1) The document summarizes a study that examined the timing of fundamental frequency (F0) in the Bantu tone language Kinyarwanda. It investigated how F0 timing was affected by tone type, word/phrase position, and tonal context. 2) Analysis of variance (ANOVA) tests were conducted separately for each of the 4 participants to examine effects. Multiple regression analyses found tone type, duration, position, and context accounted for 84-91% of F0 timing variance. 3) The statistical analyses showed F0 peak occurred later in low-to-high vs. high tones and in high vs. high-to-low tones. Phrase position also significantly affected F0

1. F0 Timing in Kinyarwanda
Scott Myers (2003)
Presented by Alexander Aldrich

2. Introduction
 Kinyarwanda is a “Bantu tone language spoken in Rwanda” and is “mutually intelligible with Kirundi,
spoken in neighboring Burundi” (p. 72).
 Can be challenging to obtain many participants due to the location of the population, which is in East
Africa.
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3. Introduction
 Noteworthy comments about the Kinyarwanda language:
 Syllable contrast affected by:
1. tone of syllable (privative—either H (high) or L (no tone), leading to three tone types – HL, LH, or H (i.e. LL).
2. location of tone in the syllable
 Tone anticipation
 hypothesized that “the syllable or mora before a high-toned one is raised in pitch” (p. 73)
Image from p. 73

4. Methodology
Research questions:
 How is F0 timing affected by the following?
 “tone type (H, HL, and LH)
 “phrase position (phrase-final word, non-phrase-final word)
 “word position (word-final syllable, non-word-final syllable)
 “tonal context (no following high tone, or high tone following after 0–3 toneless syllables)” (p. 74)

5. ANOVA
ANOVA:
 The study only includes four participants due to the difficult nature of recruiting speakers of Kinyarwanda;
therefore, a separate ANOVA was ran for each participant for each research question.
 Separate ANOVA for each participant avoids violating the assumption of independence of scores.
 The different scores for each participant are used as part of the error term instead of “subjects.” That is, the
different scores are considered different speakers within each ANOVA for each speaker.
 No need for by-subjects or by-items ANOVA tests since each speaker is treated as a unique experiment.
 Bonferroni adjustment (correction) is applied to avoid familywise error by dividing alpha by the number of
comparisons made for each research question.

6. ANOVA Results (Example)
It is not possible to report all the results in this short presentation due to the complex design of the experiment,
considering 4 ANOVA tests were run for each level of the research question. Presented here are some examples.
Effects of tone type and phrase position (2-factor between-subjects ANOVA)
 Dependent factor: Relative Peak Delay (ms) = “the peak delay divided by the test syllable duration” (p. 77)
 Independent factors: Tone Type (H, HL, LH) and Phrase Position (phrase-final word, non-phrase-final word)
 Alpha set to 0.0125 (Bonferroni adjustment = 0.05/4)
 Fisher’s PLSD
 Follow up tests were performed using Fisher’s PLSD, which is a type of t-test (GraphPad Statistics Guide, 2015), instead of
doing an ANOVA to test the simple effects. The author doesn’t explain why this method was chosen over a traditional t-test
or ANOVA.
 Keppel (1991) discourages the use of Fisher’s method, saying, “In many realistic situations, Fisher’s procedure does not
control error well and should be avoided” (p. 125).
 Additionally, no further detail regarding the test is given except that they were “significant” (p. 80).

7. ANOVA Results (Example)
Effects of tone type and phrase position
(2-factor between-subjects ANOVA)
Results:
 As seen in Table 2 (p. 80), the main effect of Phrase Position is significant for all subjects. The author opts to use a
table to report the ANOVA tests’ results instead of prose due to the number of tests run.
 The interaction of Tone Type by Phrase Position is significant at the Bonferroni level (α=.0125) for all speakers
except for Speaker 1. In fact, in most analyses performed, Speaker 1 appeared to not follow the trend of the other
speakers.
 Planned comparisons using Fisher’s method found, “Relative peak delay was greater for LH than for H, and
greater for H than for HL” (p. 80).
 That is, the relative f0 peak occurred later in Low to High syllable types than it did for simply High tone syllables,
and the f0 peak occurred later in High tone syllables than it did for High to Low syllable types.

8. Linear Regression
Linear Regression
 The author argues that a “… linear regression analysis can be applied to unbalanced data, [therefore] the entire
dataset for each speaker can be included in each regression analysis …” (p. 87).
 Similar to the ANOVA, a separate multiple regression test is ran for each speaker with different dependent
variables. On the next slide is one example.
 Dependent variable: Peak Delay (ms)
 Independent variables: Syllable Duration, Tone Type, Phrase Position, Final, and Following Tone Context

9. Linear Regression
 Table 11 (p. 88) provides the multiple regression equation, the coefficients, the R2 predictor value, and the mean
absolute residual (ms).
 Each different independent factor is broken up as a coefficient and represented in the regression equation. By
adding more independent factors, more variability in the data can be explained.
 “The R2 values indicate that the factors considered accounted for a respectable 84–91% of the variance in f0 peak
location” (p. 88).
 That is, the higher the R2 value, the greater the regression analysis was able to account for the variability in the
data set. In this case, by following the formula for speaker one, for example, one will predict the timing of the f0 in
milliseconds with 91% accuracy when taking into account the factors involved.

10. Conclusion
In sum:
 The timing of the F0 peak is studied for the Kinyarwanda language in regard to several factors including tone type, word
position, phrase position, and tonal context. ANOVA tests are used to determine the F0 timing.
 Follow-up planned comparisons are performed using Fisher’s PLSD, a method whose use is discouraged by Keppel.
 Multiple Regression analyses are carried out to determine how much of the variation in the data the independent factors
were able to predict.
Personal impressions of the statistical analyses:
 The author doesn’t make it explicit in the article whether or not ANOVA is between or within-subjects, but based on the
degrees of freedom reported (and the nature of doing a separate ANOVA counting each score as a subject) it is assumed
that the ANOVA tests were between subjects.
 The author first presents the results of Fisher’s PLSD, then the main effects, then the interactions, instead of presenting
the planned comparisons at the end. The author appeared to interpret all three of the significant findings even if there was
a significant interaction, instead of interpreting only the results of the planned comparisons.
 The paper, while very well done, is evidence of the need to collect data from a large group of participants, which was also
seen with the outlier effects produced by Speaker 1 consistently throughout the experiment.

11. Bibliography
 GraphPad Statistics Guide (2015). Retrieved November 23, 2015, from
http://www.graphpad.com/guides/prism/6/statistics/index.htm?stat_fishers_lsd.htm
 Meier, U. (2006). A note on the power of Fisher's least significant difference procedure. Pharmaceutical
statistics, 5(4), 253-263. Retrieved from http://www.ncbi.nlm.nih.gov/pubmed/17128424
 Keppel, G. (1991). Design and analysis: A researcher's handbook . Prentice-Hall, Inc.
 Foltz, B. [Brandon Foltz]. (2014, December 1). Statistics 101: Multiple Regression (Part 1), The Very Basics
[Video file]. Retrieved from https://www.youtube.com/watch?v=dQNpSa-bq4M