The choice of two-sample test statistic
Jan Vávra
Exercise 6 (9th December 2019)
To succesfully complete the following task use the following shiny app.
Use this shiny app to fill the following table with the symbols:
- 1 = the best choice,
- 2 = works well,
- 3 = not good, not bad,
- 4 = inappropriate,
- 5 = completely wrong choice,
- ? = no idea.
This symbol will represent your opinion on the choice of this particular two-sample statistic in the case of violation null hypothesis described by the plot of hazard functions.
| Statistic | Weight function | \(G(\rho, \gamma)\) |  |
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|---|---|---|---|---|---|---|---|---|---|---|---|
| Logrank (Mantel) | \(1\) | \(G(0,0)\) | |||||||||
| Gehan-Wilcoxon | \(\overline{Y}(t)\) | — | |||||||||
| Prentice-Wilcoxon | \(\widehat{S}(t-)\) | \(G(1,0)\) | |||||||||
| — | \(\left[1-\widehat{S}(t-)\right]^{\gamma}\) | \(G(0, \gamma)\) | |||||||||
| Fleming-Harrington | \(0 < \rho \leq \gamma\) | \(G(\rho, \gamma)\) |