Statistics

• Population 


  The whole set of items that are of interest
• Census 


  Observes or measures every member of a population
• Sample


  A selection of observations taken from a subset of the population which is used to find out information about the population as a whole
• Sampling frame


  When sampling units of a population are individually named or numbered to form a list
• Qualitative data 


  Variables or data associated with non-numerical observations
• Quantitative data 


  Variables or data associated with numerical observations
• Continuous variable 


  A variable that can take any value in a given range
• Discrete variable 


  A variable that can take only specific values in a given range
• Name the types of random sampling

  1. Simple random sampling
  2. Systematic sampling
  3. Stratified sampling
• Name the types of non-random sampling

  1. Opportunity sampling
  2. Quota sampling
• Interpolation


  Making an estimate of the value of 'y' within the range of given data
• Extrapolation 


  Making an estimate of the value of 'y' outside the range of given data
• What are the conditions for which X can be modelled as a binomial distribution B(n,p)

  1. Fixed number of trials, n
  2. Two possible outcomes (success or failure)
  3. Fixed probability of success, p
  4. Trials are independent of each other
• Bivariate data

  Data which has pairs of values for two variables
• What is the multiplication rule for probability?

  P(AUB)= P(A)+P(B)-P(ANB)
• Independent events

  When one event has no effect on the other
• Mutually exclusive events

  When two events cannot occur at the same time/ have no outcome in common
• Random variable 


  A variable whose value depends on the outcome of a random event. They are denoted by capital letters e.g. X, Y, A, B
• Sample space 


  The range of values that a random variable can take
• Discrete uniform distribution 


  When there's an equal chance for all outcomes e.g. a fair-sided dice
• Null hypothesis


  H0, is the hypothesis that we assume to be correct
• Alternative hypothesis 


  H1, is the hypothesis that tells you about the parameter if your assumption is shown to be wrong
• Critical region 


  The range of values of a test statistic "X" that would lead you to reject the null hypothesis
• Critical values 


  The boundary values of the critical region
• Acceptance region 


  The area in which we accept the null hypothesis
• Under what circumstance do we reject the null hypothesis?

  If the p-value is lower than the significance level
• Under what circumstance do we accept the null hypothesis?

  If the p-value is greater than the significance level
• Actual significance level


  The probability of incorrectly rejecting the null hypothesis; calculated by adding the probabilities within the critical region
• Product moment correlation coefficient (PMCC)

  Describes the linear correlation between two variables; takes values between -1 and 1
• What are the meanings of different PMCC values?

  • r= 1; perfect positive correlation
  • r= -1; perfect negative correlation
  • r= 0; no correlation
  • r= +/-0.8 onwards; strong correlation
• What is meant by P(B|A)?

  The probability that B occurs given that A has already occurred
• For independent events what is P(A|B) and P(B|A)?

  • P(A|B) = P(A|B') = P(A)
  • P(B|A) = P(B|A') = P(B)
• Under what conditions can you approximate binomial as normal?

  • If n is large
  • If p is close to 0.5
• Characteristics of a normal distribution

  1. Parameters, μ the mean and σ2 the variance
  2. Symmetrical mean=median=mode
  3. Total area under curve= 1
  4. Points of inflection, μ +/- σ
  5. Has P(X=a)=0 for any a; true for any continuous distribution
  6. Bell-shaped curve with asymptotes at either end
• Stratified sampling

  Divide the population into homogeneous groups (strata) and randomly select samples from each group

  1. Calculate the number of people/items you need from each strata using the formula: Number sampled in stratum= number in stratum/number in population x overall sample size
  2. Allocate each person a unique number
  3. Carry out a simple random sample for each stratum
• Simple random sampling

  
  

  A sample of size "n" where every sample of size "n" has an equal chance of being selected

  1. Form a sampling frame (obtain a list of items/people)
  2. Assign each item/person a unique number
  3. Using a random number generator, select n of these
• Systematic sampling


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

  1. Form a sampling frame/ calculate how many people or items needed in the sample
  2. Allocate each person/ item a unique number
  3. Randomly select a number from a given/ calculated range (e.g. 1-10) using a random number generator
  4. Then select every 10th (for example) until the required amount of people/ items are selected
• Opportunity sampling


  Consists of taking the sample from people who are available at the time the study is carried out and who fit the criteria you are looking for
• Quota sampling


  An interviewer or researcher selects a sample that reflects the characteristics of the whole population
• Advantages of a census

  It should give a completely accurate result