HaDPop S4 - Sources of Variation Flashcards
Explain the concept of random variation
Coins tend to produce equal numbers of heads and tails, but what we observe may depart from this by random variation
Give an example of the difference between tendency and observed values
- Tendency: the “true” or “underlying” tendency is for 4 cases per month of meningitis in Leicestershire
- Observation: in January, February and March this year, we observed 2, 5 and 4 cases respectively
- N.B. Our “observed” value is our best estimate of the “true” or “underlying” tendency
Define hypothesis
A hypothesis is a statement that an underlying tendency of scientific interest takes a particular quantitative value e.g. true prevalence of tuberculosis in a given population is 2 per 10,000 people
What is formal hypothesis testing?
Calculate the probability of getting an observation as extreme as, or more extreme than, the one observed assuming that the stated hypothesis is true. If the probability is very small, it is reasonable to conclude that the data and the stated hypothesis are incompatible. Therefore with a small probability, EITHER something very unlikely has occurred (and hypothesis true) or the stated hypothesis is wrong
What is the p-value?
Calculated probability
Why do we use p=0.05?
Purely conventional
What is the interpretation of different p-values?
P-value 0.05
- Cannot reject
- Does NOT mean that the hypothesis has been proven
Why isn’t rejecting a hypothesis always useful?
- p
What is statistical significance?
Results haven’t occurred by chance alone. More confident that we are observing a “true” result
What are almost all observed quantities e.g. rate ratio in medical science subject to?
Variation by chance
How can we make rational inferences about the real size of a quantity of importance given the variation?
Use the 95% confidence interval
Give an example of a confidence interval
0.59—–0.87—–1.14
Point estimate (“best guess”) = 0.87
95% confidence limits are 0.59 and 1.14
Our best guess is that the “true” rate ratio is 0.87 and we can be 95% certain that the “true” rate ratio lies somewhere between 0.59 and 1.14
What is a confidence interval (CI)?
CI expresses the precision of an estimate and is often presented alongside the results of a study. The narrower the interval, the more precise the estimate
What is the 95% confidence interval?
The range within which we can be 95% certain that the “true” value of the underlying tendency really lies. The range is centred on the observed value because it is always our best guess at the “true” underlying value. Therefore the “observed” value is always within the 95% CI - it cannot be anywhere else
What and who does a prevalence survey measure?
- What? Case definition
- Who? Sampling frame, sampling proportion, sampling technique, response
