diff --git a/.JuliaFormatter.toml b/.JuliaFormatter.toml
new file mode 100644
index 0000000..76c30b0
--- /dev/null
+++ b/.JuliaFormatter.toml
@@ -0,0 +1,3 @@
+always_for_in = true
+short_to_long_function_def = true
+always_use_return = true
diff --git a/.github/workflows/CI.yml b/.github/workflows/CI.yml
index e3b752b..5cc6786 100644
--- a/.github/workflows/CI.yml
+++ b/.github/workflows/CI.yml
@@ -18,7 +18,6 @@ jobs:
       fail-fast: false
       matrix:
         version:
-          - '1.6'
           - '1.8'
           - 'nightly'
         os:
diff --git a/.gitignore b/.gitignore
index 5bf4af9..b200bf8 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1,2 +1,4 @@
 /Manifest.toml
-.vscode
\ No newline at end of file
+.vscode
+
+.DS_Store
\ No newline at end of file
diff --git a/Project.toml b/Project.toml
index 0338a13..62e01c5 100644
--- a/Project.toml
+++ b/Project.toml
@@ -4,19 +4,34 @@ authors = ["Philipp Gewessler <p.gewessler@gmx.at> and constributors"]
 version = "0.1.0"
 
 [deps]
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 [extras]
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
diff --git a/README.md b/README.md
index 1efafe0..1944c7f 100644
--- a/README.md
+++ b/README.md
@@ -1,7 +1,50 @@
-# ClassicalTestTheory
+# ClassicalTestTheory.jl
 
 [![Stable](https://img.shields.io/badge/docs-stable-blue.svg)](https://p-gw.github.io/ClassicalTestTheory.jl/stable)
 [![Dev](https://img.shields.io/badge/docs-dev-blue.svg)](https://p-gw.github.io/ClassicalTestTheory.jl/dev)
 [![Build Status](https://github.com/p-gw/ClassicalTestTheory.jl/actions/workflows/CI.yml/badge.svg?branch=main)](https://github.com/p-gw/ClassicalTestTheory.jl/actions/workflows/CI.yml?query=branch%3Amain)
 [![Coverage](https://codecov.io/gh/p-gw/ClassicalTestTheory.jl/branch/main/graph/badge.svg)](https://codecov.io/gh/p-gw/ClassicalTestTheory.jl)
 
+ClassicalTestTheory.jl is a Julia package for data analysis using [Classical Test Theory](https://en.wikipedia.org/wiki/Classical_test_theory#:~:text=It%20is%20a%20theory%20of,the%20reliability%20of%20psychological%20tests.).
+
+## Installation
+```julia
+] add https://github.com/p-gw/ClassicalTestTheory.jl.git
+```
+
+## Getting started
+ClassicalTestTheory.jl provides two entry points to doing data analsis. 
+The input data can either be a numeric `Matrix` or a [`PsychometricTest`](https://github.com/JuliaPsychometrics/PsychometricTests.jl). 
+While `Matrix` methods provide full functionality, `PsychometricTest` methods provide some 
+additional convenience such as scale analysis. 
+For details on how to use ClassicalTestTheory.jl with `PsychometricTest` see [XXX](#).
+
+Consider some input data `x`,
+
+```julia-repl
+julia> n_persons = 100;
+julia> n_items = 8;
+
+julia> x = rand(0:100, n_persons, n_items);
+```
+
+we can get some descriptive analysis of the items,
+
+```julia
+itemanalysis(x)
+```
+
+or estimate the internal consistency (e.g. using Cronbach's alpha)
+
+```julia
+reliability(x, Alpha())
+```
+
+The package will automatically calculate the coefficient from the data and construct appropriate confidence intervals.
+
+To get multiple estimates of reliability just pass a vector of methods:
+
+```julia
+coefficients = [Alpha(), GLB(), Mu(2)]
+reliability(x, coefficients)
+```
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new file mode 100644
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index 0000000..866d178
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diff --git a/benchmark/reliability.jl b/benchmark/reliability.jl
new file mode 100644
index 0000000..79d0b40
--- /dev/null
+++ b/benchmark/reliability.jl
@@ -0,0 +1,50 @@
+using ClassicalTestTheory
+using PsychometricTests
+using DelimitedFiles
+using CSV
+using DataFrames
+
+data = CSV.read("benchmark/attitude.csv", DataFrame)
+m = Matrix(data)
+test = PsychometricTest(data)
+
+ia = ClassicalTestTheory.itemanalysis(test)
+
+ClassicalTestTheory.reliability(m, ClassicalTestTheory.PSYCH_METHODS)
+
+# lambda1
+lambda1(m)
+lambda1(test)
+lambda1(test_scales)
+lambda1(test_scales, nothing)
+
+@benchmark lambda1($m)
+@benchmark lambda1($test)
+@benchmark lambda1($test_scales)
+@benchmark lambda1($test_scales, $:a)
+@benchmark lambda1($test_scales, $nothing)
+
+@profview [lambda1(m) for _ in 1:10_000]
+@profview [lambda1(test) for _ in 1:10_000]
+@profview [lambda1(test_scales) for _ in 1:10_000]
+
+@profview_allocs lambda1(test_scales, :a) sample_rate = 1
+
+@code_warntype lambda1(test)
+@code_warntype lambda1(test_scales)
+@code_warntype lambda1(test_scales, :a)
+
+# maxlambda4
+
+# find
+find(test, 6)
+
+@benchmark find($test, $6)
+
+@code_warntype find(test, 6)
+
+@profview_allocs find(test, 6, criterion = alpha) sample_rate = 1
+
+# test bootstrapping
+using Bootstrap
+
diff --git a/src/ClassicalTestTheory.jl b/src/ClassicalTestTheory.jl
index 53e8720..efec878 100644
--- a/src/ClassicalTestTheory.jl
+++ b/src/ClassicalTestTheory.jl
@@ -1,36 +1,53 @@
 module ClassicalTestTheory
 
-using Base: split
+using Base: @kwdef
+using Bootstrap
 using Combinatorics
-using SCS
 using Distributions
-using InvertedIndices
 using JuMP
 using LinearAlgebra
+using OrderedCollections
+using Printf
 using ProgressMeter
 using Random
+using Reexport
+using SCS
+using StatsAPI
 using StatsBase
-using Statistics
-
-export Test, SubTest
-export eachitem, eachperson
-export scores, responses, nitems, npersons
+using Tables
+using Term
 
-export split, splithalf
+@reexport import StatsAPI: confint, stderror
+import Base: split
 
-export difficulty, facility, itc
+# reliability measures
+export lambda1, lambda2, lambda3, lambda4, maxlambda4, lambda5, lambda6, alpha
+export L1, L2, L3, L4, L5, L6, Alpha
+export GUTTMAN_METHODS, PSYCH_METHODS, mu_up_to
 
-export λ1, λ2, λ3, λ4, maxλ4, λ5, λ6
-export α
 export kr20, kr21
-export glb
+export KR20, KR21
+
+export glb, mu
+export GLB, Mu
+
+export reliability
+
+export estimate, bootstrap_sample
+
+# item statistics
+export itc, itemanalysis
+
+# find
 export find
 
+include("references.jl")
 include("utils.jl")
-include("types.jl")
 include("split.jl")
+include("reliability/reliability.jl")
 include("item_statistics.jl")
-include("reliability.jl")
 include("find.jl")
 
+include("precompile.jl")
+
 end
diff --git a/src/find.jl b/src/find.jl
index a80cf3d..87e8f37 100644
--- a/src/find.jl
+++ b/src/find.jl
@@ -1,23 +1,58 @@
 """
-    find(t::AbstractTest, n; criterion=glb)
-
-Perform an exhaustive search to find the optimal subtest of `t` with `n` items.
+    find(m::AbstractMatrix, n::Int; criterion = glb, progress = true)
 
+Perform an exhaustive search to find the subset of `n` items with maximum reliability.
 """
-function find(t, n; criterion=glb)
-    is = vcat(trues(n), falses(nitems(t) - n))
-    perms = multiset_permutations(is, length(is))
-    n_perms_iter = Int(length(perms) / 2)
+function find(m::AbstractMatrix, args...; kwargs...)
+    is = _find(m, args...; kwargs...)
+    return m[:, is]
+end
+
+function _find(
+    m::AbstractMatrix,
+    n::Int;
+    criterion::F = glb,
+    progress = true,
+    kwargs...,
+) where {F}
+    if n >= size(m, 2)
+        throw(
+            ArgumentError(
+                "The subset size must be smaller than the size of the orginial test.",
+            ),
+        )
+    end
+
+    is = axes(m, 2)
+    combs = combinations(is, n)
 
-    optimal_subtest = is
+    optimal_is = zeros(Int, n)
     max_crit = -Inf
-    @showprogress for perm in Iterators.take(perms, n_perms_iter)
-        subtest, _ = split(t, perm)
-        crit = criterion(subtest)
+
+    prog = Progress(
+        length(combs),
+        dt = 0.5,
+        barglyphs = BarGlyphs("[=> ]"),
+        enabled = progress,
+    )
+
+    for (i, c) in enumerate(combs)
+        subtest = view(m, :, c)
+        crit = criterion(subtest; kwargs...)
+
         if crit > max_crit
             max_crit = crit
-            optimal_subtest = subtest
+            optimal_is = c
         end
+
+        ProgressMeter.update!(
+            prog,
+            i,
+            showvalues = [(:items, optimal_is), (:reliability, max_crit)],
+        )
     end
-    return optimal_subtest
+
+    ProgressMeter.finish!(prog)
+
+    return optimal_is
 end
diff --git a/src/item_statistics.jl b/src/item_statistics.jl
index f0f44ec..9e29735 100644
--- a/src/item_statistics.jl
+++ b/src/item_statistics.jl
@@ -47,44 +47,102 @@ Henrysson, S. (1963). Correction of item-total correlations in item analysis. *P
 Zubin, J. The method of internal consistency for selecting test items. *J. educ. Psychol,
 1934, 25*, 345-356.
 """
-function itc(x, i::Int; correction=true)
-    if correction in (true, :henrysson)
-        return _itc_henrysson(x, i)
-    elseif correction == false
-        return _itc_uncorrected(x, i)
-    elseif correction == :zubin
-        return _itc_zubin(x, i)
-    elseif correction == :guilford
-        return _itc_guilford(x, i)
+function itc(x, i; corrected = true, standardize = false)
+    if corrected in (true, :henrysson)
+        return _itc_henrysson(x, i; standardize)
+    elseif corrected == false
+        return _itc_uncorrected(x, i; standardize)
+    elseif corrected == :zubin
+        return _itc_zubin(x, i; standardize)
+    elseif corrected == :guilford
+        return _itc_guilford(x, i; standardize)
     else
-        error("Unknown correction type: $(correction)")
+        error("Unknown correction type: $(corrected)")
     end
 end
 
-function _itc_uncorrected(x, i)
-    return cor(responses(x, i), scores(x))
+function _itc_uncorrected(m::AbstractMatrix, i; standardize)
+    responses = vec(m[:, i])
+    total_scores = vec(sum(m, dims = 2))
+    return cor(responses, total_scores)
 end
 
-function _itc_henrysson(x, i)
-    # here the second value returns the test with all items except i
-    _, corrected_test = split(x, i)
-    return cor(responses(x, i), scores(corrected_test))
+function _itc_henrysson(m::AbstractMatrix, i; standardize)
+    is = filter(x -> x != i, axes(m, 2))
+    corrected_m = view(m, :, is)
+    responses = vec(m[:, i])
+    total_scores = vec(sum(corrected_m, dims = 2))
+    return cor(responses, total_scores)
 end
 
-function _itc_zubin(x, i)
-    itc = _itc_uncorrected(x, i)
-    st = std(scores(x))
-    fv = facility(x, i)
-    y = cdf(Normal(), fv)
-    pqy = fv * (1 - fv) / y
-    return (itc * st - pqy) / sqrt(st^2 + 1 - 2 * itc * st)
+struct ItemStatistics{Ti,T<:Real}
+    item::Ti
+    n::Int
+    missings::Int
+    itc::T
+    itc_std::T
+    itc_corrected::T
+    mean::T
+    std::T
 end
 
-function _itc_guilford(x, i)
-    itc = _itc_uncorrected(x, i)
-    st = std(scores(x))
-    fv = facility(x, i)
-    y = cdf(Normal(), fv)
-    pqy = fv * (1 - fv) / y
-    return (itc * st - pqy) / sqrt(st^2 + pqy^2 - 2 * itc * st * pqy)
+function ItemStatistics(name, test_data, item_data, item_index)
+    return ItemStatistics(
+        string(name),
+        sum(!ismissing, item_data),
+        sum(ismissing, item_data),
+        itc(test_data, item_index, corrected = false),
+        itc(test_data, item_index, corrected = false, standardize = true),
+        itc(test_data, item_index, corrected = :henrysson),
+        mean(item_data),
+        std(item_data),
+    )
+end
+
+function ItemStatistics(m::AbstractMatrix, j; name = "Item " * string(j))
+    item_responses = vec(m[:, j])
+    return ItemStatistics(name, m, item_responses, j)
+end
+
+struct ItemAnalysis
+    statistics::Vector{ItemStatistics}
+end
+
+function Base.show(io::IO, items::ItemAnalysis)
+    tbl = Tables.columns(items.statistics)
+
+    rounded_cols = [:itc, :itc_std, :itc_corrected, :mean, :std]
+
+    for col in rounded_cols
+        coldata = Tables.getcolumn(tbl, col)
+        coldata .= round.(coldata, digits = 2)  # TODO: keep trailing digits
+    end
+
+    header = ["item", "N", "missings", "itc", "itc (std)", "itc (cor)", "mean", "std"]
+    print(
+        io,
+        Term.Panel(
+            Term.Table(
+                tbl;
+                header,
+                header_style = "green bold",
+                columns_style = ["bold yellow", "", "", "", "", "", "", ""],
+                style = "dim",
+                box = :SIMPLE,
+                compact = false,
+            ),
+            title = "{dim}Item Analysis",
+            style = "dim",
+            subtitle = "{dim}ClassicalTestTheory.jl",
+            subtitle_justify = :right,
+            fit = true,
+        ),
+    )
+
+    return nothing
+end
+
+function itemanalysis(m::AbstractMatrix)
+    item_statistics = [ItemStatistics(m, j) for j in axes(m, 2)]
+    return ItemAnalysis(item_statistics)
 end
diff --git a/src/precompile.jl b/src/precompile.jl
new file mode 100644
index 0000000..281bfa9
--- /dev/null
+++ b/src/precompile.jl
@@ -0,0 +1,32 @@
+using PrecompileTools
+
+@setup_workload begin
+    m = rand(0:100, 20, 4)
+
+    @compile_workload begin
+        # reliability measures
+        methods = [GLB(), GUTTMAN_METHODS..., KR20(), KR21(), mu_up_to(1)...]
+        reliability(m, methods)
+
+        result = reliability(m, Alpha())
+
+        data(result)
+        sampling_method(result)
+        ci_method(result)
+        estimate(result)
+        estimate(result, "Alpha")
+        confint(result)
+        confint(result, "Alpha")
+        bias(result)
+        bias(result, "Alpha")
+        stderror(result)
+        stderror(result, "Alpha")
+        samples(result, "Alpha")
+
+        # item statistics
+        ia = itemanalysis(m)
+
+        # find
+        find(m, 2, criterion = alpha)
+    end
+end
diff --git a/src/references.jl b/src/references.jl
new file mode 100644
index 0000000..85acf68
--- /dev/null
+++ b/src/references.jl
@@ -0,0 +1,4 @@
+const GUTTMAN1945 = "Guttman, L. (1945). A basis for analyzing test-retest reliability. *Psychometrika, 10*(4), 255-282."
+const WOODHOUSE1977 = "Woodhouse, B., & Jackson, P. H. (1977). Lower bounds for the reliability of the total score on a test composed of non-homogeneous items: II: A search procedure to locate the greatest lower bound. *Psychometrika, 42*(4), 579-591."
+const TENBERGE1978 = "Ten Berge, J. M., & Zegers, F. E. (1978). A series of lower bounds to the reliability of a test. *Psychometrika, 43*, 575-579."
+const KUDERRICHARDSON1937 = "Kuder, G. F., & Richardson, M. W. (1937). The theory of the estimation of test reliability. *Psychometrika, 2*(3), 151–160."
diff --git a/src/reliability.jl b/src/reliability.jl
deleted file mode 100644
index a0477c5..0000000
--- a/src/reliability.jl
+++ /dev/null
@@ -1,232 +0,0 @@
-const GUTTMAN1945 = "Guttman, L. (1945). A basis for analyzing test-retest reliability. *Psychometrika, 10*(4), 255-282."
-
-"""
-   λ1(m::Matrix)
-   λ1(t::Test)
-
-Return the lower bound estimate of the reliability L₁ described in $GUTTMAN1945
-
-``\\lambda_1 = 1 - \\frac{\\sum_{j=1}^{n} s_j^2}{s_t^2}``
-"""
-function λ1(m::Matrix)
-    sum_sj = sum(x -> var(x), eachitem(m))
-    st = var(scores(m))
-    return 1 - (sum_sj / st)
-end
-
-function λ1(t::AbstractTest)
-    sum_sj = tr(t.itemcov)
-    st = var(scores(t))
-    return 1 - (sum_sj / st)
-end
-
-"""
-    λ2(m::Matrix)
-    λ2(t::Test)
-
-Return the lower bound estimate of the reliability λ₂ described in $GUTTMAN1945
-
-``\\lambda_2 = \\lambda_1 + \\frac{\\sqrt{\\frac{n}{n-1}C_2}}{s_t^2}``
-"""
-function λ2(x)
-    n = nitems(x)
-    C2 = cov(x) .^ 2
-    zerodiag!(C2)
-    st = var(scores(x))
-    return λ1(x) + sqrt(n / (n - 1) * sum(C2)) / st
-end
-
-"""
-    λ3(m::Matrix)
-    λ3(t::Test)
-
-Return the lower bound estimate of the reliability λ₃ described in $GUTTMAN1945
-
-``\\lambda_3 = \\frac{n}{n-1}\\lambda_1``
-"""
-function λ3(x)
-    n = nitems(x)
-    return n / (n - 1) * λ1(x)
-end
-
-"""
-    α(x)
-
-Estimate Cronbach's α. `α` is an alias for [`λ3`](@ref).
-"""
-const α = λ3
-
-"""
-    λ4(m::Matrix)
-    λ4(t::Test)
-
-Return the lower bound estimate of the reliability λ₄ described in $GUTTMAN1945
-
-``\\lambda_4 = 2\\( 1 - \\frac{s_a^2 + s_b^2}{s_t^2} \\)``
-
-The calculation of λ₄ is based on splitting `t` in half.
-It is a lower bound of the reliability no matter how the test is split.
-
-The split of the test can be controlled by the `type` keyword argument (see also [`splithalf`](@ref)).
-
-To get the maximum lower bound see [`maxλ4`](@ref).
-"""
-function λ4(x; kwargs...)
-    subtests = splithalf(x; kwargs...)
-    st = var(scores(x))
-    vars = var.(scores.(subtests))
-    return 2 * (1 - sum(vars) / st)
-end
-
-function λ4(x, is)
-    subtests = split(x, is)
-    st = var(scores(x))
-    vars = var.(scores.(subtests))
-    return 2 * (1 - sum(vars) / st)
-end
-
-"""
-    maxλ4(x; method=:auto, n_samples=1_000)
-
-Return the maximum lower bound estimate of the reliability λ₄ described in $GUTTMAN1945
-
-By default (if `n_samples=nothing`) the maximum value is found by brute force iteration over
-the split-half permutations of `x`.
-As the number of permutations grows, this method becomes infeasible.
-For large numbers of items a (local) maximum of λ₄ can be found by sampling random split-half
-permutations.
-To use sampling, specify `n_samples::Int`.
-
-See also [`λ4`](@ref).
-"""
-function maxλ4(x; method=:auto, n_samples=10_000)::Float64
-    if method == :auto
-        if nitems(x) <= 25
-            maxλ = _maxλ4_brute_force(x)
-        else
-            maxλ = _maxλ4_random(x, n_samples)
-        end
-    elseif method == :bruteforce
-        maxλ = _maxλ4_brute_force(x)
-    elseif method == :sample
-        maxλ = _maxλ4_random(x, n_samples)
-    else
-        error("Unknown method")
-    end
-
-    return maxλ
-end
-
-function _maxλ4_brute_force(x)
-    n = nitems(x)
-    n_include = ceil(Int, n / 2)
-    is = vcat(trues(n_include), falses(n - n_include))
-
-    perms = multiset_permutations(is, length(is))
-    n_perms_iter = Int(length(perms) / 2)
-
-    if n_perms_iter > 1e6
-        @info "Brute forcing $(n_perms_iter) permutations. Adjust your expectations accordingly..."
-    end
-
-    # we only need to iterate over the first half of the permutations, because
-    # multiset_permutations(...) returns a sorted vector and λ4 is symmetric with regards
-    # to the splits, e.g. [0, 1] and [1, 0] yield identical values of λ4.
-    maxλ = maximum(λ4(x, perm) for perm in Iterators.take(perms, n_perms_iter))
-    return maxλ
-end
-
-function _maxλ4_random(x, n_samples::Int)
-    n = nitems(x)
-    n_include = ceil(Int, n / 2)
-    is = vcat(trues(n_include), falses(n - n_include))
-    maxλ = maximum(λ4(x, shuffle!(is)) for _ in 1:n_samples)
-    return maxλ
-end
-
-"""
-    λ5(x)
-
-Return the lower bound estimate of the reliability λ₅ described in $GUTTMAN1945
-
-``\\lambda_5 = \\lambda_1 + \\frac{2\\sqrt{\\bar{C}_2}}{s_t^2}``
-"""
-function λ5(x)
-    covmat = LowerTriangular(copy(cov(x)))
-    zerodiag!(covmat)
-    C2 = sum(covmat .^ 2, dims=1)
-    C2_max = maximum(C2)
-    st = var(scores(x))
-    return λ1(x) + 2 * sqrt(C2_max) / st
-end
-
-"""
-    λ6(x)
-
-Return the lower bound estimate of the reliability λ₆ described in $GUTTMAN1945
-
-``\\lambda_6 = 1 - \\frac{\\sum_{j=1}^n e_j^2}{s_t^2}``
-"""
-function λ6(x)
-    covmat = cov(x)
-    inv_covmat = inv(covmat)
-    smc = 1 .- 1 ./ diag(inv_covmat)
-    return 1 - sum(1 .- smc) / sum(covmat)
-end
-
-"""
-    kr20
-"""
-function kr20(x)
-    n = nitems(x)
-    item_facilities = facility.(eachitem(x))
-    item_difficulties = 1 .- item_facilities
-    st = var(scores(x))
-    return (n / (n - 1)) * ((st - sum(item_facilities .* item_difficulties)) / st)
-end
-
-"""
-    kr21
-"""
-function kr21(x)
-    n = nitems(x)
-    avg_facility = mean(facility.(eachitem(x)))
-    avg_difficulty = 1 - avg_facility
-    st = var(scores(x))
-    return (n / (n - 1)) * ((st - n * avg_difficulty * avg_facility) / st)
-end
-
-"""
-    glb(x)
-
-Return the greatest lower bound estimate (glb) of the reliability as described in
-Woodhouse, B., & Jackson, P. H. (1977). Lower bounds for the reliability of the total score on a test composed of non-homogeneous items: II: A search procedure to locate the greatest lower bound. *Psychometrika, 42*(4), 579-591.
-"""
-function glb(x)
-    n = nitems(x)
-
-    C = cov(x)
-    C̃ = zerodiag(C)
-    upr = diag(C)
-    lwr = zeros(n)
-
-    model = Model(SCS.Optimizer)
-    set_silent(model)
-    set_string_names_on_creation(model, false)
-
-    @variable(model, y[1:n])
-    @expression(model, A, Symmetric(C̃ + diagm(y)))
-
-    @objective(model, Min, sum(y))
-    @constraint(model, lwr .<= y .<= upr)
-    @constraint(model, A in PSDCone())
-
-    optimize!(model)
-
-    if termination_status(model) == OPTIMAL
-        sum_y = sum(value.(y))
-        return (sum(C̃) + sum_y) / sum(C)
-    else
-        error("something went wrong")
-    end
-end
diff --git a/src/reliability/glb.jl b/src/reliability/glb.jl
new file mode 100644
index 0000000..d902b2b
--- /dev/null
+++ b/src/reliability/glb.jl
@@ -0,0 +1,36 @@
+"""
+    glb(m::AbstractMatrix)
+
+Return the greatest lower bound estimate (glb) of the reliability as described in
+$WOODHOUSE1977
+"""
+function glb(m::AbstractMatrix)
+    n = size(m, 2)
+
+    C = cov(m)
+    C̃ = zerodiag(C)
+    upr = diag(C)
+    lwr = zeros(n)
+
+    model = JuMP.Model(SCS.Optimizer)
+
+    set_silent(model)
+    set_string_names_on_creation(model, false)
+
+    @variable(model, y[1:n])
+    @expression(model, A, Symmetric(C̃ + diagm(y)))
+
+    @objective(model, Min, sum(y))
+    @constraint(model, lwr .<= y .<= upr)
+    @constraint(model, A >= 0, PSDCone())
+
+    optimize!(model)
+
+    termination_status(model) == OPTIMAL || error("Failed to optimize GLB of reliability")
+
+    sum_y = sum(value.(y))
+    return (sum(C̃) + sum_y) / sum(C)
+end
+
+struct GLB <: ReliabilityMeasure end
+(method::GLB)(data) = glb(data)
diff --git a/src/reliability/guttman.jl b/src/reliability/guttman.jl
new file mode 100644
index 0000000..12569c8
--- /dev/null
+++ b/src/reliability/guttman.jl
@@ -0,0 +1,221 @@
+"""
+    lambda1(m::AbstractMatrix)
+
+Calculate the lower bound estimate of the reliability L₁ described in $GUTTMAN1945
+"""
+function lambda1(m::AbstractMatrix)
+    sum_sj = sum(var, eachcol(m))
+    st = var(sum(m, dims = 2))
+    λ = 1 - (sum_sj / st)
+    return λ
+end
+
+struct L1 <: ReliabilityMeasure end
+(method::L1)(data) = lambda1(data)
+
+"""
+    lambda2(scale::AbstractScale)
+
+Calculate the lower bound estimate of the reliability lambda₂ described in $GUTTMAN1945
+"""
+function lambda2(m::AbstractMatrix)
+    n = size(m, 2)
+    C = cov(m)
+    zerodiag!(C)
+    st = var(sum(m, dims = 2))
+    λ = lambda1(m) + sqrt(n / (n - 1) * sum(abs2, C)) / st
+    return λ
+end
+
+struct L2 <: ReliabilityMeasure end
+(method::L2)(data) = lambda2(data)
+
+"""
+    lambda3(m::AbstractMatrix)
+
+Calculate the lower bound estimate of the reliability lambda₃ described in $GUTTMAN1945
+"""
+function lambda3(m::AbstractMatrix)
+    n = size(m, 2)
+    λ = n / (n - 1) * lambda1(m)
+    return λ
+end
+
+struct L3 <: ReliabilityMeasure end
+(method::L3)(data) = lambda3(data)
+
+"""
+    alpha(m::AbstractMatrix)
+
+Estimate Cronbach's alpha. `alpha` is an alias for [`lambda3`](@ref).
+"""
+const alpha = lambda3
+
+struct Alpha <: ReliabilityMeasure end
+(method::Alpha)(data) = alpha(data)
+
+"""
+    lambda4(m::AbstractMatrix; type::Symbol = :firstlast)
+
+Return the lower bound estimate of the reliability lambda₄ described in $GUTTMAN1945
+
+The calculation of lambda₄ is based on splitting the test in half.
+It is a lower bound of the reliability no matter how the scale is split.
+
+The split of the scale can be controlled by the `type` keyword argument.
+The following options are available for `type`:
+- `:firstlast`: Split the test by first and last half
+- `:oddeven`: Split the test by odd and even indices
+- `:random`: Split the test by random indices
+
+To get the maximum lower bound see [`maxlambda4`](@ref).
+"""
+function lambda4(m::AbstractMatrix; type::Symbol = :firstlast)
+    splits = splithalf(m; type)
+    st = var(sum(m, dims = 2))
+
+    s1 = var(sum(splits[1], dims = 2))
+    s2 = var(sum(splits[2], dims = 2))
+
+    λ = 2 * (1 - (s1 + s2) / st)
+    return λ
+end
+
+function lambda4(m::AbstractMatrix, is)
+    splits = split(m, is)
+    st = var(sum(m, dims = 2))
+
+    s1 = var(sum(splits[1], dims = 2))
+    s2 = var(sum(splits[2], dims = 2))
+
+    λ = 2 * (1 - (s1 + s2) / st)
+    return λ
+end
+
+"""
+    maxlambda4(m::AbstractMatrix; method = :auto, n_samples = 10_000)
+
+Calculate the maximum lower bound estimate of the reliability lambda₄ described in $GUTTMAN1945
+
+The `method` keyword argument determines the way the bound is estimated. Available options
+are:
+- `:bruteforce`: Calculate lambda₄ for each split-half combination.
+- `:sample`: Calculate lambda₄ for `n_samples` samples of split-half combinations.
+- `:auto` (the default): if the number of items is below 25, `:bruteforce` is applied,
+  `:sample` otherwise.
+
+See also [`lambda4`](@ref).
+"""
+struct Lambda4{F,E,S}
+    statistic::F
+    estimate::E
+    samples::S
+end
+
+Base.show(io::IO, lambda4::Lambda4) = print(io, lambda4.estimate)
+
+function lambda4(
+    statistic::F,
+    m::AbstractMatrix;
+    method = :auto,
+    n_samples = 10_000,
+) where {F}
+    method = method == :auto && size(m, 2) <= 25 ? :bruteforce : :sample
+    samples = lambda4_samples(m; method, n_samples)
+
+    λ = statistic(samples)
+    return Lambda4(statistic, λ, samples)
+end
+
+function lambda4_samples(m::AbstractMatrix; method = :bruteforce, n_samples = 10_000)
+    if method == :bruteforce
+        λ = _lambda4_brute_force(m)
+    elseif method == :sample
+        λ = _lambda4_random(m, n_samples)
+    else
+        error("Unknown method")
+    end
+    return λ
+end
+
+function _lambda4_brute_force(m::AbstractMatrix)
+    n = size(m, 2)
+    n_include = ceil(Int, n / 2)
+    is = axes(m, 2)
+
+    combs = combinations(is, n_include)
+    ncombs = length(combs)
+
+    if ncombs > 1e6
+        @info "Brute forcing $(ncombs) combinatinos. Adjust your expectations accordingly..."
+    end
+
+    λ = [lambda4(m, c) for c in combs]
+
+    return λ
+end
+
+function _lambda4_random(m::AbstractMatrix, n_samples::Int)
+    n = size(m, 2)
+    n_include = ceil(Int, n / 2)
+    is = axes(m, 2)
+    λ = [lambda4(m, sample(is, n_include, replace = false)) for _ in 1:n_samples]
+    return λ
+end
+
+@kwdef struct L4{F} <: ReliabilityMeasure
+    statistic::F = maximum
+    method::Symbol = :auto
+    n_samples::Int = 10_000
+end
+
+function (method::L4)(data)
+    λ = lambda4(
+        method.statistic,
+        data,
+        method = method.method,
+        n_samples = method.n_samples,
+    )
+    return λ.estimate
+end
+
+name(r::L4) = "L4($(r.statistic), :$(r.method), $(r.n_samples))"
+
+"""
+    lambda5(m::AbstractMatrix)
+
+Return the lower bound estimate of the reliability lambda₅ described in $GUTTMAN1945
+"""
+function lambda5(m::AbstractMatrix)
+    C = LowerTriangular(cov(m))
+    zerodiag!(C)
+    sj = sum(abs2, C, dims = 1)
+    Cmax = maximum(sj)
+    st = var(sum(m, dims = 2))
+    return lambda1(m) + 2 * sqrt(Cmax) / st
+end
+
+struct L5 <: ReliabilityMeasure end
+(method::L5)(data) = lambda5(data)
+
+"""
+    lambda6(m::AbstractMatrix)
+
+Return the lower bound estimate of the reliability lambda₆ described in $GUTTMAN1945
+"""
+function lambda6(m::AbstractMatrix)
+    C = cov(m)
+    Cinv = inv(C)
+    smc = 1 .- 1 ./ diag(Cinv)
+    return 1 - sum(1 .- smc) / sum(C)
+end
+
+struct L6 <: ReliabilityMeasure end
+(method::L6)(data) = lambda6(data)
+
+"""
+    GUTTMAN_METHODS
+
+A collection of reliability measures described in $GUTTMAN1945
+"""
+const GUTTMAN_METHODS = [L1(), L2(), L3(), L4(), L5(), L6()]
diff --git a/src/reliability/kuder_richardson.jl b/src/reliability/kuder_richardson.jl
new file mode 100644
index 0000000..586332f
--- /dev/null
+++ b/src/reliability/kuder_richardson.jl
@@ -0,0 +1,28 @@
+"""
+    kr20(m::AbstractMatrix)
+"""
+function kr20(m::AbstractMatrix)
+    n = size(m, 2)
+    item_facilities = mean(m, dims = 1)
+    item_difficulties = 1 .- item_facilities
+    st = var(sum(m, dims = 2))
+    return (n / (n - 1)) * ((st - sum(item_facilities .* item_difficulties)) / st)
+end
+
+struct KR20 <: ReliabilityMeasure end
+(method::KR20)(data) = kr20(data)
+
+"""
+    kr21(m::AbstractMatrix)
+"""
+function kr21(m::AbstractMatrix)
+    n = size(m, 2)
+    item_facilities = mean(m, dims = 1)
+    avg_facility = mean(item_facilities)
+    avg_difficulty = 1 - avg_facility
+    st = var(sum(m, dims = 2))
+    return (n / (n - 1)) * ((st - n * avg_difficulty * avg_facility) / st)
+end
+
+struct KR21 <: ReliabilityMeasure end
+(method::KR21)(data) = kr21(data)
diff --git a/src/reliability/reliability.jl b/src/reliability/reliability.jl
new file mode 100644
index 0000000..13da634
--- /dev/null
+++ b/src/reliability/reliability.jl
@@ -0,0 +1,232 @@
+const DEFAULT_BOOSTRAP_CI = BCaConfInt(0.95)
+const DEFAULT_BOOSTRAP_SAMPLING = BasicSampling(1000)
+
+"""
+    ReliabilityMeasure
+
+A reliability measure is the reliability interface for end users.
+All low-level reliability estimates should define a callable struct `T <: ReliabilityMeasure`
+that takes a single argument, the data, and return the reliability estimate.
+
+## Methods
+- `(method::T)(data)`: The reliability algorithm
+- `name(method::T)`: The name of the reliability algorithm for pretty printing
+"""
+abstract type ReliabilityMeasure <: Function end
+
+name(r::ReliabilityMeasure) = string(nameof(r))
+
+include("guttman.jl")
+include("glb.jl")
+include("kuder_richardson.jl")
+include("ten_berge.jl")
+
+"""
+    PSYCH_METHODS
+
+A collection of reliability measures used by the `psych` R package.
+"""
+const PSYCH_METHODS = [L4(), L6(), L3(), L2()]
+
+"""
+    ReliabilityResult
+
+A data structure that holds results from reliability analysis.
+
+## Methods
+- `bias`
+- `ci_method`
+- `confint`
+- `data`
+- `estimate`
+- `samples`
+- `sampling_method`
+- `stderror`
+"""
+struct ReliabilityResult{D,B,S,C}
+    data::D
+    bootstrap_samples::B
+    sampling_method::S
+    ci_method::C
+end
+
+"""
+    data(result::ReliabilityResult)
+
+Get the data used to calculate `result`.
+"""
+data(result::ReliabilityResult) = result.data
+
+"""
+    sampling_method(result::ReliabilityResult)
+
+Get the sampling method used to calculate the bootstrap samples in `result`.
+"""
+sampling_method(result::ReliabilityResult) = result.sampling_method
+
+"""
+    ci_method(result::ReliabilityResult)
+
+Get the method used to calculate the bootstrap confidence interval in `result`.
+"""
+ci_method(result::ReliabilityResult) = result.ci_method
+
+"""
+    estimate(result::ReliabilityResult)::OrderedDict{String, Float64}
+    estimate(result::ReliabilityResult, method::String)::Float64
+
+Get the point estimate of the reliability.
+"""
+function estimate(result::ReliabilityResult, method::String)
+    samples = result.bootstrap_samples[method]
+    return first(original(samples))
+end
+
+function estimate(result::ReliabilityResult)
+    samples = result.bootstrap_samples
+    return OrderedDict(key => estimate(result, key) for key in keys(samples))
+end
+
+"""
+    confint(result::ReliabilityResult)::OrderedDict{String, Tuple{Float64, Float64}}
+    confint(result::ReliabilityResult, method::String)::Float64
+
+Get the bootstrap confidence intervals for the reliability estimates of `result`.
+"""
+function StatsAPI.confint(result::ReliabilityResult, method::String)
+    samples = result.bootstrap_samples
+    ci = confint(samples[method], result.ci_method)
+    _, lwr, upr = first(ci)
+    return lwr, upr
+end
+
+function StatsAPI.confint(result::ReliabilityResult)
+    samples = result.bootstrap_samples
+    return OrderedDict(key => confint(result, key) for key in keys(samples))
+end
+
+"""
+    bias
+"""
+function Bootstrap.bias(r::ReliabilityResult, method::String)
+    b = Bootstrap.bias(r.bootstrap_samples[method])
+    return first(b)
+end
+
+function Bootstrap.bias(r::ReliabilityResult)
+    return OrderedDict(key => bias(r, key) for key in keys(r.bootstrap_samples))
+end
+
+"""
+    stderror
+"""
+function Bootstrap.stderror(r::ReliabilityResult, method::String)
+    b = Bootstrap.stderror(r.bootstrap_samples[method])
+    return first(b)
+end
+
+function Bootstrap.stderror(r::ReliabilityResult)
+    return OrderedDict(key => stderror(r, key) for key in keys(r.bootstrap_samples))
+end
+
+"""
+    samples
+"""
+function samples(r::ReliabilityResult, method::String)
+    b = straps(r.bootstrap_samples[method])
+    return first(b)
+end
+
+function samples(r::ReliabilityResult)
+    return OrderedDict(key => samples(r, key) for key in keys(r.bootstrap_samples))
+end
+
+"""
+    reliability(m::AbstractMatrix, method::ReliabilityMeasure; kwargs...)
+    reliability(m::AbstractMatrix, methods::Vector{<:ReliabilityMeasure}; kwargs...)
+
+Estimate the reliability of `m` for a given `method` or multiple `methods`.
+
+## Arguments
+- `m`: The input data
+- `method`: A `ReliabilityMeasure` to estimate
+
+## Keyword arguments
+- `ci_method`: The method used to calculate the bootstrap confidence intervals. Defaults to `$(DEFAULT_BOOSTRAP_CI)`
+- `sampling_method`: The method used to draw boostrap samples from `m`. Defaults to `$(DEFAULT_BOOSTRAP_SAMPLING)`
+"""
+function reliability(
+    m::AbstractMatrix,
+    methods::Vector{<:ReliabilityMeasure};
+    ci_method = DEFAULT_BOOSTRAP_CI,
+    sampling_method = DEFAULT_BOOSTRAP_SAMPLING,
+)
+    bootstrap_samples = OrderedDict(
+        name(method) => bootstrap(method, m, sampling_method) for method in methods
+    )
+
+    return ReliabilityResult(m, bootstrap_samples, sampling_method, ci_method)
+end
+
+function reliability(m::AbstractMatrix, method::ReliabilityMeasure; kwargs...)
+    return reliability(m, [method]; kwargs...)
+end
+
+function Base.show(io::IO, mime::MIME"text/plain", result::ReliabilityResult)
+    ci = confint(result)
+
+    fmt = x -> @sprintf "%.2f" x
+
+    ci_method_name = methodname(ci_method(result))
+    ci_level = level(ci_method(result))
+    quant_lwr, quant_upr = quantilesfromlevel(ci_level)
+
+    sampling_method_name = methodname(sampling_method(result))
+    n_samples = nrun(sampling_method(result))
+
+    partable = OrderedDict(
+        "method" => collect(keys(result.bootstrap_samples)),
+        "estimate" => fmt.(values(estimate(result))),
+        "stderror" => fmt.(values(stderror(result))),
+        prettyquantile(quant_lwr) => fmt.(first.(values(ci))),
+        prettyquantile(quant_upr) => fmt.(last.(values(ci))),
+    )
+
+    header = OrderedDict(
+        "1" => [
+            "confidence interval method:",
+            "confidence level:",
+            "bootstrap sampling method:",
+            "bootstrap iterations",
+        ],
+        "2" => [
+            "{cyan}$(ci_method_name){/cyan}",
+            "{magenta}$(ci_level){/magenta}",
+            "{cyan}$(sampling_method_name){/cyan}",
+            "{magenta}$(n_samples){/magenta}",
+        ],
+    )
+
+    print(
+        io,
+        CTTPanel(
+            "",
+            Term.Table(
+                header,
+                box = :NONE,
+                compact = true,
+                show_header = false,
+                columns_justify = :left,
+            ),
+            Term.Table(
+                partable,
+                header_style = "green bold",
+                columns_style = ["bold red", "", "", "", ""],
+                style = "dim",
+                box = :SIMPLE,
+            ),
+            title = "Reliability Analysis",
+        ),
+    )
+    return nothing
+end
diff --git a/src/reliability/ten_berge.jl b/src/reliability/ten_berge.jl
new file mode 100644
index 0000000..eca0a80
--- /dev/null
+++ b/src/reliability/ten_berge.jl
@@ -0,0 +1,72 @@
+"""
+    mu(m::AbstractMatrix, r::Int)
+
+Calculate the lower bound of the reliability mu derived in $TENBERGE1978
+
+## Notes
+- If `r = 0` then mu is equivalent to Cronbach's alpha.
+- If `r = 1` then mu is equivalent to Guttman's lambda₂.
+"""
+function mu(m::AbstractMatrix, r::Int)
+    n = size(m, 2)
+    C = cov(m)
+    zerodiag!(C)
+
+    st = var(sum(m, dims = 2))
+    μ = _mu(C, st, n, r)
+    return μ
+end
+
+function mu(::Type{T}, m::AbstractMatrix, r::Int) where {T}
+    n = size(m, 2)
+    C = T.(cov(m))
+    zerodiag!(C)
+
+    st = var(sum(m, dims = 2))
+    μ = _mu(C, st, n, r)
+    return μ
+end
+
+function _mu(C, st, n, r::Int)
+    r >= 0 || throw(ArgumentError("r must be non-negative."))
+
+    p_sum = zero(eltype(C))
+
+    for h in Iterators.reverse(0:r)
+        p_h = sum(c -> c^(2.0^h), C)
+
+        if h == r
+            p_h *= n / (n - 1)
+        end
+
+        if h == 0
+            p_sum += p_h
+        else
+            p_sum = sqrt(p_sum + p_h)
+        end
+    end
+
+    return p_sum / st
+end
+
+@kwdef struct Mu <: ReliabilityMeasure
+    r::Int
+end
+
+(method::Mu)(data) = mu(data, method.r)
+name(r::Mu) = "Mu($(r.r))"
+
+"""
+    mu_up_to(r::Int)
+
+Generate a vector of reliability measures `Mu` from 0 to `r`.
+
+```jldoctest
+julia> mu_up_to(2)
+3-element Vector{Mu}:
+ (::Mu) (generic function with 1 method)
+ (::Mu) (generic function with 1 method)
+ (::Mu) (generic function with 1 method)
+```
+"""
+mu_up_to(r::Int) = [Mu(i) for i in 0:r]
diff --git a/src/split.jl b/src/split.jl
index b84eb9d..72e6fbc 100644
--- a/src/split.jl
+++ b/src/split.jl
@@ -6,22 +6,12 @@ Split a matrix by arbitrary indices `is`.
 Returns a `Tuple` of matrices `m1`, `m2` with `size(m1, dims=1) == length(is)` and `size(m2, dims=1) == size(m, dims=1) - length(is)`.
 """
 function Base.split(m::AbstractMatrix, is)
+    not_is = setdiff(axes(m, 2), is)
     m1 = view(m, :, is)
-    m2 = view(m, :, Not(is))
+    m2 = view(m, :, not_is)
     return m1, m2
 end
 
-"""
-    split(t::Test, is)
-
-Split a test by arbitrary indices `is`.
-"""
-function Base.split(t::AbstractTest, is)
-    t1 = SubTest(t, is)
-    t2 = SubTest(t, Not(is))
-    return t1, t2
-end
-
 """
     splithalf(m::AbstractMatrix; type::Symbol)
 
@@ -33,13 +23,13 @@ The type of split is determined by `type`
 - `:firstlast`: Split the matrix by first and last half
 - `:random`: Split the matrix by random indices
 """
-function splithalf(x; kwargs...)
-    n = nitems(x)
+function splithalf(m::AbstractMatrix; kwargs...)
+    n = size(m, 2)
     is = getsplitindices(1:n; kwargs...)
-    return split(x, is)
+    return split(m, is)
 end
 
-function getsplitindices(x; type::Symbol=:firstlast)
+function getsplitindices(x; type::Symbol)
     if type == :oddeven
         is = _oddeven_is(x)
     elseif type == :firstlast
@@ -52,10 +42,10 @@ function getsplitindices(x; type::Symbol=:firstlast)
     return is
 end
 
-_oddeven_is(is) = iseven.(is)
-_firstlast_is(is) = is .<= ceil(length(is) / 2)
+_oddeven_is(is) = filter(iseven, is)
+_firstlast_is(is) = filter(i -> i <= ceil(length(is) / 2), is)
 
 function _random_is(is)
-    s = sample(is, ceil(Int, length(is) / 2), replace=false)
-    return [i in s for i in is]
+    s = sample(is, ceil(Int, length(is) / 2), replace = false, ordered = true)
+    return is[s]
 end
diff --git a/src/types.jl b/src/types.jl
deleted file mode 100644
index 0b2e9a3..0000000
--- a/src/types.jl
+++ /dev/null
@@ -1,49 +0,0 @@
-abstract type AbstractTest end
-
-struct Test{T<:Real} <: AbstractTest
-    data::Matrix{T}
-    itemcov::Matrix{Float64}
-    scores::Vector{T}
-end
-
-struct SubTest <: AbstractTest
-    is
-    data
-    itemcov
-    scores
-end
-
-Test(m::AbstractMatrix) = Test{eltype(m)}(m, cov(m), scores(m))
-Test(st::SubTest) = Test{eltype(st.data)}(st.data, st.itemcov, st.scores)
-
-function SubTest(t::Test, is)
-    dview = view(t.data, :, is)
-    return SubTest(
-        is,
-        dview,
-        view(t.itemcov, is, is),
-        scores(dview)
-    )
-end
-
-eachitem(m::AbstractMatrix) = eachcol(m)
-eachitem(t::AbstractTest) = eachcol(t.data)
-
-eachperson(m::AbstractMatrix) = eachrow(m)
-eachperson(t::AbstractTest) = eachrow(t.data)
-
-scores(v::AbstractVector) = v
-scores(m::AbstractMatrix) = vec(sum(m, dims=2))
-scores(t::AbstractTest) = t.scores
-
-responses(m::AbstractMatrix) = m
-responses(t::AbstractTest) = t.data
-responses(x, i::Int) = responses(x)[:, i]
-
-nitems(m::AbstractMatrix) = size(m, 2)
-nitems(t::AbstractTest) = nitems(t.data)
-
-npersons(m::AbstractMatrix) = size(m, 1)
-npersons(t::AbstractTest) = npersons(t.data)
-
-Statistics.cov(t::AbstractTest) = t.itemcov
diff --git a/src/utils.jl b/src/utils.jl
index b4420b6..7a6e218 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -1,7 +1,36 @@
 function zerodiag!(m)
     dims = size(m)
     foreach(i -> m[i, i] = zero(eltype(m)), 1:dims[2])
-    return nothing
+    return m
 end
 
 zerodiag(m) = m - diagm(diag(m))
+
+function CTTPanel(args...; title = nothing)
+    return Term.Panel(
+        args...;
+        title = isnothing(title) ? nothing : "{dim}" * title * "{/dim}",
+        style = "dim",
+        subtitle = "{dim}ClassicalTestTheory.jl{/dim}",
+        subtitle_justify = :right,
+        fit = true,
+    )
+end
+
+const pretty_names = Dict(
+    :lambda1 => "Guttman L₁",
+    :lambda2 => "Guttman L₂",
+    :lambda3 => "Guttman L₃ / Cronbachs α",
+    :lambda4 => "Guttman L₄",
+    :lambda5 => "Guttman L₅",
+    :lambda6 => "Guttman L₆",
+    :glb => "GLB",
+)
+
+prettify(s::Symbol) = pretty_names[s]
+
+
+methodname(x) = typeof(x).name.name
+
+quantilesfromlevel(l::Real) = ((1 - l) / 2, (1 + l) / 2)
+prettyquantile(q::Real) = @sprintf("%.1f", q * 100) * "%-quantile"
diff --git a/test/reliability.jl b/test/reliability.jl
index 279e0af..1ca5305 100644
--- a/test/reliability.jl
+++ b/test/reliability.jl
@@ -1,7 +1,5 @@
 @testset "Reliability" begin
     # set up some irt style test data with correlated responses
-    Random.seed!(859345)
-
     difficulties = randn(10)
     abilities = randn(100)
 
@@ -15,32 +13,33 @@
         end
     end
 
-    t = ClassicalTestTheory.Test(m)
-
-    @testset "equality of Matrix and Test methods" begin
-        @test λ1(m) ≈ λ1(t)
-        @test λ2(m) ≈ λ2(t)
-        @test λ3(m) ≈ λ3(t)
-        @test λ4(m) ≈ λ4(t)
-        @test maxλ4(m, method=:bruteforce) ≈ maxλ4(t, method=:bruteforce)
-        @test λ5(m) ≈ λ5(t)
-        @test λ6(m) ≈ λ6(t)
-
-        @test kr20(m) ≈ kr20(t)
-        @test kr21(m) ≈ kr21(t)
-
-        @test glb(m) ≈ glb(t)
-
+    @testset "lambda" begin
+        # theoretical guarantees
+        @test lambda1(m) > 0
+        @test lambda1(m) <
+              lambda3(m) <=
+              lambda2(m) <=
+              lambda4(maximum, m, method = :bruteforce).estimate
+        @test alpha(m) == lambda3(m)
+        @test lambda4(maximum, m, method = :sample, n_samples = 100).estimate <=
+              lambda4(maximum, m, method = :bruteforce).estimate
     end
 
-    @testset "theoretical guarantees of λ" begin
-        @test λ1(t) > 0
-        @test λ1(t) < λ3(t) <= λ2(t) <= maxλ4(t, method=:bruteforce)
-        @test α(t) == λ3(t)
+    @testset "glb" begin
+        # theoretical guarantees
+        @test lambda4(maximum, m, method = :bruteforce).estimate <= glb(m)
     end
 
-    # theoretical guarantees of glb
-    @testset "theoretical guarantees of glb" begin
-        @test maxλ4(t, method=:bruteforce) <= glb(t)
+    @testset "mu" begin
+        @test_throws ArgumentError mu(m, -1)
+        @test mu(m, 1) ≈ mu(BigFloat, m, 1)
+
+        # theoretical guarantees
+        for r in 1:10
+            @test mu(BigFloat, m, r - 1) <= mu(BigFloat, m, r)
+        end
+
+        @test mu(m, 0) ≈ alpha(m)
+        @test mu(m, 1) ≈ lambda2(m)
     end
 end
diff --git a/test/runtests.jl b/test/runtests.jl
index 6d4ee33..ad90437 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -1,12 +1,8 @@
 using ClassicalTestTheory
 using Distributions
-using Random
-using StatsBase
-using Statistics
 using Test
 
 @testset "ClassicalTestTheory.jl" begin
-    include("types.jl")
     include("reliability.jl")
     include("split.jl")
 end
diff --git a/test/split.jl b/test/split.jl
index 3cc25c1..366220f 100644
--- a/test/split.jl
+++ b/test/split.jl
@@ -1,36 +1,22 @@
 @testset "Test splitting" begin
     m = zeros(4, 4)
-    t = ClassicalTestTheory.Test(m)
 
     @testset "by UnitRange" begin
-        msplit = split(m, 1:2)
-        @test length(msplit) == 2
-        @test size(first(msplit)) == (4, 2)
-        @test size(last(msplit)) == (4, 2)
-
-        tsplit = split(t, 1:2)
-        @test length(tsplit) == 2
-        @test size(first(tsplit).data) == (4, 2)
-        @test size(last(tsplit).data) == (4, 2)
+        s = split(m, 1:2)
+        @test length(s) == 2
+        @test size(first(s)) == (4, 2)
+        @test size(last(s)) == (4, 2)
     end
 
     @testset "by Int" begin
-        msplit = split(m, 3)
-        @test size(first(msplit)) == (4,)
-        @test size(last(msplit)) == (4, 3)
-
-        tsplit = split(t, 3)
-        @test size(first(tsplit).data) == (4,)
-        @test size(last(tsplit).data) == (4, 3)
+        s = split(m, 3)
+        @test size(first(s)) == (4,)
+        @test size(last(s)) == (4, 3)
     end
 
     @testset "by Array" begin
-        msplit = split(m, [1, 3])
-        @test size(first(msplit)) == (4, 2)
-        @test size(last(msplit)) == (4, 2)
-
-        tsplit = split(t, [1, 3])
-        @test size(first(tsplit).data) == (4, 2)
-        @test size(last(tsplit).data) == (4, 2)
+        s = split(m, [1, 3])
+        @test size(first(s)) == (4, 2)
+        @test size(last(s)) == (4, 2)
     end
 end
diff --git a/test/types.jl b/test/types.jl
deleted file mode 100644
index f352ee1..0000000
--- a/test/types.jl
+++ /dev/null
@@ -1,56 +0,0 @@
-@testset "Types" begin
-    @testset "Matrix methods" begin
-        m = [1 0; 0 1; 1 1]
-
-        @test scores(m) == [1, 1, 2]
-
-        @test responses(m) == m
-        @test responses(m, 1) == [1, 0, 1]
-        @test responses(m, 2) == [0, 1, 1]
-        @test_throws BoundsError responses(m, 3)
-
-        @test nitems(m) == 2
-        @test npersons(m) == 3
-    end
-
-    @testset "Test" begin
-        m = [1 0; 0 1; 1 1]
-        t = ClassicalTestTheory.Test(m)
-
-        @test scores(t) == [1, 1, 2]
-        @test responses(t) == m
-        @test responses(t, 1) == [1, 0, 1]
-        @test_throws BoundsError responses(t, 5)
-
-        @test cov(t) == t.itemcov == cov(m)
-    end
-
-    @testset "SubTest" begin
-        m = [1 0; 0 1; 1 1]
-        t = ClassicalTestTheory.Test(m)
-
-        @testset "is::Int" begin
-            st = SubTest(t, 1)
-            @test scores(st) == [1, 0, 1]
-            @test responses(st) == [1, 0, 1]
-            @test responses(st, 1) == [1, 0, 1]
-            @test_throws BoundsError responses(st, 2)
-        end
-
-        @testset "is::UnitRange" begin
-            st = SubTest(t, 1:2)
-            @test scores(st) == [1, 1, 2]
-            @test responses(st) == m
-            @test responses(st, 1) == [1, 0, 1]
-            @test_throws BoundsError responses(st, 3)
-        end
-
-        @testset "is::Vector" begin
-            st = SubTest(t, [1, 2])
-            @test scores(st) == [1, 1, 2]
-            @test responses(st) == m
-            @test responses(st, 1) == [1, 0, 1]
-            @test_throws BoundsError responses(st, 3)
-        end
-    end
-end