Equate test scores under the equivalent or non-equivalent group with anchor test design.
-
SG (Single Group design)
- Linear
- Mean
- Equipercentile
-
NEAT (Non-Equivalent group design with Anchor Test design)
- Tucker (Linear equating under some assumptions)
- Braun & Holland (Linear equating using synthetic population)
- Chained Linear (also Mean)
- Chained Equipercentile
- Frequency Estimation (Equipercentile equating using synthetic population)
-
Presmoothing
- Log linear smoothing with an arbitrary degree.
-
Kernel smoothong
- Gaussian kernel is only supported now.
- The optimal bandwidth can be estimated.
- Prepare data set. Integer or Float vector.
using Distributions, Random
Random.seed!(1234)
X = rand(BetaBinomial(100, 4, 10), 500);
Y = rand(BetaBinomial(100, 6, 10), 500);
- Convert the data vector to
FreqTab
# `data` must be Real vector
julia> ftX = freqtab(X; scale = 0:1:100)
Frequency table stats.
N : 500
Missing : 0
min : 1
maxs : 71
μ : 28.39000
σ : 12.68921
kurtosis : 0.00127
skewness : 0.52615
julia> ftY = freqtab(Y; scale = 0:1:100)
Frequency table stats.
N : 500
Missing : 0
min : 6
maxs : 77
μ : 37.04000
σ : 13.11115
kurtosis : -0.44152
skewness : 0.22442
- Presmoothing by using
presmoothing - (Optional) Continuization by using
KernelSmoothing - Equate score X to scale Y by the arbitrary method.
# Linear Equating
julia> eq_lin = Linear(ftX, ftY)
Equating design: EG
Equated method: Linear.
To show the table, extract `table` element.
# Equipercentile equating
julia> eq_eqp = Equipercentile(ftX, ftY)
Equating design: EG
Equated method: Equipercentile(lower).
To show the table, extract `table` element.
- Evaluate SEE (Standard Error of Equating). Now, Only
BasicSampling(n)is supported.
julia> using Bootstrap, Random
julia> Random.seed!(1234)
julia> @time bootse_lin = bootstrap(x -> coef(Linear(x...)), eq_lin.data, BasicSampling(1000))
1.727280 seconds (10.12 M allocations: 458.347 MiB, 5.56% gc time, 63.60% compilation time)
Bootstrap Sampling
Estimates:
Var │ Estimate Bias StdError
│ Float64 Float64 Float64
─────┼─────────────────────────────────
1 │ 1.03325 0.000560431 0.043795
2 │ 7.70597 0.00756638 1.2771
Sampling: BasicSampling
Samples: 1000
Data: NamedTuple{(:X, :Y), Tuple{Equate.FreqTab, Equate.FreqTab}}: { X 500 × Y 500 }