How Do I Know If I Am Right?

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How Do I Know If I Am Right?

• Checking Quantitative HypothesesSheila
  Embleton, Dorin Uritescu, Eric S. WheelerYork
  University, Toronto, Canada

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Doubts

• For any quantitative result, there is always the
  question Is it right?
• The mathematics
• The application to the subject
• Our understanding of the results
• This is the case
• for trained mathematicians and statisticians
• for linguists with less focus on math and stats.

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Romanian Online Dialect Atlas

• Online access to detailed dialect data
• Search and count functions to find patterns of
  interest
• Dynamic maps to display the results
• And more...

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MDS Analysis

• RODA has analytic tools such as MDS
  (multidimensional scaling)
• MDS displays a 2-D map of a 120-D space of
  dialect distances
• The result is (?) the dialect situation when all
  the data is considered

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Question about MDS

• 1. If you add, subtract or change some of the
  data, what happens to this map?
• 2. What is the right data to use to define a
  dialect area

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Stability of MDS

• Look at the underlying distance matrices
• Take random samples of data, from 98 to 10 of
  the original data (10 runs at each level)
• Compare the variation in distance matrices

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Variation
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Variation
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Result

• A partial-data matrices are closer to the
  full-data-matrix than to the extremes of their
  set
• Variation in partial-data matrices grows as their
  share of the data gets smaller
• Small changes in the data set (editorial changes,
  data entry errors) do not change the MDS picture
  much
• You will not get a startlingly different view of
  the data by tweaking the data
• The MDS picture is stable

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2. What data to use?

• In our Finnish (and English) studies, geography
  was close to linguistic distance.
• geographically local area were linguistically
  close
• broad geographical areas were recognizable in the
  the linguistic data
• The correlation was obvious (if not exact)

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Finnish
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North-West Romanian all data
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Interpretive Data

• Finnish and English studies used
  interpretations of the data
• When we used interpretations of the Romanian
  data, the dialects were more obvious and more in
  keeping with traditional analyses

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MDS on 237 Interpretive Maps
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MDS on 237 Interpretive Maps 2
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Quantitative Measures Raised, word-final /e/ vs
schwa

• Data from
• 407 maps
• Field 1
• Raised /e/ (horizontal)
• Raised schwa (vertical)
• Raised schwa is also wide-spread but does not
  always coincide with raised /e/
• (cf. 158, 159)

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Quantitative Measures

• Examples
• Is there vowel raising? (Answer can cover many
  degrees of raising)
• How many occurrences of syllabic /u/ vs.
  non-syllabic /u/ (Answers range from 0 to 400)

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Quantity in Dialect Structure

• At any level of dialect structure, the
  distinction between regions can be variable
  because of
• The quantitative nature of what is being measured
  
• The quantity of occurrences
• Where we choose to set the threshold.
• This threshold is part of the dialect structure
  too.

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Dialect Structure

• Hierarchy of levels
• Ground level, intermediate levels, top level
• Thresholds for variable measures
• Views of the whole structure
• View dialect map at a given level and threshold
• MDS can provide one top-level view, where every
  measured features has equal weight

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Lessons Learned

• 1. Simulations can illustrate the properties of
  our analytic approaches, and confirm the validity
  of what we are doing.
• We need to do this.
• 2. Quantitative studies are sensitive to
• What we measure (raw data vs interpretations)
• How we measure (thresholds)
• 3. With more data and more numbers, we get a
  richer view of the subject
• We need more imagination to understand it