Comparing two means (t-test)

Question 1

What is the difference between paired and unpaired samples?

Answer 1

Paired (matched) samples
Un-paired (independent) samples

Question 2

How do we go from sample to population?

Answer 2

Question 3

What must you do in a paired t-test?

Answer 3

Paired t-test: Compare two population Means

Question 4

Steps

Answer 4

Hypothesis testing:
* Formulate a specific hypothesis
* Evaluate the strength of evidence: use estimates from the sample
* Decide whether or not the data supports the hypothesis
* Does an average reduction of 13.8 mm Hg in 10 patients provide enough evidence that all similar patients would benefit?
* Start with null hypothesis that there is no real effect in the population (i.e. Mean difference=0)

Question 5

What is the strict wording of null hyoithesis?
What do we assess?

Answer 5

Null Hypothesis (H0): strict wording
* In the population of South London Stroke patients, the mean change in SBP between 24 hours and one week following treatment is zero.
* If H0 true: expect sample “mean difference” in SBP close to zero
* How close / far from zero??
* Do the t-test to asses that.
* Find the 95% confidence intervals and the p value.

Question 6

Do the t-test ?
Find the 95% confidence intervals and p value ?

Answer 6

How to calculate the

Question 7

How to work out the 95% Cl for un-paired test?

Answer 7

Question 8

What is P-value ?

Answer 8

• Probability of getting a sample mean difference as far as that obtained by the current trial (experiment /sample data) or further away from what was specified if the null hypothesis is true
• If this probability (P-value) is small, then there is evidence against the Null Hypothesis
• How small? is judged by a criteria we choose. Most common is P ≤ 0.05.

Question 9

Interpretation of the P-value

Answer 9

If the null hypothesis were true there would be a 0.16% chance of seeing such a sample mean difference (0.093 meter, approximately 9.3 centimetres)
There’s sufficient evidence to conclude that there is a difference between heights of girls and boys of MBBS1 students

Question 10

Assumptions of t test

Answer 10

• Quantitative (continuous or discrete data); Normally distributed; can be checked visually for symmetry using a dot plot, histogram, or Normal plot.
• Variances (standard deviations) are the same: can be checked by inspecting the standard deviations.
• Statistical programs have formal tests for equality of variance and may be used.

Question 11

When do Assumptions not hold?

Answer 11

• The statistical test is doubtful and the P value may be wrong
• Try transformation of data (may use log transformation)
• Note that the t-test is quite robust to slight skewness if two samples are the same size but is less robust if variances are clearly different
• Skewness and non-similar standard deviation often go together and correcting one by transforming the data may correct the other as well