The normal distribution and estimation Flashcards
What is the relative frequency density graph?
Like a histogram but y axis is now density. the area under the histogram is 1. density is defined as the proportion of observations per unit interval of the x-axis
What is probability density function?
With an increasing sample size the width intervals on the histogram - with an infinite sample size the line is smooth.
The area under the curve is one
The AUC can be used to calculate the probability within a range of values of interest
What is the normal distribution?
Describes a family of bell-shaped probability functions which are totally specified by two parameters
What are the parameters of normal distribution?
mean value and standard deviation
What is variance?
SD squared
What happens with an N(0,1) distribution?
the x-axis is usually labelled z and the cumulative distribution function (c.d.f) denoted … is the probability that a value chosen at random from N(0,1) distribution is less than or equal to z
How do you assess the normality of data?
the mean and median should be approximately equal
the box plot should be symmetric
95% of the data should lie within 2SDs of the mean and almost all within 3SDs
Normal probability plot should be linear
What is the standard error?
SE = (population SD) / square root (n)
How do we estimate the population mean?
If we assume that the distribution of the sample means in Normal, then we expect 95% of the sample means to lie within 1.96 standard errors of the true population mean
What is the 95% confidence interval?
the sample mean +/- (1.96 X SE) and will contain the population mean in 95% of the samples
What can we say about a 95% confidence interval?
The limits of a 95% confidence interval contain the true population parameter with 95% confidence
What does the width of the confidence interval indicate?
how precisely we have measure the mean - the narrower the interval, the better the precision
