Topic 4 - Normal model Flashcards
1
Q
LO
A
- LO4 Apply the Normal approximation to data, with consideration of measurement error.
2
Q
The normal curve
A
- A probability density function (pdf) f(x)
- A PDF is a function which describes the chance assiciated with a continuous variable x, for all its possible values x
3
Q
2 Types of curve
A
Standard normal curve
General normal curve
4
Q
Standard and general normal curves
A
Standard (z) has mean 0 and SD1 = Z ~ N(0,1)
General (x) has any mean and any SD
= X ~ N(μ, σ^2)
5
Q
Area under the curve (CDF)
A
Cumulative distribution function
- The area under the normal curve ist eh chance of those particular values of x occuring
6
Q
The normal model on a histogram
A
- Whole histogram = 100%
- Normal curve ontop of a histogram is an approximation of the histogram
- Allows us to easily see the mean and symmetry and create predictions
7
Q
Special properties to the normal curve
A
- All noraml curves satisfy the 68,95,99.7% rule
- General Normal can be rescaled into the standard normal (only need to changet he x-axis to make it the same)
8
Q
Finding the area under the curve
A
- 68,95,99.7% rule is meh, only gives approximation
- Using R is best, Uses pnorm(), given the threshold, mean & SD
9
Q
To find percentiles on a normal curve
A
Using R:
qnorm() function
- calculates the threshold given a certain area
10
Q
Measurement error
A
- individual measurement often differes from exact value
- Individual measurement = exact value + chance error + bias
11
Q
Chance error
A
- Might get differnet results each measurement
- Calculate SD and replicate with same conditions inorder to estimate chance error
12
Q
Outliers
A
- Extreme percentiles are expected to occur in large series of data
- Commonly seen as data outside of 3 SD of the mean
- Following a normal curve, should only be 0.3% of values.
