Question

1. Perform a hypothesis testing using Kendall’s Tau method to check if the distribution of peak flows does not change as a function of time. Data is below please show step by step. I will rate afterwards.

Year	Peak Flow
1947	15500
1948	27400
1949	27500
1950	43000
1951	19100
1952	17600
1953	15800
1954	8600
1955	9950
1956	35400
1957	34700
1958	37000
1959	26000
1960	27000
1961	42300
1962	26300
1963	41600
1964	50500
1965	15500
1966	6710
1967	31000
1968	31700
1969	36100
1970	16900
1971	26700
1972	23700
1973	17500
1974	22900
1975	27500
1976	20300
1977	13200
1978	26600
1979	28700
1980	21600
1981	23800
1982	19500
1983	15200
1984	18400
1985	29800
1986	29200
1987	21800
1988	18500
1989	27000
1990	31300
1991	48600
1992	20400
1993	26600
1994	49500
1995	20900
1996	27600
1997	22900
1998	39600
1999	34600
2000	10600
2001	16800
2002	38300
2003	65700
2004	30800

Answer 1

We firstly look at the distribution of the peak flow:

Now we use the Kendall’s Tau method to check if the distribution of peak flows does not change as a function of time.

Here, in the image we can observe that (Prob>|z| = 0.351) which is simply the p-value of the test.

Now, the null hypothesis states that Peak flow and year are independent. Here, since p-value is greater than 0.05, thus, we fail to reject the null hypotheisis. Hence, peak flow and time are independent.