disp: Calculate parts-based dispersion measures

In tlda: Tools for Language Data Analysis

Calculate parts-based dispersion measures

Description

This function calculates a number of parts-based dispersion measures and allows the user to choose the directionality of scaling, i.e. whether higher values denote a more even or a less even distribution. It also offers the option of calculating frequency-adjusted dispersion scores.

Usage

disp(
  subfreq,
  partsize,
  directionality = "conventional",
  freq_adjust = FALSE,
  freq_adjust_method = "even",
  unit_interval = TRUE,
  digits = NULL,
  verbose = TRUE,
  print_score = TRUE,
  suppress_warning = FALSE
)

Arguments

subfreq	A numeric vector of subfrequencies, i.e. the number of occurrences of the item in each corpus part
partsize	A numeric vector specifying the size of the corpus parts
directionality	Character string indicating the directionality of scaling. See details below. Possible values are "conventional" (default) and "gries"
freq_adjust	Logical. Whether dispersion score should be adjusted for frequency (i.e. whether frequency should be 'partialed out'); default is FALSE
freq_adjust_method	Character string indicating which method to use for devising dispersion extremes. See details below. Possible values are "even" (default) and "pervasive"
unit_interval	Logical. Whether frequency-adjusted scores that exceed the limits of the unit interval should be replaced by 0 and 1; default is TRUE
digits	Rounding: Integer value specifying the number of decimal places to retain (default: no rounding)
verbose	Logical. Whether additional information (on directionality, formulas, frequency adjustment) should be printed; default is TRUE
print_score	Logical. Whether the dispersion score should be printed to the console; default is TRUE
suppress_warning	Logical. Whether warning messages should be suppressed; default is FALSE

Details

This function calculates dispersion measures based on two vectors: a set of subfrequencies (number of occurrences of the item in each corpus part) and a matching set of part sizes (the size of the corpus parts, i.e. number of word tokens).

• Directionality: The scores for all measures range from 0 to 1. The conventional scaling of dispersion measures (see Juilland & Chang-Rodriguez 1964; Carroll 1970; Rosengren 1971) assigns higher values to more even/dispersed/balanced distributions of subfrequencies across corpus parts. This is the default. Gries (2008) uses the reverse scaling, with higher values denoting a more uneven/bursty/concentrated distribution; use directionality = "gries" to choose this option.

• Frequency adjustment: Dispersion scores can be adjusted for frequency using the min-max transformation proposed by Gries (2022: 184-191; 2024: 196-208). The frequency-adjusted score for an item considers the lowest and highest possible level of dispersion it can obtain given its overall corpus frequency as well as the number (and size) of corpus parts. The unadjusted score is then expressed relative to these endpoints, where the dispersion minimum is set to 0, and the dispersion maximum to 1 (expressed in terms of conventional scaling). The frequency-adjusted score falls between these bounds and expresses how close the observed distribution is to the theoretical maximum and minimum. This adjustment therefore requires a maximally and a minimally dispersed distribution of the item across the parts. These hypothetical extremes can be built in different ways. The method used by Gries (2022, 2024) uses a computationally expensive procedure that finds the distribution that produces the highest value on the dispersion measure of interest. The current function constructs extreme distributions in a different way, based on the distributional features pervasiveness ("pervasive") or evenness ("even"). You can choose between these with the argument freq_adjust_method; the default is even. For details and explanations, see vignette("frequency-adjustment").

  • To obtain the lowest possible level of dispersion, the occurrences are either allocated to as few corpus parts as possible ("pervasive"), or they are assigned to the smallest corpus part(s) ("even").

  • To obtain the highest possible level of dispersion, the occurrences are either spread as broadly across corpus parts as possible ("pervasive"), or they are allocated to corpus parts in proportion to their size ("even"). The choice between these methods is particularly relevant if corpus parts differ considerably in size. See documentation for find_max_disp() and vignette("frequency-adjustment").

The following measures are computed, listed in chronological order (see details below):

• R_{rel} (Keniston 1920)

• D (Juilland & Chang-Rodriguez 1964)

• D_2 (Carroll 1970)

• S (Rosengren 1971)

• D_P (Gries 2008; modification: Egbert et al. 2020)

• D_A (Burch et al. 2017)

• D_{KL} (Gries 2024)

In the formulas given below, the following notation is used:

• k the number of corpus parts

• T_i the absolute subfrequency in part i

• t_i a proportional quantity; the subfrequency in part i divided by the total number of occurrences of the item in the corpus (i.e. the sum of all subfrequencies)

• W_i the absolute size of corpus part i

• w_i a proportional quantity; the size of corpus part i divided by the size of the corpus (i.e. the sum of the part sizes)

• R_i the normalized subfrequency in part i, i.e. the subfrequency divided by the size of the corpus part

• r_i a proportional quantity; the normalized subfrequency in part i divided by the sum of all normalized subfrequencies

• N corpus frequency, i.e. the total number of occurrence of the item in the corpus

Note that the formulas cited below differ in their scaling, i.e. whether 1 reflects an even or an uneven distribution. In the current function, this behavior is overridden by the argument directionality. The specific scaling used in the formulas below is therefore irrelevant.

R_{rel} refers to the relative range, i.e. the proportion of corpus parts containing at least one occurrence of the item.

D denotes Juilland's D and is calculated as follows (this formula uses conventional scaling); \bar{R_i} refers to the average over the normalized subfrequencies:

1 - \sqrt{\frac{\sum_{i = 1}^k (R_i - \bar{R_i})^2}{k}} \times \frac{1}{\bar{R_i} \sqrt{k - 1}}

D_2 denotes the index proposed by Carroll (1970); the following formula uses conventional scaling:

\frac{\sum_i^k r_i \log_2{\frac{1}{r_i}}}{\log_2{k}}

S is the dispersion measure proposed by Rosengren (1971); the formula uses conventional scaling:

\frac{(\sum_i^k r_i \sqrt{w_i T_i}}{N}

D_P represents Gries's deviation of proportions; the following formula is the modified version suggested by Egbert et al. (2020: 99); it implements conventional scaling (0 = uneven, 1 = even) and the notation min\{w_i: t_i > 0\} refers to the w_i value among those corpus parts that include at least one occurrence of the item.

1 - \frac{\sum_i^k |t_i - w_i|}{2} \times \frac{1}{1 - min\{w_i: t_i > 0\}}

D_A is a measure introduced into dispersion analysis by Burch et al. (2017). The following formula is the one used by Egbert et al. (2020: 98); it relies on normalized frequencies and therefore works with corpus parts of different size. The formula represents conventional scaling (0 = uneven, 1 = even):

1 - \frac{\sum_{i = 1}^{k-1} \sum_{j = i+1}^{k} |R_i - R_j|}{\frac{k(k-1)}{2}} \times \frac{1}{2\frac{\sum_i^k R_i}{k}}

The current function uses a different version of the same formula, which relies on the proportional r_i values instead of the normalized subfrequencies R_i. This version yields the identical result:

1 - \frac{\sum_{i = 1}^{k-1} \sum_{j = i+1}^{k} |r_i - r_j|}{k-1}

D_{KL} refers to a measure proposed by Gries (2020, 2021); for standardization, it uses the odds-to-probability transformation (Gries 2024: 90) and represents Gries scaling (0 = even, 1 = uneven):

\frac{\sum_i^k t_i \log_2{\frac{t_i}{w_i}}}{1 + \sum_i^k t_i \log_2{\frac{t_i}{w_i}}}

Value

A numeric vector of seven dispersion scores

Author(s)

Lukas Soenning

References

Burch, Brent, Jesse Egbert & Douglas Biber. 2017. Measuring and interpreting lexical dispersion in corpus linguistics. Journal of Research Design and Statistics in Linguistics and Communication Science 3(2). 189–216. \Sexpr[results=rd]{tools:::Rd_expr_doi("doi:10.1558/jrds.33066")}

Carroll, John B. 1970. An alternative to Juilland’s usage coefficient for lexical frequencies and a proposal for a standard frequency index. Computer Studies in the Humanities and Verbal Behaviour 3(2). 61–65. \Sexpr[results=rd]{tools:::Rd_expr_doi("doi:10.1002/j.2333-8504.1970.tb00778.x")}

Egbert, Jesse, Brent Burch & Douglas Biber. 2020. Lexical dispersion and corpus design. International Journal of Corpus Linguistics 25(1). 89–115. \Sexpr[results=rd]{tools:::Rd_expr_doi("doi:10.1075/ijcl.18010.egb")}

Gries, Stefan Th. 2008. Dispersions and adjusted frequencies in corpora. International Journal of Corpus Linguistics 13(4). 403–437. \Sexpr[results=rd]{tools:::Rd_expr_doi("doi:10.1075/ijcl.13.4.02gri")}

Gries, Stefan Th. 2020. Analyzing dispersion. In Magali Paquot & Stefan Th. Gries (eds.), A practical handbook of corpus linguistics, 99–118. New York: Springer. \Sexpr[results=rd]{tools:::Rd_expr_doi("doi:10.1007/978-3-030-46216-1_5")}

Gries, Stefan Th. 2021. A new approach to (key) keywords analysis: Using frequency, and now also dispersion. Research in Corpus Linguistics 9(2). 1–33. \Sexpr[results=rd]{tools:::Rd_expr_doi("doi:10.32714/ricl.09.02.02")}

Gries, Stefan Th. 2022. What do (most of) our dispersion measures measure (most)? Dispersion? Journal of Second Language Studies 5(2). 171–205. \Sexpr[results=rd]{tools:::Rd_expr_doi("doi:10.1075/jsls.21029.gri")}

Gries, Stefan Th. 2024. Frequency, dispersion, association, and keyness: Revising and tupleizing corpus-linguistic measures. Amsterdam: Benjamins. \Sexpr[results=rd]{tools:::Rd_expr_doi("doi:10.1075/scl.115")}

Juilland, Alphonse G. & Eugenio Chang-Rodríguez. 1964. Frequency dictionary of Spanish words. The Hague: Mouton de Gruyter. \Sexpr[results=rd]{tools:::Rd_expr_doi("doi:10.1515/9783112415467")}

Keniston, Hayward. 1920. Common words in Spanish. Hispania 3(2). 85–96. \Sexpr[results=rd]{tools:::Rd_expr_doi("doi:10.2307/331305")}

Lijffijt, Jefrey & Stefan Th. Gries. 2012. Correction to Stefan Th. Gries’ ‘Dispersions and adjusted frequencies in corpora’. International Journal of Corpus Linguistics 17(1). 147–149. \Sexpr[results=rd]{tools:::Rd_expr_doi("doi:10.1075/ijcl.17.1.08lij")}

Rosengren, Inger. 1971. The quantitative concept of language and its relation to the structure of frequency dictionaries. Études de linguistique appliquée (Nouvelle Série) 1. 103–127.

See Also

For finer control over the calculation of several dispersion measures:

• disp_R() for Range

• disp_DP() for D_P

• disp_DA() for D_A

• disp_DKL() for D_{KL}

Examples

disp_DP(
  subfreq = c(0,0,1,2,5), 
  partsize = rep(1000, 5),
  directionality = "conventional",
  freq_adjust = FALSE)

tlda documentation built on June 8, 2025, 11:41 a.m.