sscore {exametrika} | R Documentation |
Standardized Score
Description
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 |
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)