diff --git a/README.md b/README.md
index 057c879ae..dfcb1b1aa 100644
--- a/README.md
+++ b/README.md
@@ -287,11 +287,11 @@ Currently, the `@compat` macro supports the following syntaxes:
 
 * `Compat.mv` and `Compat.cp` with `force` keyword argument ([#26069]).
 
-* `Compat.accumulate`, `Compat.accumulate!`, `Compat.all`, `Compat.any`, `Compat.cor`,
-  `Compat.cov`, `Compat.cumprod`, `Compat.cumprod!`, `Compat.cumsum`, `Compat.cumsum!`,
+* `Compat.accumulate`, `Compat.accumulate!`, `Compat.all`, `Compat.any`,
+  `Compat.cumprod`, `Compat.cumprod!`, `Compat.cumsum`, `Compat.cumsum!`,
   `Compat.findmax`, `Compat.findmin`, `Compat.mapreduce`, `Compat.maximum`, `Compat.mean`,
   `Compat.median`, `Compat.minimum`, `Compat.prod`, `Compat.reduce`, `Compat.sort`,
-  `Compat.std`, `Compat.sum`, `Compat.var`, and `Compat.varm` with `dims` keyword argument ([#25989],[#26369]).
+  and `Compat.sum`  with `dims` keyword argument ([#25989],[#26369]).
 
 * `selectdim` to obtain a view of an array with a specified index for a specified dimension ([#26009]).
 
diff --git a/src/Compat.jl b/src/Compat.jl
index 3944760c6..562eacad7 100644
--- a/src/Compat.jl
+++ b/src/Compat.jl
@@ -500,6 +500,7 @@ if VERSION < v"0.7.0-DEV.755"
     # This is a hack to only add keyword signature that won't work on all julia versions.
     # However, since we really only need to support a few (0.5, 0.6 and early 0.7) versions
     # this should be good enough.
+    # TODO add deprecation warning to switch to StatsBase
     let Tf = typeof(Base.cov), Tkw = Core.Core.kwftype(Tf)
         @eval begin
             @inline function _get_corrected(kws)
@@ -1760,6 +1761,7 @@ if VERSION < v"0.7.0-DEV.4064"
             end
         end
     end
+    # TODO add deprecation warning to switch to StatsBase to var and std
     for f in (:var, :std, :sort)
         @eval begin
             $f(a::AbstractArray; dims=nothing, kwargs...) =
@@ -1772,6 +1774,7 @@ if VERSION < v"0.7.0-DEV.4064"
     end
 end
 if VERSION < v"0.7.0-DEV.4064"
+    # TODO add deprecation warning to switch to StatsBase to varm, cov, and cor
     varm(A::AbstractArray, m; dims=nothing, kwargs...) =
         dims===nothing ? Base.varm(A, m; kwargs...) : Base.varm(A, m, dims; kwargs...)
     if VERSION < v"0.7.0-DEV.755"
diff --git a/test/runtests.jl b/test/runtests.jl
index f298ae4a7..d98de0e90 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -834,11 +834,13 @@ end
 @test Base.rtoldefault(Float64, Float64, 1.0) === 0.0
 
 # 0.7
-@test cov([1 2; 3 4], 1, corrected=true) == fill(2.0, 2, 2)
-@test cov([1 2; 3 4], 1, corrected=false) == fill(1.0, 2, 2)
-@test cov([1 2; 3 4], [0 4; 8 9], 1, corrected=true) == [8.0 5.0; 8.0 5.0]
-@test cov([1 2; 3 4], [0 4; 8 9], 1, corrected=false) == [4.0 2.5; 4.0 2.5]
-if VERSION >= v"0.6"
+if VERSION  < v"0.7.0-DEV.5238"
+    # Test the extended cov if cov is part of Base. In the future, this will be dealt with
+    # in StatsBase
+    @test cov([1 2; 3 4], 1, corrected=true) == fill(2.0, 2, 2)
+    @test cov([1 2; 3 4], 1, corrected=false) == fill(1.0, 2, 2)
+    @test cov([1 2; 3 4], [0 4; 8 9], 1, corrected=true) == [8.0 5.0; 8.0 5.0]
+    @test cov([1 2; 3 4], [0 4; 8 9], 1, corrected=false) == [4.0 2.5; 4.0 2.5]
     @test cov([1, 2], corrected=true) === 0.5
     @test cov([1, 2], corrected=false) === 0.25
     @test cov([1, 2], [0, 10], corrected=true) === 5.0
@@ -1569,36 +1571,40 @@ Issue26488 && @test Compat.prod(x -> x+1, [1 2; 3 4], dims=2) == hcat([6; 20])
 @test Compat.findmin([1 2; 3 4]) == (1, CartesianIndex(1, 1))
 @test Compat.findmin([1 2; 3 4], dims=1) == ([1 2], [CartesianIndex(1, 1) CartesianIndex(1, 2)])
 @test Compat.findmin([1 2; 3 4], dims=2) == (hcat([1; 3]), hcat([CartesianIndex(1, 1); CartesianIndex(2, 1)]))
-@test Compat.varm([1 2; 3 4], -1) == 18
-@test Compat.varm([1 2; 3 4], [-1 -2], dims=1) == [20 52]
-@test Compat.varm([1 2; 3 4], [-1, -2], dims=2) == hcat([13, 61])
-@test Compat.var([1 2; 3 4]) == 5/3
-@test Compat.var([1 2; 3 4], dims=1) == [2 2]
-@test Compat.var([1 2; 3 4], dims=2) == hcat([0.5, 0.5])
-@test Compat.var([1 2; 3 4], corrected=false) == 1.25
-@test Compat.var([1 2; 3 4], corrected=false, dims=1) == [1 1]
-@test Compat.var([1 2; 3 4], corrected=false, dims=2) == hcat([0.25, 0.25])
-@test Compat.std([1 2; 3 4]) == sqrt(5/3)
-@test Compat.std([1 2; 3 4], dims=1) == [sqrt(2) sqrt(2)]
-@test Compat.std([1 2; 3 4], dims=2) == hcat([sqrt(0.5), sqrt(0.5)])
-@test Compat.std([1 2; 3 4], corrected=false) == sqrt(1.25)
-@test Compat.std([1 2; 3 4], corrected=false, dims=1) == [sqrt(1) sqrt(1)]
-@test Compat.std([1 2; 3 4], corrected=false, dims=2) == hcat([sqrt(0.25), sqrt(0.25)])
-@test Compat.cov([1 2; 3 4]) == [2 2; 2 2]
-@test Compat.cov([1 2; 3 4], dims=1) == [2 2; 2 2]
-@test Compat.cov([1 2; 3 4], dims=2) == [0.5 0.5; 0.5 0.5]
-@test Compat.cov([1 2; 3 4], [4; 5]) == hcat([1; 1])
-@test Compat.cov([1 2; 3 4], [4; 5], dims=1) == hcat([1; 1])
-@test Compat.cov([1 2; 3 4], [4; 5], dims=2) == hcat([0.5; 0.5])
-@test Compat.cov([1 2; 3 4], [4; 5], corrected=false) == hcat([0.5; 0.5])
-@test Compat.cov([1 2; 3 4], [4; 5], corrected=false, dims=1) == hcat([0.5; 0.5])
-@test Compat.cov([1 2; 3 4], [4; 5], corrected=false, dims=2) == hcat([0.25; 0.25])
-@test Compat.cor([1 2; 3 4]) ≈ [1 1; 1 1]
-@test Compat.cor([1 2; 3 4], dims=1) ≈ [1 1; 1 1]
-@test Compat.cor([1 2; 3 4], dims=2) ≈ [1 1; 1 1]
-@test Compat.cor([1 2; 3 4], [4; 5]) ≈ [1; 1]
-@test Compat.cor([1 2; 3 4], [4; 5], dims=1) ≈ [1; 1]
-@test Compat.cor([1 2; 3 4], [4; 5], dims=2) ≈ [1; 1]
+if VERSION  < v"0.7.0-DEV.5238"
+    # Test these functions if their counterparts are defined in Base. In the future, this
+    # will be dealt with in StatsBase
+    @test Compat.varm([1 2; 3 4], -1) == 18
+    @test Compat.varm([1 2; 3 4], [-1 -2], dims=1) == [20 52]
+    @test Compat.varm([1 2; 3 4], [-1, -2], dims=2) == hcat([13, 61])
+    @test Compat.var([1 2; 3 4]) == 5/3
+    @test Compat.var([1 2; 3 4], dims=1) == [2 2]
+    @test Compat.var([1 2; 3 4], dims=2) == hcat([0.5, 0.5])
+    @test Compat.var([1 2; 3 4], corrected=false) == 1.25
+    @test Compat.var([1 2; 3 4], corrected=false, dims=1) == [1 1]
+    @test Compat.var([1 2; 3 4], corrected=false, dims=2) == hcat([0.25, 0.25])
+    @test Compat.std([1 2; 3 4]) == sqrt(5/3)
+    @test Compat.std([1 2; 3 4], dims=1) == [sqrt(2) sqrt(2)]
+    @test Compat.std([1 2; 3 4], dims=2) == hcat([sqrt(0.5), sqrt(0.5)])
+    @test Compat.std([1 2; 3 4], corrected=false) == sqrt(1.25)
+    @test Compat.std([1 2; 3 4], corrected=false, dims=1) == [sqrt(1) sqrt(1)]
+    @test Compat.std([1 2; 3 4], corrected=false, dims=2) == hcat([sqrt(0.25), sqrt(0.25)])
+    @test Compat.cov([1 2; 3 4]) == [2 2; 2 2]
+    @test Compat.cov([1 2; 3 4], dims=1) == [2 2; 2 2]
+    @test Compat.cov([1 2; 3 4], dims=2) == [0.5 0.5; 0.5 0.5]
+    @test Compat.cov([1 2; 3 4], [4; 5]) == hcat([1; 1])
+    @test Compat.cov([1 2; 3 4], [4; 5], dims=1) == hcat([1; 1])
+    @test Compat.cov([1 2; 3 4], [4; 5], dims=2) == hcat([0.5; 0.5])
+    @test Compat.cov([1 2; 3 4], [4; 5], corrected=false) == hcat([0.5; 0.5])
+    @test Compat.cov([1 2; 3 4], [4; 5], corrected=false, dims=1) == hcat([0.5; 0.5])
+    @test Compat.cov([1 2; 3 4], [4; 5], corrected=false, dims=2) == hcat([0.25; 0.25])
+    @test Compat.cor([1 2; 3 4]) ≈ [1 1; 1 1]
+    @test Compat.cor([1 2; 3 4], dims=1) ≈ [1 1; 1 1]
+    @test Compat.cor([1 2; 3 4], dims=2) ≈ [1 1; 1 1]
+    @test Compat.cor([1 2; 3 4], [4; 5]) ≈ [1; 1]
+    @test Compat.cor([1 2; 3 4], [4; 5], dims=1) ≈ [1; 1]
+    @test Compat.cor([1 2; 3 4], [4; 5], dims=2) ≈ [1; 1]
+end
 @test Compat.median([1 2; 3 4]) == 2.5
 @test Compat.median([1 2; 3 4], dims=1) == [2 3]
 @test Compat.median([1 2; 3 4], dims=2) == hcat([1.5; 3.5])