diff --git a/.github/workflows/CI.yml b/.github/workflows/CI.yml
index 14f5eaa1..d9800b5d 100644
--- a/.github/workflows/CI.yml
+++ b/.github/workflows/CI.yml
@@ -14,9 +14,10 @@ jobs:
       fail-fast: false
       matrix:
         version:
-          - '1.6'
+          - 'min'
+          - 'lts'
           - '1'
-          - 'nightly'
+          - 'pre'
         os:
           - ubuntu-latest
         arch:
diff --git a/Project.toml b/Project.toml
index 2759d394..2673c385 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "MCMCDiagnosticTools"
 uuid = "be115224-59cd-429b-ad48-344e309966f0"
 authors = ["David Widmann", "Seth Axen"]
-version = "0.3.11"
+version = "0.3.12"
 
 [deps]
 AbstractFFTs = "621f4979-c628-5d54-868e-fcf4e3e8185c"
@@ -44,7 +44,7 @@ StatsBase = "0.33.7, 0.34"
 StatsFuns = "1"
 Tables = "1.11"
 Test = "1.6"
-julia = "1.6"
+julia = "1.8"
 
 [extras]
 Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
diff --git a/src/mcse.jl b/src/mcse.jl
index 3bc12728..c2b41886 100644
--- a/src/mcse.jl
+++ b/src/mcse.jl
@@ -95,6 +95,9 @@ end
 
 function _mcse_quantile(x, p, Seff)
     Seff === missing && return missing
+    if isnan(Seff)
+        return oftype(oneunit(eltype(x)) / 1, NaN)
+    end
     S = length(x)
     # quantile error distribution is asymptotically normal; estimate σ (mcse) with 2
     # quadrature points: xl and xu, chosen as quantiles so that xu - xl = 2σ
@@ -133,6 +136,10 @@ function _mcse_sbm(f, x, batch_size)
     any(x -> x === missing, x) && return missing
     n = length(x)
     i1 = firstindex(x)
+    if allequal(x)
+        y1 = f(view(x, i1:(i1 + batch_size - 1)))
+        return oftype(y1, NaN)
+    end
     v = Statistics.var(
         f(view(x, i:(i + batch_size - 1))) for i in i1:(i1 + n - batch_size);
         corrected=false,
diff --git a/test/mcse.jl b/test/mcse.jl
index 4a8c2e48..35a7d408 100644
--- a/test/mcse.jl
+++ b/test/mcse.jl
@@ -83,6 +83,23 @@ using StatsBase
         end
     end
 
+    @testset "mcse for scalar array is always a NaN" begin
+        x = ones(100)
+        @testset for kind in [
+            mean,
+            median,
+            std,
+            mad,
+            # uses sbm
+            x -> mean(x),
+            x -> median(x),
+            x -> std(x),
+            x -> mad(x),
+        ]
+            @test isnan(mcse(x; kind))
+        end
+    end
+
     @testset "estimand is within interval defined by MCSE estimate" begin
         # we check the MCSE estimates by simulating uncorrelated, correlated, and
         # anticorrelated chains, mapping the draws to a target distribution, computing the