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Statistics > Sampling And Distributions > Flashcards

Sampling And Distributions Flashcards

1
Q

Advantages of sampling

A

Cheap and quick

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2
Q

Disadvantages of sampling

A

Can be biased and unaccurate

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3
Q

Advantages of a census

A

Gives a completely accurate result

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4
Q

Disadvantages of a census

A

Time consuming and expensive

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5
Q

What is a sampling frame?

A

A list of the people in a sample

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6
Q

What is a sampling unit?

A

Each individual thing in the population

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7
Q

What is the population mean?

A

It is a parameter

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8
Q

What is the sample mean?

A

It is a statistic

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9
Q

How does a random sample eliminate bias?

A

Everyone has an equal chance of being chosen
All subsets of population size n must be possible
Every possible sample of size n must be equally likely to occur

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10
Q

Simple random sampling

A

Each thing has an equal chance of being selected
Each element of the sampling frame is assigned a number
Advantages:
Free if biased
Easy to use
Everyone has an equal chance of being chosen
Disadvantages:
Not representative
Not suitable for large populations

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11
Q

Systematic sampling

A

Required elements are chosen at regular intervals in an ordered list e.g. take every Kth element where (image)
Advantages:
Simple
Suitable for large samples
Disadvantages:
Relies on a sampling frame to be randomly ordered

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12
Q

Stratified sampling

A

Population is divided into strata and a simple random sample is carried out in each group
Sample proportion:
(Image)
Sampled from each strata
Used when sample is large and population naturally divides into groups
Advantages:
Can give more accurate estimates
Reflects the population structure
Disadvantages:
Problems the same as any simple random sample
If strata are not clearly defined they may overlap

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13
Q

Disproportionate stratified sampling

A

After the population has been divided into strata sometimes, the sample size of each sample may be chosen to be equal regardless of the strata propertion

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14
Q

Quota sampling

A

Population is divided into strata, the sample size for the strata can be found using known proportions like stratified or an attempt can be made to estimate them
An opportunity sample is taken to ‘fill’ the required quota
Once filled ignore any others
Advantages:
A chance for proportional representation
Fairly easy and cheap
Disadvantages:
Non random sample isn’t taken to generate each quota sample
As it is non random it can be easily biased
Could take a long time to fill each quota if samples taken are for any quota already filled

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15
Q

Opportunity sample

A

Ask people walking past to take part
Advantages:
Quick, cheap and easy
Disadvantages:
Can be very biased due to personal preference
People may not want to take part

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16
Q

Cluster sampling

A

Split the population into clusters
Number each from 1 - n
Use a RNG to select a sample of clusters and choose the corresponding clusters
Number all subjects in cluster from 1 - n
Use a RNG to select a small sample from the cluster and choose the corresponding subject
Repeat for all clusters
Advantages:
Non random with an element of randomness to aid against bias
If an equivalent simple random sample of a given population requires lots of travel/work
This provides an easier time efficient way to sample
Disadvantages:
No random, be aware of bias
Samples taken may not be representative of the whole population

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17
Q

Snowball sampling

A

Primary data sources are found and then they are asked to identify other samples that are relevant for the sample e.g. a drug user can be asked to identify another
Advantages:
Useful when samples possess rare/difficult characteristics and hence cannot be easily obtained
Disadvantages:
Non random and is only accurate as the referrals from the initial samples
Could be time consuming

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18
Q

Judgmental sampling
(Used when a quick sample is required)

A

The researchers own judgement is used to select the sample for example a snap election is called and a tv political commentator needs a quick sample of opinions from the general public
Advantages:
Can be quick and convenient
Can be cheap to do
Disadvantages:
Researcher is using their own judgement to generate a sample therefore there is a high chance of bias

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19
Q

How to estimate the mode from a histogram?

A
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20
Q

Probability notation

A
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21
Q

A random variable has three things associated with it…

A

1) the outcomes
2) the probability function
3) parameters - values we cannot control, but do not change across different outcomes

22
Q

Advantages of probability function

A

Can have a rule/expression based on the outcome
Particularly for continuous random variables, it would be impossible to list the probability for every outcome

23
Q

Advantages of distribution

A

The probability for each outcome is more explicit

24
Q

Cumulative distribution function (CDF)

A

The CDF is F

25
Q

Expected value E(X)

A

It represents the mean outcome we would expect if we were to do the experiment multiple times
It is a population paramtere

26
Q

The mean of the squares

A
27
Q

Population variance Var(X)

A

Mean of the squares - square of the mean

28
Q

Uniform/rectangular distribution notation

A
29
Q

Probability density function (p.d.f)

A
30
Q

Area of rectangular distribution

A
31
Q

Height of rectangular distribution

A
32
Q

E(X) for rectangular distribution

A
33
Q

Var(X) for rectangular distribution

A
34
Q

E(X^2) for rectangular distribution

A
35
Q

Quartiles in a rectangular distribution

A
36
Q

Mode in a continuous distribution

A

The mode is the value where the pdf is greatest (the peak or turning point)

37
Q

The conditions for binomial distribution

A

Fixed number of trials
Probability of success and failure must be constant
All events must be independent
Fixed number of outcomes (success and failure)

38
Q

The Bernoulli distribution

A

The most simple distribution
Models an experiment with two outcomes, success or failure
A sequence of Bernoulli trials is a Bernoulli process
Binomial distribution is an example of the Bernoulli distribution

39
Q

Binomial distribution

A
40
Q

The binomial formula

A
41
Q

The binomial distribution formula

A
42
Q

The binomial coefficient

A
43
Q

Comment on the suitability of using a binomial distribution

A

Consider the 4 conditions for binomial
Is it suitable?

44
Q

Greater than probabilities for binomial CD

A
45
Q

Expected value for binomial

A

Np
Number of trials x probability

46
Q

Variance for binomial

A

Np (1 - p)
Number of trials x probability (1 - probability)

47
Q

Structuring a hypothesis test

A

A hypothesis is a statement about a given population and its parameters
From a given situation in your enquiry, the ‘norm’ is known as the null hypothesis. This is a statement that what is believed about the null hypothesis is true
The null hypothesis is denoted by H0

48
Q

Stages of a hypothesis test

A

1) state the null hypothesis
2) state the alternative hypothesis
3) make your assumptions
4) prove/disprove your hypothesis
5) conclude

49
Q

State the null hypothesis

A

H0: p =

50
Q

State the alternative hypothesis

A

An alternative hypothesis is denoted H1 and will be either
One tail (P> )
Or
Two tail (P doesn’t equal )

51
Q

Make your assumptions

A

After you have stated your hypothesis you must make a statement that you are assuming the null hypothesis

52
Q

Proving / disproving your hypothesis

A

You are looking to not reject or reject the null hypothesis
We are aiming to find out the chance of the outcomes occurring

Statistics (3 decks)

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