Population + Normal distribution Flashcards
Median
n+1/2 if even. Middle value if odd
Descriptive tests
Median , IQR
Statistical tests
SD, mean, SE
IQR range
75%-25% i = 0.25(n+1)
Spread
Distribution of data = IQR and range
Location
Mean and median
5 figure summary and how is it displayed
Median, Range (Max/min). Upper quartile, Lower quartile. Box and whisker plot
Histograms
Display distribution of data, large samples and appropriate bin size make this easier
u and sigma (o)
u = population mean, o = population SD
Qualitative vs Quantitative data
Qualitative = categorical Quantitative = numerical data - continuous
Normal distribution
Bell shaped curve - symmetrical equal populations located same distance away from mean
Peak located at u, width determined by sigma
Mean
Average m = x1+x2+x3/n
Standard deviation
Deviation around mean s = SD
Sum of each value ((x) - mean)2 ( squared to remove - then square rooted to remove square. Divide sum of the mean by n-1
AUC
Always =1
x=u + zo (sigma)
P depends on the value of z. For given values of z allows the visualisation of the values that differ by a set SD from the mean
1SD
P = 0.84, 2P-1 = 0.68
Cumulative probability
Value of P for a given value of X
2SD
P = 0.977, 2P-1 = 0.954
1.96 SD
0.95
UP/Lq
u +/- 0.675o
Importance of normal distribution
Arises empirically - statistical test assume/require normally distributed data.
Variables normally distributed due to biological mechanisms
Rapid screen of normality
- 5% of population below u-2o
16. 5% population below u-o
Distribution free methods
Don’t require statistical tests - Assumption of normality isn’t critical. At best hypothesis tests and cannot cope with anything but the simplest structure
Best way to assess normality
Probability plot. Large samples clustering of data around u, largest and smallest will symmetrically vary around u by o
3 SD
99.7%
Outliers effect on median and mean
Mean often skewed by outliers. Median more resistant may be a better descriptor