5 - Comparing 2 samples

Question 1

What is the Central Limit Theorem?

Answer 1

“the sum of a large number of independent and
identically-distributed random variables will be
approximately normally distributed”

Question 2

Which test would you do for two samples which:

a) Parametric (normally distributed) and not paired
b) Parametric and paired
c) Non-parametric and not paired
d) Non-parametric and paired

Answer 2

a) t-test
b) paired t-test
c) Mann-Whitney
d) Wilcoxon

Question 3

t-test:
for two unmatched \_\_\_\_\_\_ random samples 
assumes \_\_\_\_\_\_ distribution of residuals
assumes \_\_\_\_\_ variances
data should be continuous/discontin? (or nearly so)
tests for difference in \_\_\_\_\_
special case of \_\_\_\_\_

Answer 3

t-test
for two unmatched independent random samples
assumes normal distribution of residuals
assumes equal variances
data should be continuous (or nearly so)
tests for difference in mean
special case of one-way ANOVA (next lecture)

Question 4

Mann-Whitney U-test
for two unmatched \_\_\_\_\_ random samples 
distribution\_\_\_\_\_\_\_\_ for both samples
data does OR does not need to be continuous?
tests for difference in \_\_\_\_\_
numbers are \_\_\_\_\_

Answer 4

Mann-Whitney U-test
for two unmatched independent random samples
any distribution ok, but same for both samples
data do not need to be continuous
tests for difference in median
numbers are ranked

Question 5

Give some examples of matched pairs

in this instance what would you calculate?

Answer 5

left arm and right arm of patients
before and after a treatment
amount of time spent in choice of two 
areas by individual animal
Calculate the difference

Question 6

How do you calculate t?

Answer 6

(mean-specified value) / (Standard dev / sqrt of sample size)

Question 7

paired t-test
for two \_\_\_\_\_ samples 
assumes \_\_\_\_ distribution of residuals
assumes \_\_\_\_ variances
data should be \_\_\_\_\_\_
tests for \_\_\_\_\_\_ difference not equal to zero

Answer 7

paired t-test
for two paired samples 
assumes normal distribution of residuals
assumes equal variances
data should be continuous (or nearly so)
tests for mean pair difference not equal to zero