The Normal "Gaussian" Distribution Flashcards
Where does the Gaussian Distribution get its name from?
German Mathematician Carl Freidrich Gauss (1775-1855)
What two parameters define a normal distribution?
Its mean and its standard deviation
The normal distribution is an example of a probability distribution. What is this?
A probability distribution is specified mathematically and can be used to calculate the theoretical probability of different values occurring. That is why the y-axis in the plot of a normal distribution is called ‘probability’ or ‘probability density’ (which is technically the correct term to use for the y-axis).
What is the use of the standard normal curve?
Any probability distribution that is normal or can be approximated as normal can be transformed into a standard normal and we can then find out the probability density of an event occurrence to test hypotheses.
What information do standard normal tables provide?
Z-score shows the values of the standard normal distribution
P-lower - reports the proportion of the area under the curve to the left of z
P-upper - reports the proportion of the area under the curve to the right of z
How do you standardise value?
- Subtract the mean from the original values
- Divide by the standard deviation
(there are no units because the denominator and the numerator have the same units)
What is the rule of thumb when dealing with data that cannot have a negative value in asumming it is normally distributed?
The SD must be less than half the value of the mean
What statistical tests can formally assess whether a variable is normally distributed?
Shapiro-Wilk test
How can right-skewed distributions be normalised?
Logarithmic transformation
What are logarithms?
They are functions of mathematics related to orders of magnitude
What types of logs are important in the field of pharmacokinetics?
Terminal elimination half-lives are calculated by logs e.g. an elimination by a factor of 8 is equivalent to three half lives because 8 = 2^3. I.e. a log (base two) of 8 = 3.
What is a natural log?
A logarithm at base e (Euler’s number) = 2.71…
How is a natrual log denoted?
ln(x)
What is the opposite of a log?
An antilog
If log e (x) = u then the anti log would be x = e^u
Define an exponential function
Exponential function = e^u and is often written as exp(u)
Outline the log laws
log(1) = 0
log(x × y) = log(x) + log(y)
log(x / y) = log(x) − log(y)
log (x^n) = n x log(x)
Logarithms can only be applied to positive numbers (log of zero = - infinity)
How can left-skewed distributions be made to be roughly normal?
Taking the square of the original values
What does the term parametric mean?
Most statistical methods are termed parametric because they assume the observed data is drawn from a particular known probability distribution and that certain parameters are estimated e.g. mean.
When are parametric methods valid?
When the assumption that the data follows a particular distribution is valid or can be transformed to roughly follow a known distribution.
What is meant by the term non-parametric?
Data that does not have a known probability function and in cases where it is not indicated to transform the data, statistical techniques that are described as non-parametric can be employed. Generally they take no or few assumptions about the data.
Outline the formula of the normal distribution
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