Maths stats Flashcards by Mark Kennedy

What is a census

Measures or observes every member

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What is a sample

Selection of observation taken from subset of pop used to find out about whole pop

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Advantages of census

Results should be completely accurate

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Disadvantages of census

Time consuming, expensive, cannot be used when testing destroys process and hard to process large quantity of data

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Advantages of sample

Less time consuming and cheaper, fewer people have to respond, less data needs to be processed

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What is random sampling

Each member of pop has equal chance of being selected

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What is simple random sampling

Everything has equal chance of being selected

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Advantages of simple random sampling

Free of bias, easy and cheap for small samples and pops and each sampling unit has known and equal chance of selectionDi

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sadvantages of simple random sampling

Sampling frame needed and not suitable for large samples and populations

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What is systematic sampling

The required elements are chosen at regular intervals from and ordered list

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Advantages of systematic sampling

Simple and quick to use, suitable for large samples and large populations

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Disadvantages of systematic sampling

A sampling frame is needed and bias introduced if sampling frame is needed, Bias introduced if sampling frame is not random

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What is stratified sampling

The population is divided into mutually exclusive strata and a random sample is taken from each strata in proportion to size of strata

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Equation for stratified sampling

(number in stratum x overall sample size) / number in population

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Advantages of stratified sampling

Sample accurately reflects population structure, proportional representation of group within population

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DIsadvantages of stratified sampling

Population must be clearly classified into distinct strata, same disadvantages as simple random within each strata

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Two types of non random sampling

Quota sampling and opportunity sampling

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What is quota sampling

An interviewer selects a sample that reflects the charecteristics of the whole opulation

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Advantages of quote sampling

Allows small sample to still be representational of whole pop, so sampling frame, quick and cheap and easy comparison between different groups within a population

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Disadvantages of quota sampling

Non random sampling can introduce bias, population must be divided into groups which can be costly or innacurate, increasing scope of study increases number of groups which adds time and money, non responses not recorded

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What is opportunity sampling

Sample is taken from people who are available at the time and who fits criteriaA

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Advantages of opportunity sampling

Easy and inexpensive

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Disadvantages of opportuinity sampling

Unlikely to provide a representitative result and highly dependant on researches

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Criteria for a binomial dist

The number of observations n is fixed.
Each observation is independent.
Each observation represents one of two outcomes (“success” or “failure”).

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To make binomial suitable what would be ideal

LARGER N

Conditions for normal aproximation of binomial

Large n and p close to 0.5

State one disadvantage of using quota sampling compared with simple random sampling.

nOT RANDOM SO CANNOT USE RELIABLY FOR INFERENCES

Mutually exclusive

Both cannot happen at once

P(A or B) mutulaly excluvive

P(A) + P(B)

Independent P(A GIVEN B )

P(A)

Reason to include outliers

It is a piece of data and we should include all pieces of data

Reasons to not include outliers

It is extreme and could unduly influence anaylsis or could be a mistake

Do you include NA at all when calculating mean

State the assumption involved with using class midpoints to calculate an estimate of a mean from a grouped frequency table.

Assumes values are uniformly distributed within the classes

Why could random sampling not be used

It is not possible to have a sampling frame

Conditions for normal dist

Variable has to be continuous

P(x=5) for continuous

0 as continous

+- standard deviation for normal

Point of inflection

Numbers not in table

3sf

Numbers in talbe

4 dp

For normal mean=

Mode = median

x-mew / o

Standard deviation binomial

np(1-p) root that

Why would oyu have to times p vbalue by 2

For normal dist, it is ewual on both sides

For cumalitive frequenct what value do you plot

Top value

Histogram height

Work out area scale factor in relation to frequency (double check this )

What is extrapolating

Estimate outside range (unreliable )

What is interpolation

Estimate inside range

What is the explanatory variables

The one thrat explains the other and that causes change

What does close to 1 mean

Positive correlation

Normal aprox

Make binomial and then make normal from that i think

list

aDD 1/2 FOR MEDIAN

Conditions for poisson aprox of binomial

Large n small p np <10

variance of (3x-1)

square 3

variance poisson

Mean or np(1-p)

Conditions for poisson

Events must occur independently, events must occur singly, events cannot occur at same time, events occur at constant

H0 for chi squared test

No difference between theoretical frequency and observed frequency

Binomial need thing

Need to either succeed or fail

What is area

Significance level

DOR

(rows-1)(columns-1)

Row time column over grand

What is needed for central limit theorum

Large sample size unless data is already normally distributed

mean for nb

r/p

variacne for nb

r(1-p)/p squared

What is a type 1 erro

Actual significance error (chance they are lucky)

What is type 2 error

Incorrectly accept h0 p(not critical region given h1 i true)

What will reducing significane level (type 1 error) do

Increase type 2 error

What does increasing n do to erorrs

Reduces type 2

What is size

Type 1 errorh

What is power

1-type 2 error

size

Rejecting h0 given h0 is true

Power

rejecting h0 given h1 is true

variance

Dont divide by n if its a discrete uniform distribution

If chi squared greater than critical value

Reject that it is a fitable modle

g(1) always =

Remember you can rearrange var formula for e(x)squared

What happens if proportion of defective things stays same and dof stays same but proportions can be ree allocated

No change in test statistic

) Explain the relevance of the Central Limit Theorem in part (a)

CLT applies since the sample size is large B1 3.5b CLT states that the sample mean/ S is (approximately) normally distributed

formula for chi squared

(o-e)squared/E

E in 2 wasy

Row total times column total / grand total

Dof 2 way

(r-1)(c-1)