textbook on statistics for details.) Example: Because a anthropogenic intervention had altered the Viege watershed in 1964, the peak discharge series is separated into two samples: x , x,…., x (peak discharge 1922 to 1963), and y , y,…., y (peak discharge 1964 to 1996). : (97.5%) = 1.72. Given that 1.31 is less than 1.97, we cannot reject the null hypothesis that the variances are equal and we can apply the Student test for the two samples. Since we know what kind of effects result from dam construction, we would expect to see a significant reduction in discharge in the second sample, which leads us to formulate the alternative assumption to test the homogeneity of the samples starting

doi:10.1201/b10426-71

Chapter

textbook on statistics for details.) Example: Because a anthropogenic intervention had altered the Viege watershed in 1964, the peak discharge series is separated into two samples: x , x,…., x (peak discharge 1922 to 1963), and y , y,…., y (peak discharge 1964 to 1996).

Chapter

ABSTRACT

Example: We want to know if the series of peak discharges discussed above follows a normal distribution. Let Z be the random variable representing the discharges. We can have the following null and alternative hypotheses:

(9.16)

The two parameters of the normal distribution are estimated by the sample average and the sample variance, respectively. This gives us:

Then we proceed to divide the observations into 12 classes – this is an arbitrary choice - and after calculating the observed and theoretical frequencies, we finally

obtain = 14.12.