estimate based on the difference between measured sample means)
- independent t-test: between participants
- paired t-test: within participants
independent t-test: what contributes to variance: between IV levels
- manipulation of the IV (treatment effects)
- individual differences
- experimental error (random/constant error)
independent t-test: what contributes to variance: within IV levels
- individual differences
- experimental error (random error)
the null hypothesis - t-distribution
- under the null the sampling distibution of differences will have a mean of 0
- the t-distribution represents the distribution of sampled mean differences when the null is true
- mean = 0
- the extent to which an individual sampled mean difference deviates from 0 expressed in standard error units
- we convert the difference between sample means x(line)^D into a t-value (by expressing the difference in SE units)
standard error of differences
- how do we convert sample mean difference (X(line)^D) to t? (express it in SE units)
- first we need to know the SE of this sampling distribution of mean differences (SE^D) - but this is a hypothetical distribution
- we can estimate SE^D based on the sample standard deviations (s) and sample sizes (n)
- ESE^D (learn formula) is also equal to variance within IV levels
t- ratio: independent designs
- t is a ratio
- reflects the difference between the sample means, expressed in standard erro units
- can use the t-distribution to determine the probability fo measuring a t-value of the magnitude obtained (or greater), if the null were true
t = X(line)^D/ ESE^D
t = variance between IV levels / variance within IV levels
values of t-ratio
- t-value close to 0: small variance between IV levels realtive to within IV levels
- t-value further from 0: large variance between IV levels relative to within IV levels
degrees of freedom
the difference between the number of measurements made and the number of parameters estimated (i.e. sample size - no. parameters)
the larger the degrees of freedom in an estimate, the more reliavle the estimate
df for independent t-test
df = n(total) - 2
t-distribution
the t-distribution is mediated by degrees of freedom, greater degrees of freedom, closer to true normal distribution
interpreting p-values
using the t-dist we can determine the probability of obtaining a t-value of a given magnitude when the null is true
- this is out p-value
a (alpha) is the value we measure p against
- p < (or equal) a : reject null
- P > a : fail to reject null
assumptions: independent t-test
- normality: the DV should be normally distributed, under each level of the IV
- homogeneity of variance: the variance in the DV, under each level of the IV, should be (reasonably) equivalent (SPSS checks with levenes test)
- equivalent sample size: sample size under eache level of the IV should be roughly equal
- independence of observations: scores under each level of the IV should be independent
if data seriously violates, non parametric equivalent: Mann-Whitney U Test
paired t-test
- used for within-subjects/repeated measures designs
- also looks at the ratio of the variance between IV levels to the variance within IV levels
- however, the calculations are different (different scores calculated for each participant)
paired t-test: what contributes to variance: between IV levels
- manipulation of IV (treatment effects)
- experimental error
RM designs: variance due to individual differences is absent (each particpant acts as his/her own control)
paired t-test: what contributes to variance: within IV levels
- experimental error
RM designs: we can discount variance due to individual differences (leaving only the variance due to error)
