I'm trying to perform a Mann-Kendall Test of some data. I'm using the code in the following link (https://github.com/mps9506/Mann-Kendall-Trend/blob/master/mk_test.py) modified a little bit bellow for the result to be in an array and it only gives back a p-value (p) and a tau value (z).
def mk_test(x, alpha=0.05): """ This function is derived from code originally posted by Sat Kumar Tomer (firstname.lastname@example.org) See also: http://vsp.pnnl.gov/help/Vsample/Design_Trend_Mann_Kendall.htm The purpose of the Mann-Kendall (MK) test (Mann 1945, Kendall 1975, Gilbert 1987) is to statistically assess if there is a monotonic upward or downward trend of the variable of interest over time. A monotonic upward (downward) trend means that the variable consistently increases (decreases) through time, but the trend may or may not be linear. The MK test can be used in place of a parametric linear regression analysis, which can be used to test if the slope of the estimated linear regression line is different from zero. The regression analysis requires that the residuals from the fitted regression line be normally distributed; an assumption not required by the MK test, that is, the MK test is a non-parametric (distribution-free) test. Hirsch, Slack and Smith (1982, page 107) indicate that the MK test is best viewed as an exploratory analysis and is most appropriately used to identify stations where changes are significant or of large magnitude and to quantify these findings. Input: x: a vector of data alpha: significance level (0.05 default) Output: trend: tells the trend (increasing, decreasing or no trend) h: True (if trend is present) or False (if trend is absence) p: p value of the significance test z: normalized test statistics` Examples -------- >>> x = np.random.rand(100) >>> trend,h,p,z = mk_test(x,0.05) """ n = len(x) # calculate S s = 0 for k in range(n-1): for j in range(k+1, n): s += np.sign(x[j] - x[k]) # calculate the unique data unique_x = np.unique(x) g = len(unique_x) # calculate the var(s) if n == g: # there is no tie var_s = (n*(n-1)*(2*n+5))/18 else: # there are some ties in data tp = np.zeros(unique_x.shape) for i in range(len(unique_x)): tp[i] = sum(x == unique_x[i]) var_s = (n*(n-1)*(2*n+5) - np.sum(tp*(tp-1)*(2*tp+5)))/18 if s > 0: z = (s - 1)/np.sqrt(var_s) #result = (s - 1)/np.sqrt(var_s) elif s == 0: z = 0 #result = 0 elif s < 0: z = (s + 1)/np.sqrt(var_s) #result = (s + 1)/np.sqrt(var_s) # calculate the p_value p = 2*(1-norm.cdf(abs(z))) # two tail test result= np.append(p,z) h = abs(z) > norm.ppf(1-alpha/2) return np.array(result)
I am then using the following code to perform the test.
out = np.empty((0)) for i in range(145): for j in range(192): out1 = mk_test(yrmax[:,i,j], alpha=0.05) out = np.append(out, out1, axis=0)
I think something is going wrong somewhere while performing the test because I would expect to get z values between -1 and 1, but I'm getting back some values that are greater than 1. Is the coding going wrong or am I misunderstanding what z is and it's not actually tau and hence why I'm getting values I'm not expecting?