exametrika (version 1.6.0)

TestStatistics: Simple Test Statistics

Description

Calculates descriptive statistics for test scores, providing a comprehensive summary of central tendency, variability, and distribution shape. Different statistics are calculated based on the data type (binary, ordinal, rated, or nominal).

Usage

TestStatistics(U, na = NULL, Z = NULL, w = NULL)
# S3 method for default
TestStatistics(U, na = NULL, Z = NULL, w = NULL)
# S3 method for binary
TestStatistics(U, na = NULL, Z = NULL, w = NULL)
# S3 method for ordinal
TestStatistics(U, na = NULL, Z = NULL, w = NULL)

Value

The returned object depends on the data type:

For binary data, a list of class c("exametrika", "TestStatistics") containing:

TestLength

Length of the test. The number of items included in the test.

SampleSize

Sample size. The number of rows in the dataset.

Mean

Average number of correct answers.

SEofMean

Standard error of mean.

Variance

Variance of test scores.

SD

Standard Deviation of test scores.

Skewness

Skewness of score distribution (measure of asymmetry).

Kurtosis

Kurtosis of score distribution (measure of tail extremity).

Min

Minimum score.

Max

Maximum score.

Range

Range of scores (Max - Min).

Q1

First quartile. Same as the 25th percentile.

Median

Median. Same as the 50th percentile.

Q3

Third quartile. Same as the 75th percentile.

IQR

Interquartile range. Calculated by subtracting Q1 from Q3.

Stanine

Stanine score boundaries, see stanine.

For ordinal and rated data, the function calls ScoreReport and returns its result. See ScoreReport for details of the returned object.

For nominal data, an error is returned as this function does not support nominal data.

Arguments

U

Either an object of class "exametrika" or raw data. When raw data is given, it is converted to the exametrika class with the dataFormat function.

na

Values to be treated as missing values.

Z

Missing indicator matrix of type matrix or data.frame. Values of 1 indicate observed responses, while 0 indicates missing data.

w

Item weight vector specifying the relative importance of each item.

Examples

# Basic usage
stats <- TestStatistics(J15S500)
print(stats)

# Extract specific statistics
cat("Mean score:", stats$Mean, "\n")
cat("Standard deviation:", stats$SD, "\n")

# View score distribution summary
summary_stats <- data.frame(
  Min = stats$Min,
  Q1 = stats$Q1,
  Median = stats$Median,
  Mean = stats$Mean,
  Q3 = stats$Q3,
  Max = stats$Max
)
print(summary_stats)