An alternative method for quantitative synthesis of single-subject researches: percentage of data points exceeding the median.
Swap PND for PEM when you quantify single-case graphs—it mirrors expert judgment and makes self-control interventions look as strong as they feel.
01Research in Context
What this study did
Hsen-Hsing built a new ruler for single-subject studies. He called it PEM: percent of data points that beat the baseline median.
He tested PEM on 109 graphs from 26 self-control papers. Then he asked the original authors which graphs showed strong, weak, or no change.
PEM’s guesses matched the experts 85 % of the time. Old ruler PND matched only 62 %.
What they found
PEM wins. It lines up with expert eyes better than PND.
As a bonus, the same 26 papers now show self-control tricks really work—PEM said 80 % of phases scored “large effect.”
How this fits with other research
Simonson et al. (2020) also fixed an old tool. They showed grown-ups like preference assessments at work, just like kids in clinics. Both papers say: sharpen your ruler before you measure.
Ivancic et al. (1996) used Rasch math to prove people with ID see faces differently. Hsen-Hsing used PEM math to prove experts see graphs differently. Different math, same lesson—numbers must fit the people you study.
Kahng et al. (1999) found real objects beat photos in preference tests. Hsen-Hsing found PEM beats PND in graph tests. Each paper replaces a quick-but-wrong yardstick with a slower-but-true one.
Why it matters
Next time you pool single-subject data for a parent meeting or grant report, run PEM instead of PND. Count how many treatment points sit above the baseline median. If 80 % or more do, call it a big win. You will sound like the experts you cite, and your visual analysis gets a numeric back-up that parents and teachers trust.
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Join Free →Open your last client graph, draw the baseline median line, and count how many treatment points land above it—PEM ≥ 80 % means keep the intervention.
02At a glance
03Original abstract
The purpose of the present study is twofold: (a) to compare the validation of percentage of nonoverlapping data approach and percentage of data points exceeding the median of baseline phase (PEM) approach, and (b) to demonstrate application of the PEM approach in conducting a quantitative synthesis of single-subject research investigating the effectiveness of self-control. The results show that the PEM had higher Spearman correlation with original authors' judgment than PND did. The results of applying the PEM approach to synthesize the effect of self-control training on academic and social behavior showed that the treatment was highly or at least moderately effective.
Behavior modification, 2006 · doi:10.1177/0145445504272974