Summarizing Functional Analysis of Variance Fits

summary method for class fanova. Function returning a summary of the results of IWT for the test on a functional analysis of variance: minimum IWT-adjusted p-values of the F-tests on the whole model and on each factor are reported.

Usage

# S3 method for class 'fanova'
summary(object, ...)

Arguments

object: An object of class fanova, usually, a result of a call to functional_anova_test().
...: Further arguments passed to or from other methods.

Value

No value returned. The function summary.fanova() computes and returns a list of summary statistics of the fitted functional analysis of variance given in object, using the component call from its arguments, plus:

factors: A \(L \times 1\) matrix with columns for the factors of ANOVA, and corresponding (two-sided) IWT-adjusted minimum p-values of the corresponding tests of significance (i.e., the minimum p-value over all p basis components used to describe functional data).
R2: Range of the functional R-squared.
ftest: IWT-adjusted minimum p-value of functional F-test.

References

Pini, A., & Vantini, S. (2017). Interval-wise testing for functional data. Journal of Nonparametric Statistics, 29(2), 407-424.

Pini, A., Vantini, S., Colosimo, B. M., & Grasso, M. (2018). Domain‐selective functional analysis of variance for supervised statistical profile monitoring of signal data. Journal of the Royal Statistical Society: Series C (Applied Statistics) 67(1), 55-81.

Abramowicz, K., Hager, C. K., Pini, A., Schelin, L., Sjostedt de Luna, S., & Vantini, S. (2018). Nonparametric inference for functional‐on‐scalar linear models applied to knee kinematic hop data after injury of the anterior cruciate ligament. Scandinavian Journal of Statistics 45(4), 1036-1061.

Examples

temperature <- rbind(NASAtemp$milan, NASAtemp$paris)
groups <- c(rep(0, 22), rep(1, 22))

# Performing the IWT
IWT_result <- functional_anova_test(
  temperature ~ groups,
  B = 10L,
  correction = "IWT"
)
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#> ── Creating the p-value matrix: end of row 246 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 247 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 248 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 249 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 250 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 251 out of 365 ──────────────────────
#> 
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#> 
#> ── Creating the p-value matrix: end of row 253 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 254 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 255 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 256 out of 365 ──────────────────────
#> 
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#> 
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#> 
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#> 
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#> 
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#> 
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#> 
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#> 
#> ── Creating the p-value matrix: end of row 264 out of 365 ──────────────────────
#> 
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#> 
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#> 
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#> 
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#> 
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#> 
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#> 
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#> 
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#> 
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#> 
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#> 
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#> 
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#> 
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#> 
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#> 
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#> 
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#> 
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#> 
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#> 
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#> 
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#> 
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#> 
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#> 
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#> 
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#> 
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#> 
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#> 
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#> 
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#> 
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#> 
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#> 
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#> 
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#> 
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#> 
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#> 
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#> 
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#> 
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#> 
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#> 
#> ── Creating the p-value matrix: end of row 305 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 306 out of 365 ──────────────────────
#> 
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#> 
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#> 
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#> 
#> ── Creating the p-value matrix: end of row 310 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 311 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 312 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 313 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 314 out of 365 ──────────────────────
#> 
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#> 
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#> 
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#> 
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#> 
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#> 
#> ── Creating the p-value matrix: end of row 320 out of 365 ──────────────────────
#> 
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#> 
#> ── Creating the p-value matrix: end of row 322 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 323 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 324 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 325 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 326 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 327 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 328 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 329 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 330 out of 365 ──────────────────────
#> 
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#> 
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#> 
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#> 
#> ── Creating the p-value matrix: end of row 334 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 335 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 336 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 337 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 338 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 339 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 340 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 341 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 342 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 343 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 344 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 345 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 346 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 347 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 348 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 349 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 350 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 351 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 352 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 353 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 354 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 355 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 356 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 357 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 358 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 359 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 360 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 361 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 362 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 363 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 364 out of 365 ──────────────────────
#> 
#> ── Creating the p-value matrix: end of row 365 out of 365 ──────────────────────
#> 
#> ── Interval-Wise Testing completed ─────────────────────────────────────────────

# Summary of the IWT results
summary(IWT_result)
#> $call
#> iwt_aov(formula = formula, dx = dx, n_perm = B, method = method, 
#>     recycle = recycle)
#> 
#> $factors
#>        Minimum p-value    
#> groups               0 ***
#> 
#> $R2
#>               Range of functional R-squared
#> Min R-squared                  3.390203e-05
#> Max R-squared                  5.399620e-01
#> 
#> $ftest
#>   Minimum p-value    
#> 1               0 ***
#>