diff --git a/R/DiffCorr.R b/R/DiffCorr.R
index 95996b68e011a1be8834297889797cdf71b9bd95..a1fbae30166708861605d0c0c0f518a6f33d5a15 100644
--- a/R/DiffCorr.R
+++ b/R/DiffCorr.R
@@ -7,7 +7,7 @@
 #'correlation differences is computed with a one-sided or two-sided test for 
 #'equality of dependent correlation coefficients (Steiger, 1980; Siegert et al.,
 #'2017) using effective degrees of freedom to account for the autocorrelation of
-#'the time series (von Storch and Zwiers, 1999).
+#'the time series (Zwiers and von Storch, 1995).
 #'
 #'@param exp A named numerical array of the forecast data with at least time 
 #'  dimension. 
@@ -40,10 +40,9 @@
 #'  NA. The default value is "return.na".
 #'@param test.type A character string indicating the type of significance test. 
 #'  It can be "two-sided" (to assess whether the skill of "exp" and "ref" are 
-#'  significantly different with a z-test on Fisher z-transformed correlation 
-#'  coefficients, Hinkel et al, 1988) or "one-sided" (to assess whether the 
-#'  skill of "exp" is significantly higher than that of "ref" with the test 
-#'  described in Steiger, 1980). The default value is "two-sided".
+#'  significantly different) or "one-sided" (to assess whether the skill of  
+#'  "exp" is significantly higher than that of "ref") following Steiger (1980).
+#'  The default value is "two-sided".
 #'@param ncores An integer indicating the number of cores to use for parallel 
 #'  computation. The default value is NULL.
 #'
@@ -66,14 +65,14 @@
 #'@references 
 #'Steiger, 1980; https://content.apa.org/doi/10.1037/0033-2909.87.2.245
 #'Siegert et al., 2017; https://doi.org/10.1175/MWR-D-16-0037.1
-#'von Storch and Zwiers, 1999; https://doi.org/10.1017/CBO9780511612336
+#'Zwiers and von Storch, 1995; https://doi.org/10.1175/1520-0442(1995)008<0336:TSCIAI>2.0.CO;2
 #'
 #'@examples
 #' exp <- array(rnorm(1000), dim = c(lat = 3, lon = 2, member = 10, sdate = 50))
 #' obs <- array(rnorm(1000), dim = c(lat = 3, lon = 2, sdate = 50))
 #' ref <- array(rnorm(1000), dim = c(lat = 3, lon = 2, member = 10, sdate = 50))
-#' res_two.sided_sign <- DiffCorr(exp, obs, ref, memb_dim = 'member', alpha = 0.05)
-#' res_one.sided_pval <- DiffCorr(exp, obs, ref, memb_dim = 'member', test.type = 'one-sided')
+#' res_two.sided_sign <- DiffCorr(exp, obs, ref, memb_dim = 'member', test.type = 'two-sided', alpha = 0.05)
+#' res_one.sided_pval <- DiffCorr(exp, obs, ref, memb_dim = 'member', test.type = 'one-sided', alpha = NULL)
 #'
 #'@import multiApply
 #'@export
@@ -227,14 +226,20 @@ DiffCorr <- function(exp, obs, ref, N.eff = NA, time_dim = 'sdate',
       N.eff <- .Eno(x = obs, na.action = na.pass) ## effective degrees of freedom
     }
 
+    # Significance with one-sided or two-sided test for equality of dependent correlation coefficients (Steiger, 1980)
+    r12 <- cor.exp
+    r13 <- cor.ref
+    r23 <- cor(exp, ref)
+    R <- (1 - r12 * r12 - r13 * r13 - r23 * r23) + 2 * r12 * r13 * r23
+    t <- (r12 - r13) * sqrt((N.eff - 1) * (1 + r23) / (2 * ((N.eff - 1) / (N.eff - 3)) * R + 0.25 * (r12 + r13)^2 * (1 - r23)^3))
+    
     if (test.type == 'one-sided') {
-      # Significance with one-sided test for equality of dependent correlation coefficients (Steiger, 1980)
-      r12 <- cor.exp
-      r13 <- cor.ref
-      r23 <- cor(exp, ref)
-      R <- (1 - r12 * r12 - r13 * r13 - r23 * r23) + 2 * r12 * r13 * r23
-      t <- (r12 - r13) * sqrt((N.eff - 1) * (1 + r23) / (2 * ((N.eff - 1) / (N.eff - 3)) * R + 0.25 * (r12 + r13)^2 * (1 - r23)^3))
+      
+      ## H0: the skill of exp is not higher than that of ref
+      ## H1: the skill of exp is higher than that of ref
+      
       p.value <- pt(t, df = N.eff - 3, lower.tail = FALSE)
+      
       if (is.null(alpha)) {
         output$p.val <- p.value
       } else {
@@ -242,10 +247,11 @@ DiffCorr <- function(exp, obs, ref, N.eff = NA, time_dim = 'sdate',
       }
 
     } else if (test.type == 'two-sided') {
-      # Significance with two-sided z-test on Fisher z-transformed correlation coefficients (Hinkel et al, 1988)
-      Z <- abs(0.5 * log((1 + cor.exp) / (1 - cor.exp)) - 0.5 * log((1 + cor.ref) / (1 - cor.ref))) / sqrt(1/ (N.eff - 3) + 1/(N.eff - 3))
-      # sign <- Z >= qnorm(p = alpha/2, lower.tail = FALSE)
-      p.value <- pnorm(q = Z, lower.tail = FALSE)
+      
+      ## H0: the skill difference of exp and ref is zero
+      ## H1: the skill difference of exp and ref is different from zero
+      
+      p.value <- pt(abs(t), df = N.eff - 3, lower.tail = FALSE)
 
       if (is.null(alpha)) {
         output$p.val <- p.value
diff --git a/man/DiffCorr.Rd b/man/DiffCorr.Rd
index e0e5ec37ada8d7dc45d90ac83df33a340cc15c16..e907d3b5251f0885b80f76234c94b00835ae630d 100644
--- a/man/DiffCorr.Rd
+++ b/man/DiffCorr.Rd
@@ -59,10 +59,9 @@ NA. The default value is "return.na".}
 
 \item{test.type}{A character string indicating the type of significance test. 
 It can be "two-sided" (to assess whether the skill of "exp" and "ref" are 
-significantly different with a z-test on Fisher z-transformed correlation 
-coefficients, Hinkel et al, 1988) or "one-sided" (to assess whether the 
-skill of "exp" is significantly higher than that of "ref" with the test 
-described in Steiger, 1980). The default value is "two-sided".}
+significantly different) or "one-sided" (to assess whether the skill of  
+"exp" is significantly higher than that of "ref") following Steiger (1980).
+The default value is "two-sided".}
 
 \item{ncores}{An integer indicating the number of cores to use for parallel 
 computation. The default value is NULL.}
@@ -92,18 +91,18 @@ the reference forecast is more skillful. The statistical significance of the
 correlation differences is computed with a one-sided or two-sided test for 
 equality of dependent correlation coefficients (Steiger, 1980; Siegert et al.,
 2017) using effective degrees of freedom to account for the autocorrelation of
-the time series (von Storch and Zwiers, 1999).
+the time series (Zwiers and von Storch, 1995).
 }
 \examples{
 exp <- array(rnorm(1000), dim = c(lat = 3, lon = 2, member = 10, sdate = 50))
 obs <- array(rnorm(1000), dim = c(lat = 3, lon = 2, sdate = 50))
 ref <- array(rnorm(1000), dim = c(lat = 3, lon = 2, member = 10, sdate = 50))
-res_two.sided_sign <- DiffCorr(exp, obs, ref, memb_dim = 'member', alpha = 0.05)
-res_one.sided_pval <- DiffCorr(exp, obs, ref, memb_dim = 'member', test.type = 'one-sided')
+res_two.sided_sign <- DiffCorr(exp, obs, ref, memb_dim = 'member', test.type = 'two-sided', alpha = 0.05)
+res_one.sided_pval <- DiffCorr(exp, obs, ref, memb_dim = 'member', test.type = 'one-sided', alpha = NULL)
 
 }
 \references{
 Steiger, 1980; https://content.apa.org/doi/10.1037/0033-2909.87.2.245
 Siegert et al., 2017; https://doi.org/10.1175/MWR-D-16-0037.1
-von Storch and Zwiers, 1999; https://doi.org/10.1017/CBO9780511612336
+Zwiers and von Storch, 1995; https://doi.org/10.1175/1520-0442(1995)008<0336:TSCIAI>2.0.CO;2
 }
diff --git a/tests/testthat/test-DiffCorr.R b/tests/testthat/test-DiffCorr.R
index b8c8029ebbc41e09156d485a69b6c407418654ed..3c358187a0009c70db547eaa0dc4116c87adb6fa 100644
--- a/tests/testthat/test-DiffCorr.R
+++ b/tests/testthat/test-DiffCorr.R
@@ -18,6 +18,9 @@ set.seed(2)
 ref2 <- array(rnorm(10), dim = c(sdate = 10))
 set.seed(3)
 obs2 <- array(rnorm(10), dim = c(sdate = 10))
+## generate time auto-correlation (Eno will change)
+set.seed(3)
+obs2_2 <- array(1:10 + rnorm(10), dim = c(sdate = 10))
 
 
 ##############################################
@@ -123,8 +126,8 @@ c(0.27347087, 0.50556882, 0.08855968, 0.24199701, 0.22935182, 0.88336336),
 tolerance = 0.0001
 )
 expect_equal(
-as.vector(DiffCorr(exp1, obs1, ref1, memb_dim = 'memb')$p),
-c(0.28984782, 0.14395946, 0.41374677, 0.32253784, 0.32677872, 0.03659053),
+as.vector(DiffCorr(exp1, obs1, ref1, memb_dim = 'memb', test.type = "two-sided")$p),
+c(0.26166060, 0.15899774, 0.39264452, 0.27959883, 0.34736305, 0.07479832),
 tolerance = 0.0001
 )
 expect_equal(
@@ -155,7 +158,7 @@ tolerance = 0.0001
 )
 expect_equal(
 suppressWarnings(as.vector(DiffCorr(exp1, obs1, ref1, memb_dim = 'memb', method = "spearman")$p)),
-c(0.44479470, 0.11854232, 0.36667620, 0.49095264, 0.46962814, 0.01714977),
+c(0.4358970, 0.1341575, 0.3448977, 0.4885738, 0.4735128, 0.0437861),
 tolerance = 0.0001
 )
 expect_equal(
@@ -165,11 +168,10 @@ tolerance = 0.0001
 )
 expect_equal(
 as.vector(DiffCorr(exp1, obs1, ref1, memb_dim = 'memb', N.eff = Neff1)$p),
-c(0.30406438, 0.14395946, 0.42005522, 0.32253784, 0.33887632, 0.03659053),
+c(0.27841537, 0.15899774, 0.40096749, 0.27959883, 0.35889690, 0.07479832),
 tolerance = 0.0001
 )
 
-
 #---------------------------
 exp1[1] <- NA
 expect_equal(
@@ -217,8 +219,8 @@ dim(DiffCorr(exp2, obs2, ref2)$p),
 NULL
 )
 expect_equal(
-DiffCorr(exp2, obs2, ref2)$p,
-0.3201317,
+DiffCorr(exp2, obs2, ref2, test.type = 'two-sided')$p,
+0.3422608,
 tolerance = 0.0001
 )
 expect_equal(
@@ -227,11 +229,11 @@ DiffCorr(exp2, obs2, ref2, test.type = 'one-sided')$p,
 tolerance = 0.0001
 )
 expect_equal(
-DiffCorr(exp2, obs2, ref2, test.type = 'one-sided', alpha = 0.5)$sign,
+DiffCorr(exp2, obs2, ref2, test.type = 'one-sided', alpha = 0.7)$sign,
 FALSE
 )
 expect_equal(
-DiffCorr(exp2, obs2, ref2, test.type = 'two-sided', alpha = 0.65)$sign,
+DiffCorr(exp2, obs2, ref2, test.type = 'two-sided', alpha = 0.7)$sign,
 TRUE
 )
 expect_equal(
@@ -240,5 +242,19 @@ DiffCorr(exp2, obs2, ref2)$diff,
 tolerance = 0.0001
 )
 
+# obs2_2
+expect_equal(
+DiffCorr(exp2, obs2_2, ref2, test.type = 'two-sided')$p,
+0.4524316,
+tolerance = 0.0001
+)
+expect_equal(
+DiffCorr(exp2, obs2_2, ref2, test.type = 'one-sided')$p,
+0.5475684,
+tolerance = 0.0001
+)
+
+
+
 }) # suppressWarnings
 })