AGRI 2400 The Normal Distribution

Normal (Gaussian) Distribution

• much of the data that individuals studying life sciences collect is measured on ratio, interval, or ordinal scales

  • think of variables where it would make sense to calculate a mean for several indiv. observations

• variables measured on these scales often have a consistent, predictable, shape

Normal Distribution Requires:

• only two parameters (summary statistics) to describe it

  • mean

  • variance/standard deviation

    • either works since they are related

  • 95% of values in a normally distributed pop. will be within ± 1.96 standard deviated of the mean

Z Statistic

Z=Xi/ standard deviation

• for a normally distributed population, the difference between any value and the mean, divided by the SD gives a ratio called the Z statistic (normally distributed but with a mean of 0 and SD of 10

  • this is called a standard normal distribution
    

What Does the Z Statistic Tell us?

• (Z score) is the number of standard deviations an observed value is from the mean

• if calculated Z statistic is greater than +1.96 or less than -1.96, then the probability of observing that value from an individual in the population is less than 5%

Other Distributions

• the distributions of some variables may resemble a normal distribution (i.e. bell curve), but differ in some way

  • low degree of peakedness = platykurtic distribution , kurtosis <0

  • normal distribution = mesokurtic distribution, kurtosis = 0

  • high degree of peakedness = leptokurtic distribution, kurtosis >0