AS Statistics

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which distribution can be approximated as another?

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23 Terms

1

which distribution can be approximated as another?

binomial as Poisson

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2

when does this approximation work, and what is λ?

when p gets smaller, and n gets bigger and λ= E(x)/ the mean

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3

what characterises a Poisson distribution?

the mean and variance are equal

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4

how to calculate variance

mean of the squares-square of the mean

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5

E(aX+b)=

aE(X)+b

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6

Var(aX+b)=

a² Var(X)

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7

4 conditions that must be met for binomial distribution to work

  • 2 mutually exclusive outcomes

  • fixed number of trials

  • each event is independent of the one before

  • probability of success is constant

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8

4 conditions that must be met for Poisson distribution to work

  • event occurs randomly in space/time

  • events cannot occur simultaneously

  • each event is independent of the one before

  • the mean remains constant

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9

if X and Y are Poisson distributions, how to calculate X+Y?

X+Y∼Po(sum of means)

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10

how to calculate: P(x≥n) must be <p

P(x≤n-1) must be >(1-p)

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11

two hypotheses needed for hypothesis testing

H₀, the null hypothesis and H₁, the alternative hypothesis

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12

5 steps in a hypothesis testing question

  • let variable X= ?

  • state H₀ and H₁

  • state distribution and find probability

  • compare probability to significance level

  • state conclusion in context

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13

formula for Χ²

∑(Oᵢ²/Eᵢ) -N (where N is number of trials)

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14

how to generally calculate degrees of freedom

number of cells (after combining) - number of constraints

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15

what counts as a constraint

estimating a parameter or number of trials

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16

what does ν represent

number of degrees of freedom

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17

what does χ²₃ represent

the family of χ² distributions with 3 degrees of freedom

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18

how to combine the table whilst using a Χ² test

no expected value is allowed to be <5

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19

how to estimate p for a binomial distribution

p= (number of successes)/(number of attempts) or

p= Σ(r x fᵣ)/(N x n)

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20

how to estimate λ for a Poisson distribution

calculate it as if it were the mean of a frequency table

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21

how to do a Χ² test on observed data

calculate p or λ, then use this to generate expected frequencies, then conduct the test as normal

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22

how to calculate expected values for each box in a contingency table

Eᵢ= (row total x column total)/ grand total

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23

how to calculate ν for a contingency table

ν = (no of rows-1)(no of columns-1)

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