Lecture 5 - Key Statistical Concepts

Question 1

What is a population?

Answer 1

All possible observations of an experimental/study variable

Question 2

What is a sample?

Answer 2

A selection of observations taken from the population

Question 3

What is the role of statistics?

Answer 3

To select a sample to get information from this sample which we will use to generalise the population

Question 4

What are the 2 types of error that can influence results in a study?

Answer 4

Chance (random error)
Bias (systemic error)

Question 5

What causes random error and how can it be reduced?

Answer 5

Error due to sampling variation

Reduced as sample size increased

Question 6

What is bias?

Answer 6

The difference between the true value and the expected value

Question 7

What is the difference between bias and random error?

Answer 7

Bias is a form of systematic error (error in study design)

Increase sample size does not reduce bias

Question 8

What is Truth Vs Observed random variation?

Answer 8

When the true probability is by chance different to what is observed

True probability of getting a tail when flipping a coin is 0.5
But if you flip a coin 10 times you may get 7 tails by random chance

Question 9

What is a hypothesis?

Answer 9

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

E.g: Prevalence of TB in a given population is 2 per 10,000 people

Question 10

What is hypothesis testing?

Answer 10

When you calculate the probability of getting an observation as extreme as or more extreme than one observed assuming that the hypothesis is true

If this probability is very small it is considered that the observation and the stated hypothesis are incompatible

Calculated probability = p-value

Question 11

What is the p-value?

Answer 11

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

So if a p value = 0.05 an extreme value iis a value that is at the bottom or type 2.5% of the distribution

Question 12

What p-value do we typically reject the null hypothesis at the 5% significance level?

Answer 12

P less than 0.05

There is strong evidence to reject the null hypothesis

Question 13

What do you do with the null hypothesis if p is larger or greater than 0.05?

Answer 13

Not enough evidence to reject the hypothesis

Doesn’t mean that the hypothesis has been proven

Question 14

What is a 95% confidence interval?

Answer 14

It’s means that if 100 samples where taken, 95 of the confidence intervals will contain the true value

Question 15

About confidence intervals.

Answer 15

95% confidence interval is the range within which we can be 95% certain that the true value of the underlying truth really lies

The range is centred on the observed value because it is always our best guess at the true underlying value

Question 16

What is a null value?

Answer 16

An estimate that shows no difference between groups

Question 17

For a difference what are the null values?

Answer 17

0

Question 18

For a ratio what is the null value in a confidence interval?

Answer 18

1

Question 19

What will the null value be for 2 groups that you think have no difference between each other for a ratio?

Answer 19

1

Question 20

The confidence interval and the p-value will always agree on statistical significance.

If the null hypothesis is inside the 95% confidence interval what will the p value be?

Answer 20

P>or equal to 0.05

Question 21

The confidence interval and the p-value will always agree on statistical significance.

If the null hypothesis is outside the 95% confidence interval what will the p value be?

Answer 21

P<0.05

Question 22

When the p value = 0.01 with a 95% confidence interval, is there a statistically significant association with “the odds of developing lung cancer in smokers compared to non smokers?”

Answer 22

P < 0.05
Therefore the confidence interval shows a statistically significant difference as it does NOT contain the null value of 1

(Null value of 1 due to it being a ratio not a difference)

Question 23

When the p value = 0.001 with a 95% confidence interval, is there a statistically significant association with “HbA1C levels were 0.24%, CI 0.16 to 0.33% higher in South Asians compared to whites?”

Answer 23

P < 0.05
The confidence interval shows a statistically significant difference as it does not contain the value of 0

(Null value of 0 would indicate no difference between groups, 0 used not 1 since this is a difference in numbers not ratios)