Methods for Testing Normality of Hydrologic Time Series - Hydrologic Time Series Analysis: Theory and Practice - page 39

data points is displayed by the slope of the graph or line. Similar to the
'ranked data plot', a large amount of data points result in a flat slope, i.e., the
graph rises slowly, while a small amount of data points result in a large slope,
i.e., the graph rises quickly. A 'quantile plot' can also be used to check skewness
or symmetry of the data points. A 'quantile plot' of the right-skewed data is
steeper at the top right than at the bottom left, as shown in Fig. 3.6. A quantile
plot of the left-skewed data increases sharply near the bottom left of the
graph. If the data are symmetric about the centre point (mean or median), the
top portion of the graph will stretch to the upper right corner in the same way
the bottom portion of the graph stretches to the lower left, creating an S-shape
similar to the ranked data plot.
3.1.6 Normal Probability Plot
There are two types of quantile-quantile plots ( q - q plots). One is an empirical
quantile-quantile plot, which involves plotting the quantiles of two hydrologic
time series against each other. The other type of a quantile-quantile plot
involves plotting the quantiles of a time series against the quantiles of a
particular probability distribution. This is a technique to determine if the time
series data were generated by the theoretical distribution (USEPA, 2006). The
most common of these plots for hydrologic time series data is the 'normal
probability plot', which is also known as a 'normal q - q plot'. However, the
discussion about the 'normal probability plot' holds good for other q - q plots
as well. Being a graphical method, the normal probability plot is a visual
technique to roughly determine how well the time series data is modelled by
a normal distribution (Dixon and Massey Jr., 1983).
A 'normal probability plot' is the plot of the quantiles of a hydrologic
dataset against the quantiles of the standard normal distribution using normal
probability graph paper (Fig. 3.7). This can be accomplished by plotting the
sample quantiles against standard normal quantiles, or by plotting the sample
Fig. 3.7. Normal probability plot.