All S2 Definitions + Explanations

Thought this might be useful:

*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)

very useful thanks!

Thanks Man....very useful!!