## Results

## Weighted Average

Label | Tau | Var-Tau | Z | P-Value | CI 85% | CI 90% | CI 95% |

**NAP**(Nonoverlap of All Pairs) is a nonparametric technique for measuring nonoverlap or “dominance” for two phases. It does not include data trend. NAP is appropriate for nearly all data types and distributions, including dichotomous data. NAP has good power efficiency–about 91-94% that of linear regression for “conforming” data, and greater than 100% for highly skewed, multi-modal data. NAP is equal to the empirical AUC (Area Under the Curve) from a ROC test. Alternately, it can be derived from a Mann-Whitney U test. Also, it can be calculated by hand from small datasets. Strengths of NAP are its simplicity, its reflection of visual nonoverlap, and its statistical power. In many cases it is a better solution than tests of Mean or even Median differences across phases. [Parker, R.I., & Vannest, K.J. (2009). An improved effect size for single case research: Non-overlap of all pairs (NAP). Behavior Therapy. 40(4), 357-367. ]

- Data are input in the ten windows at the page top, each headed by a label box and a selection check.
- Type or paste data from just one phase in each input window, and label each phase above, e.g. A1, B3, 2A1, etc.
- Select only two phases for a first contrast. Select by checking beside a label.
- Click “Contrast” button. Directly below will be provided results for that contrast.
- Repeat steps 3 and 4, making all phase contrasts desired. All will be saved below.
- To combine contrasts for a single design, use the check boxes to the left of their results (left of “id”), near the middle of the page. Select as many contrast results as desired. Then click “Combine” button below. Combined NAP effect sizes are weighted averages, where weights are the inverse of their variances. The combined SD for NAP is the square root of the sum of NAP variances involved.
- The final “weighted average” button permits any combination of individual contrasts or combined contrasts, by first checking them above. The combination algorithms are the same as in #6 above.