T Tests

Question 1

What is the purpose of an unpaired t test for 2 indep means and e.g?

Answer 1

• Compares means from 2 indep samples/people e.g. comparing mean heights of boys and girls

Question 2

What is unpaired t test based on?

Answer 2

sampling dis of 2 sample means (normal)

Question 3

What does unpaired t test allow?

Answer 3

Calc of diff and CI for diff

Question 4

What is null and alt hypothesis for unpaired t test?

Answer 4

• null: 2 samples come from pops with same mean

- alt: there is mean diff between 2 samples

Question 5

What are 3 assumptions of unpaired t test?

Answer 5

1. Quant data (continuous/discrete) normally dis. Data checked for symmetry using dot plot, histogram/normal plot
2. SD are the same for both samples. Checked by inspecting them - if diff, Satterthwaite approx may be used
3. Sig tests are available to check for normality + sim of SD but not helpful guides as are often non-sig for small samples even if appears to be non-normality/diff in SD. Also tend to be sig for large samples even if skewness/diff in variance appear to be minor (so visual test may be better)

Question 6

Why might assumptions not hold for unpaired t tests?

Answer 6

• stat test is doubtful and p value is wrong

- t test quite robust to slight skewness if 2 samples are same size but less robust if variances clearly diff

Question 7

How would you try to correct assumptions that don’t hold for unpaired t test?

Answer 7

• try transformation of data (use log transformation)

- skewness + non-similar SD often go together + correcting 1 by transforming data may correct the other as well

Question 8

What parameter has t dis got?

Answer 8

degrees of freedom

Question 9

What is DOF related to?

Answer 9

sample size (which is n1+n1-2)

Question 10

Describe t dis

Answer 10

• no single t dis - each n1+n2-2 (Sample) gives diff shape

- for large sample (>100), t dis close to normal dis

Question 11

What is the unpaired t test also known as?

Answer 11

2 sample t test

Question 12

What happens to SD + SE when calc for unpaired t test?

Answer 12

• SD combined/pooled from SDs of the 2 diff samples

- SE are also combined SE based on 2 SD from both samples

Question 13

What does the paired (matched) t test do?

Answer 13

• analyses mean diff in paired sample

- each person matched to a sim/same person at diff occasions

Question 14

How do you check assumptions using a histogram to see if data are normal for unpaired data?

Answer 14

• histogram shows data close to symmetry
• 2 SDs are similar
• can conclude t est assumptions hold for these data

Question 15

What is paired t test based on?

Answer 15

• sampling dis of mean diff (normal)

Question 16

What does paired t test allow?

Answer 16

• calc of mean diff + CI for diff

Question 17

What is null hypothesis for paired t test?

Answer 17

mean change/diff is 0 in pop

Question 18

What are assumptions for paired t test?

Answer 18

• quant data follow normal dis - data can be checked visually using dot plot, histogram/normal plot
• variances (SD) don’t vary with values of data

Question 19

Why might assumptions for the paired t test not hold?

Answer 19

• stat test is doubtful and P value may be wrong
• try transformation of data - transform raw data not diff
• paired t test only requires diff to be normal. Sometimes original data can be skewed but when diff/change is calc, diff may be normally dis

Question 20

What is paired t test aka?

Answer 20

• one-sample t test

Question 21

How do you 95% CI calc for paired t test for small samples?

Answer 21

• calc t value and use this to read theological t value an n-1 DOF
• use this t value as multiplier

Question 22

How do you calc 95% CI for unpaired t test for large samples?

Answer 22

• use 1.96 instead of t value as multiplier

Question 23

How do you check assumptions to see if diff are normal for paired t test?

Answer 23

• check histogram to see if data diff fit normal dis

- can conclude t test assumptions hold for these data

Question 24

What are requirements for large sample size in unpaired and paired t test?

Answer 24

• unpaired: >50 per group
• paired: >100
• requirements for data to be normal less critical for mathematical reasons

Question 25

How do you find p value for paired t test?

Answer 25

• look for value corresponding to theoretical t value at n-1 DOF

Question 26

What is a p value?

Answer 26

• probab (value must be from 0-1) of getting sample mean diff as far/large as that obtained by current trial (exp/sample data)
• or further away from what was specified if null hypothesis is true

Question 27

What does it mean if probab (p-value) is small?

Answer 27

ev against null hypothesis

Question 28

How small should the p value be?

Answer 28

common criteria p = 0.05

Question 29

What can you say about null hypothesis for p value = 0.0016?

Answer 29

• if null hypothesis were true, there would be 0.16% chance of seeing such a sample mean diff
• conclude sig diff + reject null hypothesis

Question 30

How do you conduct hypothesis testing for a paired t-test?

Answer 30

• formulate specific hypothesis
• evaluate strength of ev: use estimates from sample
• decide whether/not data supports hypothesis
• start with null hypothesis
• look at p value to determine stat sig

Question 31

What is the strict wording of the null hypothesis and give e.g?

Answer 31

• must state the word: pop
• must state size of diff being looked at
• e.g. in pop of S London stroke patients, mean change
• in SBP between 24hrs + 1 week following treatment is 0

Question 32

What do you expect when null hypothesis is true for paired t test? What is the reason it might not be?

Answer 32

• expect sample mean diff in SBP close to 0

- if not, diff further away from 0 in either -ve/+ve direction - cast doubt on null hypothesis

Question 33

How close/far from O can null hypothesis be?

Answer 33

• use t-test to assess that

Question 34

How can 95% CI + P-value be used to accept/reject null hypothesis?

Answer 34

• if 95% CI doesn’t include null hypothesis (0 is not included within the range) - ev to reject null hypothesis