S2 Definitions + Conditions Flashcards
Actual Significance Level
The actual significance level of a test is the probability of a value falling in the critical region and hence incorrectly rejecting H0 when it is in fact true.
Census
An investigation in which every member of the population is investigated
Critical Region
The critical region is the range of values of a test statistic that would lead you to reject the null hypothesis, H0
Hypothesis Test
A hypothesis test is a mathematical procedure to examine a value of a population parameter proposed by the null hypothesis, H0, compared to the alternative hypothesis H1.
Population
A population is a collection of all items
Sampling Distribution (of a Statistic)
The probability distribution of the statistic from all possible samples.
This is the set of all possible values of the statistic together with their individual probabilities;
This is sometimes better described by giving the relevant probability density function
Sampling Frame
A list of all sampling units
Sampling Units
An individual member of a population which could be included in a sample
Statistic
A random variable that is a function of the sample which is calculated solely from the observations in the sample and contains no unknown parameters.
Finite Population
A population in which each individual can be given a number
Infinite Population
A population in which it is impossible to number each member
Sample
A selection of individual members or items from a population.
A selection of sampling units from the sampling frame.
Simple Random Sample
A sample taken so that every possible sampling unit has an equal chance of being selected.
Sample Survey
An investigation using a sample.
Advantages of taking a census
> Every member of the population is used.
> It is unbiased.
> It gives an accurate answer.
Disadvantages of taking a census
> It takes a long time
> It is costly
> It is often difficult to ensure that the whole population is surveyed
Advantages of sampling
> Sample will be representative if the population large and well mixed.
> Usually cheaper than taking a census
> Essential if testing results in destruction of sampling units (e.g. life of a light bulb, etc.).
> Data usually more readily available than in a census.
Disadvantages of sampling
> Uncertainty, due to the natural variation – two samples are unlikely to give the same result.
> Uncertainty due to bias which occurs when taking a sample which prevents it from being truly representative of the population from which it is taken.
> Bias can occur if you sample from an incomplete sampling frame, or if you get responses only from people that have a particular interest in the topic being studied.
> Bias can occur if the person taking the sample allows their personal feelings to influence their choice.
Note: Bias can be removed by increasing the size of the sample.
Null Hypothesis, H0
The hypothesis that we assume to be correct unless proved otherwise.
Alternative Hypothesis, H1
The conclusion that should be made if H0 is rejected.
Test Statistic
This is the statistic (calculated from the sample) which is tested as the last part of the significance test.
In a statistical hypothesis test the evidence comes from a sample which is summarized in the form of a statistic called the test statistic.
Conditions for modelling with a binomial distribution
> A fixed number of trails
> Each trial should be a success or a failure
> The trails are independent
> The probability of success at each trial is constant
Conditions for modelling with a Poisson distribution
> Events occur singly in the space or time
> Events occur independently of each other
> Events occur at a constant rate
> Events occur randomly
Conditions for approximating binomial with Poisson
If X - B(n, p) and
> n is large
> p is small
> np < or = 10
Conditions for approximating binomial with normal
If X - B(n, p) and
> n is large
> p is close to 0.5
And/Or
> np > 10
Note: Add Comtinuity Correction and Standerdise to get value of Z.
Conditions for approximating Poisson with normal
If X - Po(Lmda.) and
> Lmda. > 10
