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Standardized Score

Source: R/02_TestItemFunctions.R
sscore.Rd

The standardized score (z-score) indicates how far a student's performance deviates from the mean in units of standard deviation. This function is applicable only to binary response data.

The score is calculated by standardizing the passage rates: $$Z_i = \frac{r_i - \bar{r}}{\sigma_r}$$ where:

  • \(r_i\) is student i's passage rate

  • \(\bar{r}\) is the mean passage rate

  • \(\sigma_r\) is the standard deviation of passage rates

Usage

sscore(U, na = NULL, Z = NULL, w = NULL)

# Default S3 method
sscore(U, na = NULL, Z = NULL, w = NULL)

# S3 method for class 'binary'
sscore(U, na = NULL, Z = NULL, w = NULL)

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.

Value

A numeric vector of standardized scores for each student. The scores follow a standard normal distribution with:

  • Mean = 0

  • Standard deviation = 1

  • Approximately 68% of scores between -1 and 1

  • Approximately 95% of scores between -2 and 2

  • Approximately 99% of scores between -3 and 3

Note

This function is implemented using a binary data compatibility wrapper and will raise an error if used with polytomous data.

The standardization allows for comparing student performance across different tests or groups. A positive score indicates above-average performance, while a negative score indicates below-average performance.

Examples

# using sample dataset
sscore(J5S10)
#>             [,1]
#>  [1,]  0.2656845
#>  [2,]  0.9298956
#>  [3,] -1.7269490
#>  [4,]  0.9298956
#>  [5,] -0.3985267
#>  [6,] -1.0627379
#>  [7,]  0.2656845
#>  [8,] -0.3985267
#>  [9,] -0.3985267
#> [10,]  1.5941068