All S2 Definitions + Explanations
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JPDC99
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Thought this might be useful:
*Feel Free to add any I might have missed out!
S2 DEFINITIONS AND EXPLANATIONS
4 Conditions for Binomial:
In Poisson MEAN=VARIANCE
Poisson is a suitable model if events occur:
F(x) = integral of f(t) dt between “-infinity” and “x”
Mode = highest p.d.f point
Median = F(Q2) = 0.5
LQ = F(Q1) = 0.25
UQ = F(Q3) = 0.75
Uniform distribution is mainly used as:
When Uniform is not the best distribution to use:
Population - A collection of individual people or items
Census - Investigation where information is to be obtained from all members of the population
Pros of Census
Every member of the population is used
Unbiased
Accurate answer as it considers whole pop
Cons of Census
Costly
Time consuming
Hard to ensure the whole population is surveyed
A sample is used when - there is a large population where a census is impractical
Sample - A collection of individuals or items
Sampling-Unit - An individual member or element of the population or sampling frame
Sampling-Frame - A list of all sampling units or all population, - a list such as a school register
Sample Survey - Investigation using surplus
Pros of Sampling
Cheaper than Census
Quicker than Census
Useful where the testing of items results in their destruction - smashing lightbulbs
Cons of Sampling
Can be accidentally Bias
Uncertainty of sample choice could create a set of results that is not representative of the whole population
Statistic - A Quantity calculates solely from observations in a sample. It does not include any unknown parameters.
Sampling Distribution - All combinations of outcomes + their probabilities
Hypothesis Test - A mathematical procedure to examine a value of a population parameter proposed by the null hypothesis H0, compared to an alternative hypothesis H1
Test Statistic - Evidence that has come from a sample
Critical Region - The range of values of a test statistic that would lead you to reject H0
Critical Values - The boundary values of a critical region
One-Tailed Test - Looks either for an increase or for a decrease in a parameter, and has a single critical value
Two-Tailed Test - Looks for both an increase and a decrease in a parameter, and has 2 critical values
Actual Significance Level - The probability of rejecting H0 (Probability of X being less than or equal to lower critical value + Probability of X being greater than or equal to upper critical value)
*Feel Free to add any I might have missed out!
S2 DEFINITIONS AND EXPLANATIONS
4 Conditions for Binomial:
- Fixed number of trials, n
- Each Trial should be a success or failure
- Trials are independent of each other
- Probability of success is fixed
In Poisson MEAN=VARIANCE
Poisson is a suitable model if events occur:
- Singly in space or time
- Independently of each other
- At a constant rate
F(x) = integral of f(t) dt between “-infinity” and “x”
Mode = highest p.d.f point
Median = F(Q2) = 0.5
LQ = F(Q1) = 0.25
UQ = F(Q3) = 0.75
Uniform distribution is mainly used as:
- A model for errors
When Uniform is not the best distribution to use:
- likely to have higher prob. dens. near median and
- some values more than 25 m away from the median
Population - A collection of individual people or items
- Can be in/finite
Census - Investigation where information is to be obtained from all members of the population
Pros of Census
Every member of the population is used
Unbiased
Accurate answer as it considers whole pop
Cons of Census
Costly
Time consuming
Hard to ensure the whole population is surveyed
A sample is used when - there is a large population where a census is impractical
Sample - A collection of individuals or items
Sampling-Unit - An individual member or element of the population or sampling frame
Sampling-Frame - A list of all sampling units or all population, - a list such as a school register
Sample Survey - Investigation using surplus
Pros of Sampling
Cheaper than Census
Quicker than Census
Useful where the testing of items results in their destruction - smashing lightbulbs
Cons of Sampling
Can be accidentally Bias
Uncertainty of sample choice could create a set of results that is not representative of the whole population
Statistic - A Quantity calculates solely from observations in a sample. It does not include any unknown parameters.
Sampling Distribution - All combinations of outcomes + their probabilities
Hypothesis Test - A mathematical procedure to examine a value of a population parameter proposed by the null hypothesis H0, compared to an alternative hypothesis H1
Test Statistic - Evidence that has come from a sample
Critical Region - The range of values of a test statistic that would lead you to reject H0
Critical Values - The boundary values of a critical region
One-Tailed Test - Looks either for an increase or for a decrease in a parameter, and has a single critical value
Two-Tailed Test - Looks for both an increase and a decrease in a parameter, and has 2 critical values
Actual Significance Level - The probability of rejecting H0 (Probability of X being less than or equal to lower critical value + Probability of X being greater than or equal to upper critical value)
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poo man
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Antony231001
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nerdnerdvirgin
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