# Introduction to Quantitative Methods

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• Quantitative methods
• Probability
• Venn diagrams
• Not A: P(A) + P(Not A) = 1
• Not (A OR B): not mutually exclusive events P(A OR B) = P(A) + P(B) - P(A AND B)
• Not (A OR B): mutually exclusive events P(A OR B) = P(A) + P(B)
• Concepts
• Independent
• When P(A)=P(A|B) events A and B are independent
• Mutually exclusive
• No outcomes should overlap
• Dependent
• When P(A) doesn't equal P(A|B)
• Calculating
• Conditional probabilities
• P(A|B) the probability of Event A given that Event B is known to have occurred
• P(A AND B)/ P(B)
• Joint probabilities
• Dependent
• Do the P(A) then the P(B|A)
• P(A AND B) = P(A) P(B|A) (multiply the values
• Expected value
• Number of trials multiplied by the probability of success
• Variance
• Number of trials multiplied by the probability of success and failure
• Combinations
• Binominal probabilities
• Probabilities using normal distribution
• Probability
• Number of outcomes in which even occurs/total number of outcomes
• Decision trees
• Any event is composed of one or more of the terminal node outcomes
• Random variables
• Continuous
• Can take any value within a range
• Discrete
• Introduction to binominal distribution and appropriate notation
• The outcome of each trial is independent
• n identical 'trials'
• Each trial has the same probability of success
• n is the number of objects and r is how many you chose
• ! means factorial
• Shift divide function
• First number is the letters you want to choose
• Second number is all of the letters
• It tells us the number of contributions
• Choosing an appropriate distribution to model random variables
• Binominal
• When n becomes large, the binominal probabilities can be approximated by the normal distribution with the same mean n, p and variance  [np(1-p)]
• Normal
• This distribution is characterised as being bell-shaped and symmetric
• Notation: random variable x has a normal distribution with a mean of y and variance z
• N(4,2) normal distribution with mean 4 and variance 2
• Revise Chebychev's theorem
• “A proportion of at least  1-1/k^2 of a probability distribution lie within k standard deviations of the mean, regardless of the distribution of the data.”
• Standardising non-standard distributions
• For normal random variables, the number of s.d's away from the mean (z-score) does have a standard normal distribution
• To calculate the z-score for any normally distributed variable x-Mu/random variance
• Mu represents the population mean
• Where Z has a N(0,1) distribution
• Transform > compute variable
• Select "CDF & Noncentral CDF" or "Inverse DF" then Cdf.normal or Idf.Normal
• Using probability density functions to represent probabilities associated with continuous random variables
• Statistical inference
• Sampling methods
• The Central Limit Theorem
• The total (or mean) of a large number of independent random variables with the same probability distribution has a normal distribution
• Calculating and interpreting a confidence interval
• Statistical testing
• Introduction
• The four-step process
• Writing null and alternative hypotheses
• Finding and interpreting p-values
• One sample t-tests
• Theory and execution in SPSS
• Interpretation and communication of results
• Independent sample t-tests
• Independent sample t-tests
• Levene's test
• Interpretation and communication of results
• Related samples
• Theory and execution in SPSS