Lecture 9- Two Sample

Question 1

Paired vs. 2 Sample Comparisons

Answer 1

Paired– natural correspondence between individual

Question 2

Comparing means–
what is it? how is it done?

Answer 2

• tests with one categorical and one numerical variable
• GOAL: to compare the mean of a numerical variable for different groups

Question 3

Paired comparisons allow us to

Answer 3

account for a lot of extraneous variation

Question 4

2-sample methods are ______ to collect data for

Answer 4

easier

Question 5

Examples of Paired Designs

Answer 5

• Before and after treatment
• Upstream and downstream of a power plant
• Identical Twins: one with a treatment and one without
• Earwigs in each ear: how to get them out? Compare tweezers to hot oil

Question 6

Paired Designs

Answer 6

• Data from two groups paired
• Each member of pair shares much in comon with the other, except for tested categorical variable
• There is a one-to-one correspondence between the individuals in the two groups

Question 7

Paired Comparisons

Answer 7

• We have many pairs
• In each pair, there is one member that has one treatment and another who has another treatment
• (“Treatment” can mean “group”

Question 8

How do we compare two groups in paired comparisons?

Answer 8

To compare two groups, we use the mean of the difference between the two members of each pair

Question 9

Paired t test

Answer 9

• Compares the mean of the differences to a value given in the null hypothesis
• For each pair, calculate the difference
• The paired t-test is simply a one-sample t-test on the differences

Question 10

Example of paired t-test?

Answer 10

Emergency Room Admissions (4/20)
- Counted emergency room admissions in Vancouver on April 20
- Compared to average admissions one week before and after
- Each data point is one year

Hypotheses:
H0 (null): ER admissions are the same on average on 4/20 as on control days
HA: (alternative): ER admissions are different on average on 4/20 compared to control days

Question 11

Assumptions of paired t test

Answer 11

• Pairs are chosen at random
• The differences have a normal distribution
• It does not assume that the individuals values are normally distributed, only the differences

Question 12

Comparing the means of two groups

Answer 12

Hypothesis test: 2-sample t-test`

Question 15

Pooling variance

Answer 15

when you weigh the variances of both samples

Question 16

Two Sample T test

Answer 16

exact opposite of two sample one test

t= (Ybar_1 - Ybar_2)/SE_[Ybar_1-Ybar_2]

Question 17

Assumptions of 2-sample t-test

Answer 17

• Both samples are random samples
• Both populations have normal distributions
• The variance of both populations is equal

Ybar ~ normal if sigma is known
(Ybar-M)/s rad sigma ~t is estimated