T tests

Question 1

Definition of a paired/matched sample

Answer 1

Same sample of individuals tested at different points in time

Question 2

Definition of an unpaired/independent sample

Answer 2

2 data sets with different groups of people in each sample

Question 3

Definition of a p value

Answer 3

Tests for a significant difference between 2 means

Question 4

What are the 2 types of sample that can be used the t tests

Answer 4

Paired/matched
-same sample of individuals tested at different points in time

Unpaired/independent
-2 independent groups of people in each sample

Question 5

How are samples used to get info about the whole population

Answer 5

Population => sample => Inferences based on sample => data extrapolated to original population

Question 6

How would you carry out the calculations for a paired t test

How would you find your t value
How would you find the SE
How would you find the CI
How would you find the p value

Answer 6

Calculate your t value
t = ∆mean/SE of ∆mean

Calculate your SE
SE = SD/√n

Calculate the confidence interval for the mean difference
CI = ∆mean +- t(df : 1 - å)(SE)

Use theoretical t value from t table
If sample size is large, use z value (1.96)
Df = n-1
å = 0.05

Find the p value for your calculated t at (n-1) DF

Question 7

How do you interpret your CI

How do you interpret your p value

Answer 7

If CI does not include 0 => significant result
If CI includes 0 => can’t reject null

If p< 0.05 => reject null
If p ≥ 0.05 => can’t reject null

Question 8

How would you carry out the calculations for an unpaired t test

How would you find your t value
How would you find the combined SD
How would you find the combined SE
How would you find the CI
How would you find your p value

Answer 8

Calculate your t value
t = ∆mean/SE of ∆mean

Calculate your combined SD
SD combined = √((n1-1)SD1^2 + (n2-1)SD2^2)/ (n1+n2-2)

Calculate your combined SE
SE combined = √(SD1^2/n1) + (SD2^2/n2)

Calculate the confidence interval
CI = ∆mean +- t(df : 1 - å)(SE)

Use theoretical t value from t table
Df = (n1 + n2 -2)
å = 0.05

Find the p value for your calculated t at (n1 + n2 -2) degrees of freedom

Question 9

What are the 2 assumptions made when doing a t test

Answer 9

The values have a symmetric distribution

Variances are the same, can be determined by checking SD

Question 10

What should you do if the assumptions do not hold

Answer 10

P value is wrong

• use logs to transform data
• if both variances are v different/data is v skewed, transforming data may correct 1 or the other