## data_a: forecast_value, data_b: pass_value
def Welch_ttest(data_a, data_b, alpha):
    mean_a, mean_b = np.mean(data_a), np.mean(data_b)
    # squared standard error
    se_a, se_b = stats.tstd(data_a)**2.0/len(data_a), stats.tstd(data_b)**2.0/len(data_b)
    #v
    v_a, v_b = len(data_a)-1, len(data_b)-1
    # assume unequal variance
    t_stat, p_2tail = ttest_ind(data_a, data_b, equal_var=False)
    # degree of freedom
    degreeF = ( (se_a+se_b)**2.0 )/     ( ((se_a**2.0)/v_a) + ((se_b**2.0)/v_b) )
    # critical value
    cv = t.ppf(1.0-alpha, degreeF)
    # calculate the p-value,one sided
    p = (1.0-t.cdf(abs(t_stat), degreeF)) 
    # h0: mean_a-mean_b<=0 ;  h1: mean_a-mean_b>0

    if t_stat > cv and mean_a > mean_b:
        ## trend
        return 1
    else:
        ## not trend
        return 0