t tests Flashcards
when is a t test used?
when we have one IV with 2 levels
what does a t-test do?
estimates whether the population means under the 2 levels of the IV are different
assessing differences using samples
- XA - XB = XD
- determine XD for every sample
- plot all these mean differences
- the samples mean differences would build toward
a normal distribution, with a mean equivalent to the true population mean difference (UD)
-sampling distribution of differences
sampling distribution of differences
- null hypothesis (H0) states that there is no difference between population means
-H0: U1-U2= 0
-H0: U1=U2 - under the null hypothesis, the sampling distribution of differences will have a mean of 0
- T distribution represents the distribution of samples mean differences when the null hypothesis is true
t distribution
- Has a mean of 0
- The extent to which an individual samples mean difference deviates from 0
-can be expressed in standard error unit - We can convert the difference between our sample means (XD) into a t value, by expressing the difference in SE units
standard error of differences
- To convert XD to t we need to know the SE of the sampling distribution of the mean (SED)
distribution is hypothetical, would never measure the difference for all possible samples from the population - We can estimate the SED based on the sample standard deviations (s) and sample sizes (n)
T distribution: if the null hypothesis is true
95% of samples t values will fall within the 95% bounds of the t distribution
only 5% of samples will fall outside of the 95% bounds
if the magnitude of the obtained t-value is smaller than the critical value of t
we fail to reject H0
if the magnitude of the t value is smaller than the critical value of t, we reject H0
we reject H0
degrees of freedom
The difference between the number of measurements made and the number of parameters estimated
the larger the degrees of freedom in an estimate…
the more reliable the estimate
degrees of freedom and the t distribution
The t distribution is mediated by degrees of freedom
Used to determine critical values
p value
the probability of obtaining a t-value of a given magnitude when H0 is true
alpha value
the threshold value we measure p against
if p< or = a
reject the null hypothesis
if p>a
reject the null hypothesis
RMs to use independent t test
between participants/ independent groups
what is variance effected by (independent)
manipulation of the IV (treatment effects)
individual differences
experimental error
-random error
-constant error
t ratio
- Reflects the difference between the sample means, expressed in standard error units
- Can use the t-distribution to determine the probability of measuring a t-value and of the magnitude obtained (or greater), if the null hypothesis were true
variance when t value close to 0
small variance between IV levels, relative to within IV levels
variance when t value further away from 0
large variance between IV levels relative to within IV levels
assumptions of independent t test
- The DV should be normally distributed, under each level of the IV
- Homogeneity of variance
- Equivalent sample size
- Independence of observations
homogeneity of variance
the variance in the DV, under each level of the IV should be (reasonably) equivalent
how to test homogeneity of variance (SPSS)
SPSS check with Levene’s test
Null hypothesis: there is no difference between the variance under each level of the IV (homogeneity)
if p<=0.05 we reject the null hypothesis (heterogeneity)
non parametric equivalent of independent test
Mann-Whitney U test
RMs to use paired test
within participants/ repeated measures
variance in paired t test is effected by
manipulation of IV (treatment effects)
experimental error
-random error
why is variance due to individual differences absent in paired tests
each participant acts as their own control
assumptions of the paired t test
- Normality: the distribution of difference of scores between the IV levels should be approximately normal
-assume okay if n>30 - Sample size: sample size under each level of the IV should be roughly equal
non parametric equivalent of paired t test
wilcoxon t test
if the effect of the IV is consistent
result is likely to be significant
if the effect of the IV is not consistent
the result is likely to not be significant
cohen’s D
the magnitude of difference between two IV level means, expressed in standard deviation units
standardised value expressing the difference between the IV level means
ignores sample size
d= 0.2
small effect
d= 0.5
medium effect
d= 0.8
large effect
