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The Significance of Result Differences. Why Significance Tests?. everybody knows we have to test the significance of our results but do we really? evaluation results are valid for data from specific corpus extracted with specific methods for a particular type of collocations

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why significance tests
Why Significance Tests?
  • everybody knows we have to test the significance of our results
    • but do we really?
  • evaluation results are valid for
    • data from specific corpus
    • extracted with specific methods
    • for a particular type of collocations
    • according to the intuitions of one particular annotator (or two)
why significance tests1
Why Significance Tests?
  • significance tests are about generalisations
  • basic question:"If we repeated the evaluation experiment (on similar data), would we get the same results?"
  • influence of source corpus, domain, collocation type and definition, annotation guidelines, ...
a different perspective
A Different Perspective
  • pair types are described by tables (O11, O12, O21, O22) coordinates in 4-D space
  • O22 is redundant becauseO11 + O12 + O21 + O22 = N
  • can also describe pair type by joint and marginal frequencies(f, f1, f2) = "coordinates" coordinates in 3-D space
a different perspective1
A Different Perspective
  • data set = cloud of points in three-dimensional space
  • visualisation is "challenging"
  • many association measures depend on O11and E11 only(MI, gmean, t-score, binomial)
  • projection to (O11,E11) coordinates in 2-D space(ignoring the ratio f1 / f2)
n best lists in parameter space
N-best Lists in Parameter Space
  • N-best List for AM  includes all pair types where score   c(threshold c obtained from data)
  • {  c} describes a subset of the parameter space
  • for a sound association measure isoline { = c} is lower boundary(because scores should increase with O11 for fixed value of E11)
comparing precision values
Comparing Precision Values
  • number of TPs and FPs for 1000-best lists
mcnemar s test
McNemar's Test

+ = in 1000-best list – = not in 1000-best list

  • ideally: all TPs in 1000-best list (possible!)
  • H0: differences between AMs are random
mcnemar s test1
McNemar's Test

+ = in 1000-best list – = not in 1000-best list

> mcnemar.test(tbl)

  • p-value < 0.001  highly significant
lowest frequency data samples
Lowest-Frequency Data: Samples
  • Too much data for full manual evaluation  random samples
  • AdjN data
    • 965 pairs with f = 1 (15% sample)
    • manually identified 31 TPs (3.2%)
  • PNV data
    • 983 pairs with f < 3 (0.35% sample)
    • manually identified 6 TPs (0.6%)
lowest frequency data samples1
Lowest-Frequency Data: Samples
  • Estimate proportion p of TPs among all lowest-frequency data
  • Confidence set from binomial test
  • AdjN: 31 TPs among 965 items
    • p  5% with 99% confidence
    • at most  320 TPs
  • PNV: 6 TPs among 983-items
    • p  1.5% with 99% confidence
    • there might still be  4200 TPs !!
n best lists for lowest frequency data
N-best Lists for Lowest-Frequency Data
  • evaluate 10,000-best lists
    • to reduce manual annotation work,take 10% sample from each list(i.e. 1,000 candidates for each AM)
  • precision graphs for N-best lists
    • up to N = 10,000 for the PNV data
  • 95% confidence estimates for precision of best-performing AM (from binomial test)