Introduction to Key Statistical Concepts Flashcards
What are three important concepts regarding a sample with respect to population?
The sample should be representative.
The sample should be unbiased.
The sample should be precise.
How can chance/random error be reduced?
By increasing the sample size.
How do tendency and observation differ?
Observed value is our best estimate of the true or underlying tendency.
Give an example of the difference between tendency and observation.
For example in the case of a coin, a coin tends to produce equal numbers of heads and tails.
However what we observe may depart from the tendency by random variation.
How can we reduce the random error of coin flipping?
By keep flipping the coin. (Increasing sample size)
Give another example of the difference between tendency and observation.
True of underlying tendency is for four cases per month of meningitis in Leicestershire.
In January, February, and March this year, we observed 2, 5, and 4 cases respectively. This gives a best estimate of 3.7 cases per month.
Define hypothesis.
A statement that and underlying tendency of scientific interest takes a particular quantitative value.
Give some examples of an hypothesis.
The prevalence of tuberculosis in a given population is 2 per 10000 people.
The coin is fair (probability of heads is 0.5)
The new drug is neither better nor worse than the standard treatment. (ratio of survival rate = 1.0)
The new operation leads to neither more nor less post-operative pain. (difference between pain scores = 0).
How do we test a hypothesis?
By measurement of observation and then we calculate the probability of the observed values contra the hypothesis.
What is a reasonable conclusion of an hypothesis with a low probability?
That either something very unlikely has occurred and the hypothesis is true or more likely the stated hypothesis is wrong.
What is p-value?
The calculated probability of a null hypothesis. The probability of getting an observation as extreme as, or more extreme than the one observed assuming that the stated hypothesis is true.
What does a low p-value mean then?
That the probability of getting an observation as extreme or more extreme than the one observed assuming that the stated hypothesis is true. I.e. this means that it is reasonable to conclude that the observation and the stated hypothesis are incompatible.
What is the usual p-value to use in order to conclude that a null hypothesis is rejected? What is a reason for the conclusion to not be necessarily right?
A p-value of < 0.05.
Data can be inconsistent with the stated hypothesis.
The <0.05 is an arbitrary convention and does not mean that either 0.049 is enough to reject the hypothesis. or 0.051 is enough to say that the hypothesis has been proven.
It also depends on sample size.
Why are there limitations to hypothesis testing?
P-value is arbitrary.
Depends on sample size.
Statistically significant does not equal clinically important
How should we interpret a p-value of <0.05?
It does not prove that the null hypothesis is false, but it can strongly suggest that the null hypothesis is false. It is not possible to prove that a null hypothesis is either true or false, just that something strongly suggest.
