## Results

## Weighted Average

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

## Tau-U

Tau-U is a method for measuring data non-overlap between two phases (A and B). It is a “distribution free” nonparametric technique, with statistical power of 91% to 95% of (OLS) linear regression when data conform to parametric assumptions. When data do not do that (common in single case research), then the power of Tau-U can exceed the parametric techniques to 115%. So this is an index well-suited for small datasets. Tau-U follows the “S” sampling distribution (as does Mann-Whitney U and Kendall’s Rank Correlation), so p-values and confidence intervals are available. Tau-U is a novel calculation method, but rests firmly on those two nonparametric methods. Tau-U has multiple options. Most common: 1. simple non-overlap, 2. simple non-overlap controlling for positive baseline trend, 3. improvement by nonoverlap plus phase B trend. This web-based application now includes only #1, but will soon be expanded to #2.

A strength of this web application is the ability to analyze data for several phase contrasts from a single design independently. Then the software permits them to be properly averaged for an overall or omnibus effect size (Tau). For more detailed explanations, references and field tests regarding Tau-U, please see Parker, R.I., Vannest, K.J., Davis, J.L., Sauber, S.B. (2010). Combining non-overlap and trend for single case research: Tau-U.Behavior Therapy. 42, 284–299. DOI: 10.1016/j.beth.2010.08.006.

- Data are input in up to 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. It is assumed in each contrast that the baseline phase is to the left, and treatment phase to the right. Otherwise, the positive/negative sign of results must be reversed.
- Click “Contrast” button. Directly below will be provided results for that contrast. If “correct baseline” is checked prior to the Contrast, then results will reflect control of confounding baseline trend, assuming the baseline is the left-hand phase of the two.
- 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 Tau-U effect sizes are weighted averages, where weights are the inverse of their variances. The combined SDTau is the square root of the sum of Tau variances involved.
- The final “to 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.