Comparing two paired groups 2

Question 1

What does ‘comparing two paired groups’ mean?

Answer 1

Comparing two means within a repeated measures design

Interested in the difference of scores before or after test

Question 2

What test do you use for comparing two paired groups?

Answer 2

Paired samples t-test

Question 3

How does a paired samples t-test work?

Answer 3

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*

Question 4

What is the R command for a paired samples t-test?

Answer 4

pairedSamplesTTest(formula = ~ x + y, z)

x(before)

y(after)

z(data)

Question 5

paired samples t-tests are looking at the ______ in the means

Answer 5

difference

Question 6

What are the assumptions all t-tests (except student t-tests) make?

Answer 6

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)

Question 7

What is the normality assumption?

Answer 7

whether the data is ‘normal’ (normal distribution)

Question 8

What can you use to check the normality assumption (whether the data is ‘normal’)

Answer 8

Quantile-quantile (QQ) plots

Question 9

What are Quantile-quantile (QQ) plots?

Answer 9

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

Question 10

Command for QQ plots in R?

Answer 10

qqnorm(x)

Question 11

What do QQ plots look like if they are skewed?

Answer 11

Not a straight line

Question 12

What is the Shapiro-Wilk test?

Answer 12

A way of quantifying departures from normality

Question 13

What is the test statistic of the Shapiro-Wilk test?

What values of the test statistic imply deviations from normality?

Answer 13

W

Values of W less than 1 imply deviations from normality

Question 14

What is the R command for a Shapiro-Wilk test?

Answer 14

shapiro.test(x)

Question 15

If the p-value is greater than 0.05 in a Shapiro Wilk test, you ____ the null hypothesis

Answer 15

retain

(data is normal)

Question 16

What type of tests do you do if the data is not normal?

Answer 16

Non-parametric tests

Question 17

What are the features of a non-parametric test?

Answer 17

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

Question 18

What is the non-parametric version of a t-test called?

What is its test statistic?

Answer 18

Wilcoxon test

The test statistic is ‘W’ (like Shapiro-Wilk)

Question 19

What does the Wilcoxon ‘W’ calculate?

Answer 19

W counts the number of times a score from group A is larger than a score from group B.

Question 20

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?

Answer 20

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