data analysis
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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useful graphs | comparative boxplot or comparative histogram
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useful numbers | mean and standard deviation for each group
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formula for mean | x ̅=1/N ∑_((i=1))^N▒xi
preferable for approximately normal data
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formula for standard deviation | s=√(1/(N-1) ∑_(i=1)^N▒〖(xi-x)〗^2 )
preferable for approximately normal data
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an outlier is | more than 1.5 x IQR lower than Q1
more than 1.5 x IQR higher than Q3
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linear transformation | transformation of a variable from x to xnew
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examples of linear transformation use | change of units
use of normal assumption therefore to find 'z' scores
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formula for linear transformation | xnew=a+bx
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formula for mean after linear transformation | xnew=a+bx
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formula for standard deviation after linear transformation | snew=bs
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density curves | area under the curve in any range of values is the proportion of all observations that fall within that range
for a quantitative variable = like a smoothed out histogram
describes probabilistic behaviour
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total area under a density curve equals? | 1
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normality assumption | normal curve can be used if a histogram looks like a normal curve
termed 'reasonable'
must start at 0 and end at 0
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normal quantile plot | if in a straight line, or close to it, then normal and assumption is reasonable
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68-95-99.7% rule | 68% of results will be within 1 standard deviation of the mean
95% of results will be within 2 standard deviations of the mean
99.7% of data will be within 3 standard deviations of the mean
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symbol for mean of a density curve | μ
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symbol for the standard deviation of a density curve | σ
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normal distribution short hand | X = random variable
N = normal distribution
first number in brackets = mean
second number in brackets = standard deviation
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standard normal variable | Z
corresponds to the area under the curve of the corresponding region
will always be to the left
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standard normal distribution table | to find P: Z found along x and y axis
to find Z: P found in table
ordered from smallest to largest
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reverse standard normal distribution table | P(Z<c)
c = right of Z
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X is | N(μ,σ)
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standardising transformation | Z= (X-μ)/σ
used when distribution is N(0,1)(is normal but needs proportions changed)
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Created by:
Nymphette
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