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What does parsimony dictate?
 We should always choose the simplest possible model
 In psychology, the evidence must establish a need for the full model beyond reasonable doubt

What must be considered before choosing a full model?
 Does the difference between means reflect a genuine signal in the data?
 Is the apparent signal merely a result of sampling error or noise?

How can uncertainty be quantified?
 Uncertainty can never be eliminated, and data will always be noisy
 Probability theory is employed

What is the Quincunx? (bean machine)
 Invented by Frances Galton
 Serves as a manual model of residuals
 Balls are dropped into the top through a funnel, strike one of the many pins and fall into one of the buckets at the bottom

Define: Probability
The number of equally probable ways that an event can occur, divided by the total number of equally probable outcomes

How is probability calculated using the multiplication rule?
 Events are assumed to be independent
 Probability=P
 P(A+B)=P(A)xP(B)

How is probability calculated using the addition rule?
P(A or B)=P(A)+P(B)

What denotes the number of trials, with regards to binomial distribution?
n

What does P refer to, with regards to binomial distribution?
 The probability of one of the two possible outcomes occurring
 E.g (Head or tails)

What does r denote, with regards to binomial distribution?
An index of the number of times the specified number of outcomes occurs

Write an equation for the binomial distribution
 This need not be memorised as it is built into minitab

What is the binomial coefficient?


What happens as the number of observations increases?
 The observed proportion provides an increasingly accurate estimate of the probability
 This is known as the law of large numbers

What effects does increasing the sample size have?
The probability that a sample size will be close to the parameter value increases

How can probability be interpreted?
Long run relative frequency or population proportion

What is the formula for population proportion?

What happens as the number of trials increases?
The relative frequency approaches the population (true) value

How can a sample be said to be random?
Each element has an equal chance of being selected

What happens as the rows on a quincox become infinite in number?
 The outcome variable goes from being discrete to being continuous
 The binomial distribution tends towards normality

What claim is made by the central limit theorem?
A variable that is the net result of adding together a large number of contributing independent outcomes will have an approximately normal distribution

Why is the central limit theorem named as such?
 It states what will happen in the limit as the number of outcomes becomes infinite
 It is central as it is fundamental

Other than variables that come about due to addition, which other variables fall under the central limit theorem?
 Attributes that are influenced by a large number of independent factors that add to determine the final measurement
 E.g: Height
 This applies to other psychological measurements too

How are continuous variables different than discrete ones?
They have an unlimited number of possible values

Why is it inappropriate to ask for the probability associated with a single continuous value?
With continuous variables, statements of probabilities are always about ranges of values

For continuous variables, how are probabilities represented?
 Areas under the curve
 This means that the height of the distribution at any point is not the probability, but in fact the probability density

