# Introduction to Quantitative Methods

- Created by: _lucyallinson
- Created on: 09-10-16 17:32

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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)

- Independent
- 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

- Conditional probabilities
- 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

- Continuous
- 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

- Binominal
- 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

- To calculate the z-score for any normally distributed variable x-Mu/random variance
- Transform > compute variable
- Select "CDF & Noncentral CDF" or "Inverse DF" then Cdf.normal or Idf.Normal

- For normal random variables, the number of s.d's away from the mean (z-score) does have a standard normal distribution
- Using probability density functions to represent probabilities associated with continuous random variables

- Venn diagrams
- 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

- Interpretation and communication of results

- Theory and execution in SPSS
- Independent sample t-tests
- Levene's test
- Interpretation and communication of results

- Interpretation and communication of results
- Related samples
- Theory and execution in SPSS

- Theory and execution in SPSS

- Probability

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