Session 3 Lecture 1: Introduction To Key Statistical Concepts

Question 1

What type of variation may depart the observed values from the true/underlying value?

Answer 1

Random Variation

Question 2

Definition of a hypothesis

Answer 2

A statement that an underlying truth of scientific interest takes a particular quantitative value

e.g The new drug is neither better or worse than the standard treatment (ratio of survival rates = 1.0)

Question 3

What is the p-value?

Answer 3

The probability of getting an observation as extreme as or more extreme than the one observed if the hypothesis is true

Question 4

What is the interpretation of p-value < 0.05? (arbitrary convention)

Answer 4

• strong evidence to reject the hypothesis at 5% significance level but not to absolutely prove that the null hypothesis is false
• data inconsistent with the stated hypothesis
• observations are statistically significantly different

Question 5

What is the interpretation of p-value > 0.05? (arbitrary convention)

Answer 5

• failure to reject the null hypothesis
• data is consistent with the stated hypothesis
• it does not mean that the hypothesis has been proven or we accept the hypothesis
• observations are not statistically significantly different

Question 6

What are the limitations of Hypothesis testing?

Answer 6

Rejecting a hypothesis is not always useful :

• p-value < 0.05 is arbitrary, nothing special with 0.049 or 0.051
• the statistical significance depends on sample size; the bigger the sample size, the less significant it becomes
• however, statistically significance does not mean it is clinically important

Question 7

What is the confidence interval?

Answer 7

The confidence interval is an estimate of the precision of the observed values in the sample

Question 8

If the observed rate ratio is 0.87 and the 95% confidence limits are 0.59 and 1.14, what is the interpretation of this?

Answer 8

• 95% certain that the true rate ratio lies somewhere between 0.59 and 1.14
• 41% decrease in rate and 14% increase in the rate
• the null value can be found in this interval so therefore it is not statistically significant
• failure to reject the null hypothesis
• data is consistent with the null hypothesis

Question 9

If the observed rate ratio is 0.57 and the 95% confidence limits are 0.26 and 0.78, what is the interpretation of this?

Answer 9

• 95% certain that the true rate ratio lies somewhere between 0.26 and 0.78
• 74% decrease in rate and 22% decrease in the rate
• the null value cannot be found in this interval so therefore it is statistically significant
• reject the null hypothesis
• data is not consistent with the null hypothesis

Question 10

What is the link between Confidence interval and the p-value?

Answer 10

• null value inside 95% CI –> not statistically significant –> p ≥ 0.05
• null value outside 95% CI –> statistically significant –> p < 0.05