Comparing two paired groups 2 Flashcards
What does ‘comparing two paired groups’ mean?
Comparing two means within a repeated measures design
Interested in the difference of scores before or after test
What test do you use for comparing two paired groups?
Paired samples t-test
How does a paired samples t-test work?
By running a one sample t-test of the difference scores (difference before and after)
- Exactly the same as a one-sample t-test*
- H0 = mean difference is 0*
- H1 = mean difference is not 0*
What is the R command for a paired samples t-test?
pairedSamplesTTest(formula = ~ x + y, z)
x(before)
y(after)
z(data)
paired samples t-tests are looking at the ______ in the means
difference
What are the assumptions all t-tests (except student t-tests) make?
Population distribution is normal
The data are independent of except in those respects that the test specifies
(e.g. paired samples t-test implies a very specific kind of relationship between data from the same person)
What is the normality assumption?
whether the data is ‘normal’ (normal distribution)
What can you use to check the normality assumption (whether the data is ‘normal’)
Quantile-quantile (QQ) plots
What are Quantile-quantile (QQ) plots?
These are scatterplots of the actual quantiles of the observed data against the theoretical quantiles of the normal distribution
If the data are truly normally distributed, you’d expect the quantiles to be identical, giving a nice straight line
Command for QQ plots in R?
qqnorm(x)
What do QQ plots look like if they are skewed?
Not a straight line
What is the Shapiro-Wilk test?
A way of quantifying departures from normality
What is the test statistic of the Shapiro-Wilk test?
What values of the test statistic imply deviations from normality?
W
Values of W less than 1 imply deviations from normality
What is the R command for a Shapiro-Wilk test?
shapiro.test(x)
If the p-value is greater than 0.05 in a Shapiro Wilk test, you ____ the null hypothesis
retain
(data is normal)
What type of tests do you do if the data is not normal?
Non-parametric tests
What are the features of a non-parametric test?
They avoid making assumptions about the shape of the distribution (e.g. normal)
Usually not as powerful (higher type 2 error) than the corresponding parametric tests
But sometimes you have to use them
What is the non-parametric version of a t-test called?
What is its test statistic?
Wilcoxon test
The test statistic is ‘W’ (like Shapiro-Wilk)
What does the Wilcoxon ‘W’ calculate?
W counts the number of times a score from group A is larger than a score from group B.
What problem might the Shapiro-Wilk test encounter is the sample size is greater than 50?
How might you check to see if the results are accurate?
It may be significant even if the data is normal (p < .05 indicating departure from normality)
Look at QQplot or histogram to see if it looks normal
