The optimal boundary lines for the "upper" and "lower" areas of distribution of scores will demarcate the upper and lower 27% of distribution of scores if normal, 33% if platykurtic
0.27/n, wherein n = no. of students
Interrater Reliability Coefficient
0 means 0% of the variance in the scores assigned by the scorers was attributed to true differences and 100% to error
Value
P-Value ≤ ∞, reject null hypothesis
P-Value ≥ ∞, accept null hypothesis
Mean
The average of all the raw scores
Equal to the sum of the observations divided by the number of observations
Interval and ratio data (when normal distribution)
Point of least squares
Balance point for the distribution
Susceptible to outliers
Median
The middle score of the distribution
Ordinal, Interval, Ratio
For extreme scores, use median
Identical for sample and population
Also used when there has an unknown or undetermined score
Used in "open-ended" categories (e.g., 5 or more, more than 8, at least 10)
For ordinal data
If the distribution is skewed for ratio/interval data, use median
Mode
Most frequently occurring score in the distribution
Bimodal Distribution: if there are two scores that occur with highest frequency
Not commonly used
Useful in analyses of qualitative or verbal nature
For nominal scales, discrete variables
Value of the mode gives an indication of the shape of the distribution as well as a measure of central tendency
Range
Equal to the difference between highest and the lowest score
Provides a quick but gross description of the spread of scores
When its value is based on extreme scores of the distribution, the resulting description of variation may be understated or overstated
Interquartile Range
Difference between Q1 and Q2
Semi-Quartile Range
Interquartile range divided by 2
Standard Deviation
Approximation of the average deviation around the mean
Gives detail of how much above or below a score to the mean
Equal to the square root of the average squared deviations about the mean
Equal to the square root of the variance
Distance from the mean
Variance
Equal to the arithmetic mean of the squares of the differences between the scores in a distribution and their mean
Average squared deviation around the mean
Percentile or Percentile Rank
Not linearly transformable, converged at the middle and the outer ends show large interval
Expressed in terms of the percentage of persons in the standardization sample who fall below a given score
Indicates the individual's relative position in the standardization sample
Essential in creating normalized standardized scores
Quartile
Dividing points between the four quarters in the distribution
Specific point
Quarter: refers to an interval
Decile/STEN
Divide into 10 equal parts
A measure of the asymmetry of the probability distribution of a real-valued random about its mean