sign in sign up
<<
Home , Letter case, Letter frequency

Behavior Research Methods, Instruments, & Computers 2004, 36 (3), 388-396

Case-sensitive and frequency counts from large-scale English corpora

MICHAEL . JONES and . . . MEWHORT Queen’ University, Kingston, Ontario, Canada

We tabulated upper- and lowercase letter frequency using several large-scale English corpora (~183 million in total). The results indicate that the relative frequencies for upper- and lowercase let- ters are not equivalent. We report letter-naming experiment in which uppercase frequency predicted response to uppercase letters better than did lowercase frequency. Tables of case-sensitive letter and bigram frequency are provided, including common nonalphabetic characters. Because subjects are sensitive to frequency relationships among letters, we recommend that experimenters use case- sensitive counts when constructing stimuli from letters.

Familiar patterns can be identified more easily and pseudowords (Mewhort & Campbell, 1981; Miller, Bruner, quickly than unfamiliar ones. Common examples include & Postman, 1954). the advantage for high- over low-frequency words (.., Because frequency is a potential influence in any ex- Broadbent, 1967; Howes & Solomon, 1951; Krueger, periment using letters or strings of letters, it is important 1975) and a corresponding advantage for high- over low- to have an adequate measure of letter frequency. Several frequency letters (e.g., Appelman & Mayzner, 1981; methods have been tried. A quick and easy method with Bryden, 1968). Letters and strings of letters are com- which to estimate letter frequency is to conduct - monly used stimuli in experimental psychology; hence, letter counts—that is, to count the occurrence of initial it is important to anticipate potential characteristics of letters in words from a or -frequency letters that may affect results in experiments using them norm (e.g., Latimer, 1972; Tinker, 1928, Table 5). as stimuli. Accurate tabulations of frequency require large sam- High-frequency letters show an advantage over low- ples of representative text. Unfortunately, the tabulations frequency letters in letter naming (Cosky, 1976; Jones, currently available have ignored letter case (e.g., Badde- 2001), same–different matching (Egeth & Blecker, 1971; ley, Conrad, & Thompson, 1960; Gaines, 1939; Mayzner Krueger, 1973b, 1973c), and visual search (Latimer, & Tresselt, 1965; Solso & King, 1976). As a result, ex- 1972). In addition, bigram and trigram frequency affects isting counts of letter frequency are based on a mix of anagram solutions (Dominowski & Duncan, 1964) and upper- and lowercase letters, dominated by the lowercase word recognition (Broadbent & Gregory, 1968; Rice & letters, even though most experiments use uppercase let- Robinson, 1975). ters as stimuli. Subjects are sensitive to frequency relationships among As part of a project on letter matching, we wanted data letters even with stimuli that have never been seen before. to compare the relative recognizability of letters and Pseudowords that vary in order of approximation to - turned to existing confusion matrices: three uppercase glish are a example. Zero-order approximations are matrices (Gilmore, Hersh, Caramazza, & Griffin, 1979; created by taking letters at random; first-order approxi- Townsend, 1971; der Heijden, Malhas, & van den mations are created by taking letters at random from a text, Roovaart, 1984) and three lowercase matrices (Bouma, thus preserving the frequency of individual letters. Higher 1971, distance and eccentricity; Geyer, 1977). We exam- orders of approximation preserve the frequency of larger ined the confusion matrices’ diagonal, which records the units: for -order approximations, trigrams relative recognizability of the letters. for third-order approximations, and so forth. Subjects re- The mean correlation across the diagonals of the upper- port more letters from higher order than from lower order and lowercase confusion matrices was only .076. The near-zero correlation indicates very large differences in recognizability as a function of case. Part of the difference This research was supported by a grant to D.J.K.M. from the Natural reflects differences in shape for upper- and lowercase let- Sciences and Engineering Research Council of Canada (NSERC) and by ters, but part of the difference may also reflect differences an AEG grant from Sun Microsystems of Canada. M.N.J. was supported in the relative frequency of upper- and lowercase letters. by a postgraduate research scholarship from NSERC. Correspondence concerning this should be addressed to M. N. Jones, Department of When we checked frequency for upper- and lowercase let- Psychology, Queen’s University, Kingston, ON, K7L 3N6 Canada ( e- ters, we were unable to find suitable case-sensitive fre- mail: [email protected] or [email protected]). quency counts.

Copyright 2004 Psychonomic Society, Inc. 388 CASE-SENSITIVE LETTER FREQUENCY 389

Do Upper- and Lowercase Letters Have the frequency. This is probably because informal , Same Relative Frequencies? such as that found in discussion group text, often ex- Tinker (1928) is the only published study to conduct a hibits improper in comparison with text case-sensitive letter count. Tinker ranked the frequency of that has been thoroughly edited, such as that of the NYT. occurrence for upper- and lowercase letters from a type With the newsgroup corpus ignored, the mean intercor- foundry’s -replacement table and confirmed the esti- relation of uppercase counts from the remaining corpora mate by counting the upper- and lowercase letters in “sev- went up to .9268, with highest consistency among the eral pages of two journals” (p. 490). The rank order corre- edited corpora (NYT, Brown, and ). lation between Tinker’s upper- and lowercase counts was In addition to the single-letter frequencies, we cal- impressively high (rs .93). Tinker’s evidence has been culated bigram frequencies and checked them for con- accepted at face value. In their examination of the letter- sistency across the corpora. For the calculation, we de- frequency effect, for example, Appelman and Mayzner fined a bigram as directly adjacent characters within a (1981) used Tinker’s counts to conclude that “the order of word. To examine consistency of case-insensitive bigram letter frequency is quite similar for upper- and lowercase frequency among the corpora, we computed Pearson letters” (p. 437). product–moment correlation coefficients between case- Tinker’s (1928) evidence, however, is open to ques- insensitive bigram counts made on each of the corpora. tion. His counts were based on a limited sample of the Mean intercorpus correlation of case-insensitive bigram English . Furthermore, to compute a rank cor- counts was .9858, indicating that all the corpora were in relation, Tinker reduced frequency to an ordinal scale. high agreement on bigram frequency in general. Case- His transformation limited the variability among letters sensitive bigram counts were computed next. There are because he assigned a large number of tied ranks: 23 up- four categories for case-sensitive bigrams: lowercase percase letters and 5 lowercase letters were assigned a paired with lowercase (aa), lowercase followed by up- tied rank with at least one other letter (and in some in- percase (aA), uppercase followed by lowercase (Aa), and stances, three or four other letters). Because we did not uppercase followed by uppercase (AA). The correlations trust a conclusion based on such a limited sample of text, for case-sensitive bigrams were .9844 for aa, .7042 aA, we reexamined case-sensitive frequency using several .8948 for Aa, and .7602 for AA. large and representative corpora of English text. As before, case-sensitive bigram frequencies were more consistent among the edited text corpora than among the EXAMINING FREQUENCY ACROSS CASE informal corpora. The lower correlations for aA and AA categories primarily reflect improper capitalization in the Word Corpus Selection unedited corpora. In selecting a word corpus, our goal was to find one Because of the greater consistency among the edited that was representative of text that humans regularly ex- corpora, we judged the NYT corpus to be the best and perience. We examined (1) full-text articles from the most representative source, and data in the tables pre- New York (NYT) from January to March 1992 sented here were derived from it. Case-sensitive counts (~14 million words), (2) a subset of the Brown word cor- from the other corpora are available at the Psychonomic pus (Kuˇcera & Francis, 1967; ~1 million words), (3) a Society’s Web archive. commonly used online encyclopedia (~7 million words), (4) text extracted from about 100,000 randomly selected Single-Letter Frequency Web pages1 (~61 million words), and (5) newsgroup text To test the case-equivalence assumption, we corre- extracted from 400 different discussion groups lated upper- and lowercase counts. The correlation was (~100 million words). We were careful to remove for- a startlingly low .6337, quite different from Tinker’s matting symbols that would not appear in printed ver- (1928) rank–order correlation of .93. Contrary to Tin- sions of the corpora. ker’s data, our counts indicate that upper- and lowercase To examine the consistency of letter frequency in gen- letters do not have equivalent frequencies in print. Case- eral among the corpora, we computed Pearson product sensitive single-letter frequency counts from the NYT moment correlation coefficients between case-insensitive corpus are provided in Table 1. Experimenters interested single-letter counts made on each of the corpora. Mean in case-sensitive single-letter frequency can use these ta- intercorpus correlation of case-insensitive letter counts bles to help construct frequency-balanced stimulus sets. was .9963. Case-sensitive letter counts were next calcu- lated for each of the corpora. The mean correlation be- Bigram Frequency tween uppercase frequency counts from each corpus was Table 2 presents the correlation of case-sensitive .9065; for lowercase counts, the mean intercorpus corre- bigram counts from the NYT corpus. There is moderate lation was .9965. Hence, the corpora are in high agree- agreement between uppercase/uppercase and lowercase/ ment both on the frequency of letters in general and on lowercase bigram frequencies, but poor consistency be- the frequency of letters appearing in each case. tween other case-sensitive bigram counts. Hence, bigrams The correlation for the uppercase counts was lower do not have the same relative frequency in all case combi- than that for the lowercase counts because the news- nations. The Appendix contains predecessor-by-successor group corpus agreed with the others less on uppercase case-sensitive bigram counts calculated from the NYT cor- 390 JONES AND MEWHORT

Table 1 We computed single-unit and bigram frequency counts Raw Case-Sensitive Single-Letter Counts for 32 nonalphabetic characters including the 10 digits from the NYT Corpus (ASCII 33–64; ! to @). Characters commonly used as Uppercase Lowercase ƒ ƒ distractors varied quite widely in their frequencies and Letter Uppercase Lowercase Rank Rank were more commonly found as successors to letters (on A 280,937 5,263,779 3 3 the right) than as predecessors. Table 3 shows the raw fre- 169,474 866,156 8 20 2 229,363 1,960,412 5 12 quency with which each distractor flanked a D 129,632 2,369,820 12 11 letter as predecessor and successor in the NYT corpus. E 138,443 7,741,842 11 1 100,751 1,296,925 17 15 APPLYING CASE-SENSITIVE FREQUENCY G 93,212 1,206,747 19 17 123,632 2,955,858 13 9 TO LETTER IDENTIFICATION I 223,312 4,527,332 6 6 J 78,706 65,856 20 25 We have demonstrated that upper- and lowercase let- K 46,580 460,788 22 22 ters do not have equivalent relative frequencies in print. 106,984 2,553,152 15 10 As mentioned previously, experimenters often use up- M 259,474 1,467,376 4 14 N 205,409 4,535,545 7 5 percase letters as stimuli but compute frequency using 105,700 4,729,266 16 4 counts dominated by lowercase letters. We next tested P 144,239 1,255,579 10 16 the ability of the case-sensitive frequency counts to pre- 11,659 54,221 24 26 dict naming time when subjects are identifying isolated R 146,448 4,137,949 9 8 S 304,971 4,186,210 2 7 uppercase letters. Our goal was to determine whether up- T 325,462 5,507,692 1 2 percase counts provide a better prediction of reaction U 57,488 1,613,323 21 13 time than lowercase counts when uppercase letters are 31,053 653,370 23 21 used as stimuli. 107,195 1,015,656 14 19 In this experiment, the subject named a letter aloud as 7,578 123,577 25 23 94,297 1,062,040 18 18 quickly as possible. Response latency was measured as 5,610 66,423 26 24 the time between stimulus onset and initiation of the vocal response. The naming task includes both a decision and motor production component. To factor out the motor component, we subtracted motor production time from pus. Experimenters interested in controlling case-sensitive overall naming time on a per-subject (and per-letter) bigram frequency can use these tables to help construct basis. To estimate the motor component, we asked sub- frequency-balanced stimuli. jects to name a letter on a cue presented well after the de- cision process had been completed. Naming on cue con- Frequency of Other Alphanumeric Characters tains the same motor process as does the standard Numerals and other nonalphabetic characters (e.g., &, naming task but with the decision process complete. By $,%, #, @) are often used as distractors in attention experi- comparing the name-on-cue task and the standard nam- ments—as noise stimuli, for example, when one is studying ing task on a per-subject basis, we were able to subtract the interference of flanking characters on the identification the motor component from the decision component for of a target letter (e.g., Eriksen & Hoffman, 1972; Estes, each letter. 1972; Krueger, 1970, 1973a). Because flanker interference depends on the relationship of the flanking characters and Method the targets (i.e., letters produce more interference than do Subjects. Eight graduate students from Queen’s University par- nonalphabetic characters, and high-frequency bigrams pro- ticipated in the experiment. They were each paid $10, and all had normal or corrected-to-normal vision. duce more interference than do low-frequency bigrams), it Apparatus. Stimuli were presented on a 19-in. CRT monitor at a is important to know the naturally occurring frequency viewing distance of 75 cm; we used a chin bar to keep viewing dis- characteristics of distractor characters, as well as the bi- tance constant. Subjects wore a Sony Dynamic Headset (HS-65A-1) gram frequency of the target letter and noise characters. equipped with a voice–key microphone. Microphone threshold was calibrated to each subject during the practice phase of the experi- ment. At a viewing distance of 75 cm, characters subtended a max- imum visual angle of about 0.38º vertically and 0.29º horizontally. Table 2 Procedure. All subjects were given 5 min of dark adaptation be- Correlation Matrix of Case-Sensitive Bigram Combinations Computed from the NYT Corpus fore beginning the experiment. All subjects completed both the cued-production task and the standard letter-naming task so that an aa aA Aa AA estimate of production time for a letter could be subtracted from aa – .012 .587* .665* overall naming time for the same letter. Each trial (for either task) aA – .005 .008 began with a fixation cross at the center of the display. The subject Aa – .372* was instructed to focus on the cross and, when ready to proceed, to AA – press the start button with the index finger of the dominant hand. Note—Number of observations for each bigram type: aa, 48,301,606; During the production (cued-naming) task, the subjects were in- aA, 10,007; Aa, 2,446,369; and AA, 712,561. *p .001. formed that the letters would be presented in . On CASE-SENSITIVE LETTER FREQUENCY 391

Table 3 Results Single-Unit Frequency of Various Nonalphabetic Characters Decision latency was calculated by subtracting mean (ASCII 33–64), and Bigram Frequency as Predecessor (#A) or production latency for a letter (on a per-subject basis) Successor (A#) to an Alphabetic Character from each of the 12 naming trials for the same letter.The As Predecessor As Successor Character Single Unit (#A) (A#) Pearson correlation between uppercase frequency and decision latency to uppercase letters was r(25) .602, ! 2,178 58 1,866 “ 284,671 142,168 26,827 p .01. By contrast, the correlation between lowercase #10 0 0frequency and decision latency to uppercase letters was $ 51,572 427 61 r(25) .328, n.s. % 1,993 13 9 The pattern supports our presumption that uppercase & 6,523 438 350 ‘ 204,497 187,914 185,857 decision latency is predicted better by upper- than by 3 ( 53,398 43,473 55 lowercase counts. We tested the difference between ) 53,735 11 37,506 these correlations with Williams’ (1959) ratio for nonin- * 20,716 882 530 dependent correlations (see also Steiger, 1980). Upper- 309 8 112 case decision latency was predicted significantly better , 984,969 111 810,376 - 252,302 160,049 138,556 by the uppercase frequency counts than by the lowercase . 946,136 41,636 847,611 ones [t(23) 1.92, p .05]. / 8,161 3,948 4,207 The advantage for same-case prediction illustrates the 0 546,233 2,006 38 importance of using case-sensitive frequency counts in 1 460,946 959 5,792 2 333,499 1,065 2,435 single-letter identification. In the Discussion section, we 3 187,606 1,335 1,945 consider some examples of case-sensitive bigram con- 4 192,528 880 1,820 founds in a classic psychological experiment. 5 374,413 999 1,514 6 153,865 1,576 1,491 7 120,094 840 1,074 DISCUSSION 8 182,627 828 1,021 9 282,364 1,697 481 We have provided case-sensitive frequency counts for : 54,036 13 48,354 single letters and bigrams from large samples of carefully ; 36,727 58 28,301 82 74 18 selected corpora. In addition, we have demonstrated that 22 1 1 identification time for uppercase letters is predicted bet- 83 52 70 ter by frequency of uppercase letters than by frequency of ? 12,357 10 11,938 lowercase letters. The effect of case-sensitive frequency @11 1is, however, by no means limited to single-letter identifi- cation. A salient illustration of case-sensitivity from ex- perience is the proper name effect. In a series of lexical each trial, after subjects fixated the cross and pressed the start but- decision experiments, Peressotti, Cubelli, and Job (2003) ton, a letter immediately replaced the cross and remained visible found a consistent reaction time advantage for proper for a random delay period of 1–3.5 sec. Following the delay, the let- names that had the first letter capitalized, compared with ter was removed, and the screen flashed to cue the subject to re- common and proper names with the first letter in spond. The subjects’ task was to name the letter aloud as quickly as lowercase. Since proper names are experienced with the possible following this cue. Latency was defined as the elapsed first letter capitalized, the proper name effect provides time between cue and verbal response. The screen remained blank further support for the importance of accounting for case- for 1–3 sec before the next trial. During the naming task, letters were presented in random order. sensitive frequency in experimental stimuli. On each trial, after subjects fixated on the cross and pressed the Our main is that unless case is taken into account, ready button, a letter immediately replaced the cross and remained letter and bigram frequency may be an unexpected deter- visible until a response was initiated. The subjects’ task was to minant of performance. Consider the classic Posner match- name the letter aloud as quickly as they were able to identify it. La- ing task (e.g., Posner & Mitchell, 1967) still used in many tency was defined as the elapsed time between stimulus onset and experiments. Posner and Mitchell simultaneously pre- response initiation. Following the response, the screen went blank while the experimenter recorded the subjects’ accuracy. The screen sented two letters and asked subjects to respond “same” or remained blank for a random interval of 1–3 sec between trials, and “different.” Under physical matching instructions, subjects the fixation cross then reappeared to signify a new trial. were required to respond “same” only if the two letters To balance practice effects, an ABBABAAB design was used. For were physically identical (AA, aa) and “different” if not each subject, the two tasks were randomly assigned to A or B . For (AE, Aa). Under name matching instructions, subjects example, if A was assigned to the naming task and B to the produc- were asked to respond “same” if the two letters had the tion task, each A contained 3 blocks of 26 letter-naming trials in random order (each letter equally represented within a block), and same name (AA, Aa) and “different” if not (AE, Ah). each B contained 3 blocks of 26 cued-production trials. Thus, in A general finding is that same responses are faster total the data presented here represent 312 letter-naming and 312 than different responses in physical matching4 (the fast- cued-production trials per subject. same effect). This effect is troubling to theory because 392 JONES AND MEWHORT one would expect a different response to be made as soon We described initial-letter counts as a quick and as one featural mismatch has been detected between the easy method to estimate uppercase letter frequency (i.e., letters, whereas a same response requires an exhaustive counting the occurrence of initial letters in words from a search of all features to verify that the two stimuli are dictionary or word-frequency norm—e.g., Latimer, 1972; identical. Tinker, 1928, Table 5). However, we caution against the The fast-same effect has been explained as an artifact use of such a technique, which is based on the logic that the of more possible different combinations than same com- more frequently a letter occurs at the beginning of a word, binations within an experiment (Nickerson, 1973). Alter- the more often it will be capitalized. It further assumes that natively, the advantage for same responses has been at- all words are equally likely to begin a —an as- tributed to internal noise in the perceptual system (e.g., sumption that is false. We counted the number of pages Krueger, 1978), or to an encoding bias for the second let- dedicated to each letter from several and used ter primed by the first (e.g., Proctor, 1981). Before ac- this count as a predictor of uppercase frequency from the cepting any possibility, however, we note that the fast- NYT corpus, and the mean correlation was .6825. same effect is confounded with case-sensitive bigram frequency. Considering the pairs that Posner and Mitchell Obtaining the Case-Sensitive Frequency Counts (1967) used as stimuli, the mean bigram log frequency5 Raw case-sensitive frequency counts of single charac- of physically same pairs calculated from the NYT corpus ters and all possible bigrams (including the nonalpha- is 8.03, whereas the corresponding value for physically betic characters) for the corpora listed here can be found different pairs is only 7.35. Hence, the fast-same effect at the Psychonomic Society’s Web archive. We encour- may be contaminated by a frequency difference between age experimenters to consult these tables to balance fre- physically same and different letter pairs. We know that quency when constructing stimuli composed of letters. letter and bigram frequency affects processing; thus, the Learning is a product of repetition, and too often difference in frequency for same versus different pairs frequency goes ignored in the design of experiments. may partially explain the advantage of faster same re- Whether consciously or not, humans take advantage of sponses in physical matching. frequency information every day, and an experiment is cer- A common finding under name-matching instructions tainly not immune to a frequency bias. We advise experi- is that same responses are faster to pairs that are physi- menters to use frequency counts that are sensitive to letter cally the same (AA, aa) than to those that are physically case when they construct experiments using letter stimuli. different (Aa). This finding was used to argue for a tem- poral hierarchy of processing stages, the first involving REFERENCES physical stimulus examination, and the second requiring Appelman, I. B., & Mayzner, M. S. (1981). The letter-frequency ef- translation from a physical code to a name code and fect and the generality of familiarity effects on perception. Perception memory access (Posner, 1978; Posner & Mitchell, 1967). & Psychophysics, 30, 436-446. A same response to the stimulus pair Aa presumably Baddeley, A. D., Conrad, R., & Thompson, W. E. (1960). Letter takes longer because it requires translation from physi- structure in the . Nature, 186, 414-416. Bouma, H. (1971). Visual recognition of isolated lowercase letters. Vi- cal to name code, whereas a response to AA is faster be- sion Research, 11, 459-474. cause it can be accomplished by raw stimulus examina- Broadbent, D. E. (1967). Word-frequency effect and response bias. tion without the need for identification. Psychological Review, 74, 1-15. However, the temporal hierarchy explanation is also Broadbent, D. E., & Gregory, M. (1968). Visual perception of words confounded with case-sensitive bigram frequency. Mean differing in letter digram frequency. Journal of Verbal Learning & Verbal Behavior, 7, 569-571. bigram log frequency of physically same pairs (AA) Bryden, M. P. (1968). Symmetry of letters as a factor in tachistoscopic computed from the NYT corpus is 8.03, whereas for recognition. American Journal of Psychology, 81, 513-524. physically different same-name pairs (Aa) it is 3.35. Cosky, M. J. (1976). The role of letter recognition in word recognition. Faster same responses to physically same over physically Memory & Cognition, 4, 207-214. Dominowski, R. L., & Duncan, C. P. (1964). Anagram solving as a different responses in name matching may well be influ- function of bigram frequency. Journal of Verbal Learning & Verbal enced by a frequency difference. Behavior, 3, 321-325. We selected the classic Posner matching task as an ex- Egeth, H., & Blecker, D. (1971). Differential effects of familiarity on ample because there is such a wealth of letter-matching judgments of sameness and difference. Perception & Psychophysics, data that we are comfortable that case-sensitive bigram 9(4), 321-326. Eriksen, C. W., & Hoffman, J. E. (1972). Some characteristics of se- frequency can be ruled out as an explanation of any of the lective attention in visual perception determined by vocal reaction effects. For example, the bigram confound cannot account time. Perception & Psychophysics, 11, 169-171. for more recent data (e.g., Proctor, 1981). The classic Pos- Estes, W. K. (1972). Interactions of signal and background variables in ner and Mitchell (1967) experiment is an illustration of visual processing. Perception & Psychophysics, 12, 278-286. Gaines, H. F. (1939). : A study of ciphers and their solu- how, if not properly controlled when designing stimuli, tions. New York: Dover. case-sensitive frequency could confound interpretation of Geyer, L. H. (1977). Recognition and confusion of the lowercase al- experimental results. phabet. Perception & Psychophysics, 22, 487-490. CASE-SENSITIVE LETTER FREQUENCY 393

Gilmore, G. C., Hersh, H., Caramazza, A., & Griffin, J. (1979). in the English language. Behavior Research Methods & Instrumen- Multidimensional letter similarity derived from recognition errors. tation, 8, 283-286. Perception & Psychophysics, 25, 425-431. Steiger, J. H. (1980). Tests for comparing elements of a correlation Howes, D. H., & Solomon, R. L. (1951). Visual duration thresholds as matrix. Psychological Bulletin, 87, 245-251. a function of word-probability. Journal of Experimental Psychology, Tinker, M. A. (1928). The relative of the letters, the digits, 41, 401-410. and of certain mathematical signs. Journal of General Psychology, 1, Jones, M. N. (2001). T-REX: A template-resonance excitation model of 472-495. single letter classification. Master’s thesis, Queen’s University at Townsend, J. T. (1971). Theoretical analysis of an alphabetic confusion Kingston. matrix. Perception & Psychophysics, 9, 40-50. Krueger, L. E. (1970). Effect of bracketing lines on speed of “same”– van der Heijden, A. H. C., Malhas, M. S. M., & van den Roovaart, “different” judgments of two adjacent letters. Journal of Experimen- B. P. (1984). An empirical interletter confusion matrix for continuous- tal Psychology, 84, 324-330. capitals. Perception & Psychophysics, 35, 85-88. Krueger, L. E. (1973a). Effect of irrelevant surrounding material on Williams, E. J. (1959). The comparison of regression variables. Jour- speed of “same–different” judgments of two adjacent letters. Journal nal of the Royal Statistical Society: Series B, 21, 396-399. of Experimental Psychology, 98, 252-259. Krueger, L. E. (1973b). Effect of letter-pair frequency and orientation NOTES of speed of “same”–“different” judgments by children and adults. Bulletin of the Psychonomic Society, 2, 431-433. 1. An automated URL spider was sent out to collect text from 100,000 Krueger, L. E. (1973c). Effect of stimulus frequency on speed of Web pages with domain extensions .edu, .org, or .ca. The spider was re- “same”–“different” judgments. In S. Kornblum (Ed.), Attention and stricted to collecting text a maximum of three directories deep within a performance IV (pp. 497-506). New York: Academic Press. URL. Krueger, L. E. (1975). Familiarity effects in visual information pro- 2. Mean intercorpus correlation was r(21) .9373 for the symbols cessing. Psychological Bulletin, 82, 949-974. and r(9) .9482 for the digits; hence, frequency of occurrence was Krueger, L. E. (1978). A theory of perceptual matching. Psychologi- consistent across the corpora. cal Review, 85, 278-304. 3. Interestingly, logarithmic transformations on frequency did not Kuˇcera, H., & Francis, W. N. (1967). Computational analysis of present- predict latency as well as raw frequency (the opposite is usually the day American English. Providence, RI: Brown University Press. case). Latimer, C. R. (1972). Search time as a function of context letter fre- 4. Posner and Mitchell found a fast-same effect in their original study, quency. Perception, 1, 57-71. but it was not reliable. The effect had been reported earlier (Nickerson, Mayzner, M. S., & Tresselt, M. E. (1965). Tables of single-letter and 1965) and has been demonstrated many times since then. digram frequency counts for various word- and letter-position 5. The bigram frequency distributions were positively skewed, thus, combinations. Psychonomic Monograph Supplements, 1 (Whole No. the log-transformed data are described here. 2), 13-32. Mewhort, D. J. K., & Campbell, A. J. (1981). Toward a model of skilled reading: An analysis of performance in tachistoscopic tasks. ARCHIVED MATERIALS In G. E. MacKinnon & T. G. Waller (Eds.), Reading research: Ad- vances in theory and practice (Vol. 3, pp. 39-118). New York: Aca- The following materials associated with this article may be accessed demic Press. through the Psychonomic Society’s Norms, Stimuli, and Data archive, Miller, G. A., Bruner, J. S., & Postman, L. (1954). Familiarity of http://www.psychonomic.org/archive/. letter sequences and tachistoscopic identification. Journal of Gen- To access these files or links, search the archive for this article using eral Psychology, 50, 129-139. the journal (Behavior Research Methods, Instruments, & Computers), Nickerson, R. S. (1965). Response times for same–different judg- the first author’s name (Jones), and the publication year (2004). ments. Perceptual & Motor Skills, 20, 15-18. File: Jones_BRMIC_2004.zip Nickerson, R. S. (1973). Frequency, recency, and repetition effects on Description: The 590K compressed archive file contains the same same and different response times. Journal of Experimental Psy- two files (single letter and bigram counts) in four formats (tab-delimited chology, 101, 330-336. text, space-delimited ASCII, Microsoft Excel 2000, and Adobe PDF). Peressotti, F., Cubelli, R., & Job, R. (2003). On recognizing proper Jones2004_Single.* contains single-character counts (ASCII 33–126; names: The orthographic cue hypothesis. Cognitive Psychology, 47, ! to ~) separately for each of the five corpora. Each row represents one 87-116. character; each , one of the corpora (NYT, encyclopedia, Brown, Posner, M. I. (1978). Chronometric explorations of mind. Hillsdale, Web , newsgroup). : Erlbaum. Jones2004_Bigram.* contains bigram counts for each combination Posner, M. I., & Mitchell, R. F. (1967). Chronometric analysis of of characters (ASCII 33–126; ! to ~) separately for each of the five cor- classification. Psychological Review, 74, 392-409. pora. Each row represents a predecessor-by-successor bigram; each col- Proctor, R. W. (1981). A unified theory for matching-task phenom- umn, one of the corpora (NYT, Encyclopedia, Brown, Web page, news- ena. Psychological Review, 88, 291-326. group). Rice, G. A., & Robinson, D. O. (1975). The role of bigram frequency Jones2004_README.txt contains a full description of the content in the perception of words and nonwords. Memory & Cognition, 3, of Jones_BRMIC_2004.zip, including extended definitions of the vari- 513-518. ables (a 3K plain text file). Solso, R. L., & King, J. F. (1976). Frequency and versatility of letters Author’s e-mail Address: [email protected]. 394 JONES AND MEWHORT e logarithm of e logarithm ) by i x Successor Table A1 APPENDIX Uppercase-by-Uppercase Bigram Frequency Bigram Uppercase-by-Uppercase ) was transformed entry) was to its table ( i )]. i Predecessor (A_) by Successor (_A) Case-Sensitive Bigram the Counts From NYT Corpus ), i ln( ƒ x round[exp( ≈ i i ƒ x Z 5.70 1.79 3.58 2.77 4.71 .00 .69 . 5.96 . . 2.20 .69 4.58 4.32 1.95 1.95 3.53 1.79 4.83 3.89 . .00 . 2.56 4.11 ABC 5.81 7.50D 8.08 7.40 7.52 6.12E 8.21 7.12 7.70 6.69 4.33 7.34 7.40F 5.93 6.01 7.90 7.48 3.09 5.51 4.95G 3.53 8.16 7.76 6.68 6.25 4.60 6.06 5.53 6.24 6.12 7.52H 3.53 6.08 8.53 8.02 2.83 7.95 3.22 8.17 4.49 6.27 2.48 8.42 3.00 1.10I 8.34 8.46 6.05 7.26 1.79 4.28 7.16 6.05 6.11 7.06 3.22 8.79 2.71 5.2J 8.11 7.98 6.73 5.04 1.39 3.64 4.09 5.56 6.42 8.47 5.88 6.26 8.57 .00 6.60 3.14 4.96K 7.71 7.92 7.85 3.04 6.49 6.84 8.14 1.79 6.40 6.88 3.47 7.02 8.49 3.33 3.74 7.38 8.18 6.02 5.91 4.55 4.44L 3.50 6.07 5.54 7.03 8.59 4.96 1.95 6.60 8.94 2.48 6.52 5.65 8.37 7.99 3.99 7.97 3.22 6.69 6.68M 7.21 7.81 6.63 9.15 3.66 2.71 3.69 5.21 3.40 6.33 1.10 6.50 5.58 . 5.37 5.77 1.79 7.66 3.58 7.13N 3.18 .69 3.97 6.71 .00 6.13 6.84 7.24 3.14 2.56 7.33 8.81 5.96 7.34 . 3.71 .69 8.28 .00 9.39 6.88 7.46 3.40 5.16O 1.95 7.70 4.65 8.41 5.29 2.83 8.01 7.50 2.48 6.50 5.18 3.53 6.75 3.89 3.47 4.90 9.01 5.18 3.14 .00 5.85 4.49 5.23 2.89 6.59 3.04P 6.75 3.81 6.75 4.03 8.34 .00 1.61 8.61 3.69 8.32 9.74 5.34 7.92 5.02 .69 5.93 3.61 3.18 5.52 6.36 3.50 7.94 6.17 7.07Q 5.68 5.61 7.28 6.32 4.56 5.51 2.08 6.87 5.34 8.11 5.064.89 3.83 5.36 4.64 3.81 5.49 5.21 5.97 6.01 7.50R 8.07 .00 4.83 6.82 1.95 8.83 4.73 9.10 5.73 1.10 . 4.34 2.20 7.98 2.56 . 7.23 5.83 7.33 3.04 6.15 3.95 4.67S . 3.30 . 8.48 2.94 8.01 6.62 7.93 6.16 6.92 5.31 4.96 4.25 3.99 4.65 7.60 3.26 .00 4.38 .69 3.30 1.61 8.00 8.96 7.30 5.54T 9.39 4.39 2.20 3.66 8.63 8.61 6.15 6.52 6.21 7.71 8.76 8.01 2.56 6.47 7.84 6.65 3.30 5.98 7.12 6.97U 8.62 3.00 2.30 2.08 . .00 7.02 3.33 6.63 8.78 6.91 . 3.37 3.37 8.50 . 6.34 4.57 3.64 5.75 8.39 6.61 .00 1.39 7.30V 4.76 1.95 4.47 .00 7.75 2.77 6.25 1.39 9.20 6.67 2.08 3.61 1.39 6.55 1.39 7.71 7.70 9.09 3.43 7.07 4.79 7.08 6.77 5.69 3.50 7.98 6.20 6.00 3.81 5.84W 7.07 7.40 3.22 6.35 5.93 3.26 3.61 9.11 7.14 . 7.39 5.49 6.95 7.12 5.69 6.72 8.56 4.62 2.40 8.69 4.36 9.47 7.26 5.38 7.05X 3.00 .00 7.38 5.83 4.49 3.50 3.33 . 1.79 6.69 2.40 7.91 5.20 4.28 6.92 4.62 6.97 2.77 3.66 5.65 3.93 6.50 5.13 1.79 5.80Y 7.40 .69 2.30 9.08 3.74 1.39 5.56 6.21 5.16 .69 1.61 6.20 7.36 4.86 5.46 5.56 4.09 . 3.74 1.61 3.50 6.36 . 5.18 .00 6.30 3.83 8.71 8.29 2.56 1.79 4.51 7.05 3.99 5.66 5.56 7.61 6.18 5.76 . 4.88 9.39 6.85 6.37 6.84 2.94 .00 2.64 8.08 8.55 4.63 7.87 .69 3.85 8.27 3.89 1.10 5.68 .51 3.22 . 1.39 2.20 4.16 7.13 .00 3.09 7.62 6.95 6.01 5.95 4.37 3.14 2.64 5.78 5.49 1.39 6.15 2.20 5.30 6.88 3.00 .69 6.66 8.57 .00 3.69 5.27 2.83 2.40 4.26 6.49 8.46 .00 3.58 6.59 5.18 2.30 6.91 7.82 4.66 5.74 5.24 7.95 .00 6.42 .00 7.58 2.71 3.40 6.79 7.79 3.66 5.82 1.10 2.71 7.88 7.94 2.20 2.71 4.22 8.79 6.53 4.09 . 1.95 4.58 5.11 .10 5.47 7.69 8.50 6.22 8.78 4.19 2.08 1.79 5.10 3.69 8.92 7.13 4.50 . 5.83 5.68 3.26 5.68 7.04 7.30 . 2.08 7.22 3.40 7.17 1.39 6.67 . 2.83 7.37 5.37 1.10 .69 1.79 5.11 7.40 2.30 1.10 3.30 2.94 5.78 3.56 1.10 4.25 1.95 2.08 .69 .00 6.68 4.89 5.62 2.71 4.56 5.28 .69 5.58 4.44 10.2 3.50 2.40 5.02 7.32 10.4 5.33 2.64 3.93 3.40 5.63 3.00 . 3.53 3.85 1.39 4.62 . 3.81 4.60 .69 2.40 1.61 1.39 3.71 .69 2.30 3.89 2.20 7.14 5.20 5.56 1.95 1.39 2.20 . 4.75 7.60 1.39 3.83 3.89 . 3.71 3.04 1.79 2.71 3.87 1.79 1.95 .00 5.06 1.10 2.20 1.39 2.56 . . 2.48 .69 These tables contain log-transformed predecessor-by-successor case-sensitive bigram counts from the NYT corpus. frequency The i nteger case-sensitive contain log-transformed predecessor-by-successor These tables Note that due to the logarithmic transformation, cells with “.00” had so few observations that the value was rounded to zero (an exponential was transformation,that the value observations Note that due to the logarithmic cells with “.00” had so few Predecessor A B C D E F G H I J K L M N O P Q R S T U V W X Y Z frequency count of a given bigram ( ƒ count of a given frequency and an approximation may be unpacked by be unpacked may and an approximation zero is undefined). transformation will return an integer value of 1), whereas cells with missing values had observed frequencies of zero (since th cells with missing values transformation of 1), whereas will return value an integer CASE-SENSITIVE LETTER FREQUENCY 395 nopqr s tuvwxyz nopqr s tuvwxyz Successor Successor Table A2 Table A3 APPENDIX (Continued) Lowercase-by-Lowercase Bigram Frequency Bigram Lowercase-by-Lowercase Uppercase-by-Lowercase Bigram Frequency Bigram Uppercase-by-Lowercase Z 6.95 2.48 .00 3.33 6.86 . .00 5.56 6.75 .00 . .69 2.40 . 5.92 . . .69 2.71 . 5.80 4.38 4.22 . 3.43 . ABC 5.55 9.51D 8.44 9.95 9.08 4.54E 6.20 4.69 10.4 8.99 4.91 8.06F 9.87 5.74 9.89 4.69G 4.55 8.03 . 3.40 4.73 9.01 5.99 4.78H 9.04 9.83 .00 . 4.39 7.19 10.2 8.89 1.39 3.69 8.76I 10.2 8.60 2.56 9.28 3.22 5.65 8.52 .J 6.57 .00 5.44 . . 8.88 10.1 4.77 9.60 10.5 .K 9.67 7.13 .00 2.08 3.66 9.25 3.26 .00 4.33 6.18 9.79L 8.67 . 9.72 . 5.12 . 8.69 8.27 1.10 1.10 7.68 6.05 10.2 6.67M 9.88 6.34 8.94 4.49 1.10 . 8.84 . 2.71 1.79 5.71 . 2.94 6.09 8.90 3.99N . . .00 6.61 5.34 3.37 10.2 6.17 . 9.43 .00 9.82 6.01 3.71 2.40 1.10 3.74 7.51 9.30 10.1O 7.47 9.10 8.40 9.29 11.0 2.08 2.08 4.28 4.30 6.40 2.20 .00 . 4.42P .69 8.68 8.51 1.61 10.5 . . 6.70 9.60 3.95 . . 8.58 6.05 10.8 4.41 7.71 2.71 6.28Q 8.66 9.76 . 3.33 . 5.06 7.34 4.19 8.533.00 6.25 7.66 5.30 8.80 3.26 10.9 5.44 6.52 2.40 .R . . 1.95 10.9 . 6.76 2.20 7.85 9.33 4.16 . 9.33 5.11 10.2 3.30 2.48 9.43 5.83 10.1 5.09S . 9.94 3.00 3.83 .00 4.29 3.97 7.49 5.25 . 8.62 8.34 . 1.10 4.14 . 2.30 9.43 5.26T . 8.57 8.12 . 1.61 4.68 . 10.1 9.71 7.80 7.04 . .00 9.19 . 1.10 4.82 8.41 1.95 3.83 3.95 9.81U 6.05 .00 5.00 . .00 6.38 1.95 3.09 4.16 .00 . 4.82 10.0 3.18 6.45 9.53 3.37 4.93 . 11.3 4.57 . 2.71V .00 1.39 . 9.46 8.54 .69 1.39 6.79 2.64 10.3 9.39 1.39 1.39 4.60 9.36 3.58 . 5.63 8.94 . 9.68 3.00 4.73 10.1 4.23 .69 5.23W 3.99 4.30 7.57 9.34 .00 2.56 4.81 1.39 .00 3.83 6.70 4.52 4.56 . 7.94 3.87 9.47 .X . 9.26 2.64 . . 1.10 1.10 3.71 . 8.47 8.61 . . 8.57 8.94 . . 10.8 4.17 10.0 8.57 7.74 3.89 9.52 9.89 8.59Y 1.39 7.09 1.10 3.22 . 3.33 9.86 3.22 . 4.39 5.33 7.87 2.83 1.10 .00 9.32 . 5.76 11.2 8.71 . 10.1 4.13 . 7.67 9.03 . 7.74 3.00 . 10.0 . . . 4.04 4.93 7.14 9.21 4.58 2.56 3.22 8.01 . 6.30 .69 4.36 . 1.39 8.91 .69 6.02 8.54 2.20 5.61 . . 8.09 . . 7.05 7.04 4.98 1.61 1.10 2.56 6.12 . . 7.47 6.09 . . . . 5.16 . . 7.96 3.97 4.61 2.20 4.88 .00 . . . .00 6.40 10.2 . . . 5.90 1.95 6.41 10.1 1.10 1.79 12.0 . 8.98 . 6.53 7.21 . . . .69 . 9.34 .69 . 9.57 7.06 8.21 4.13 1.95 . 9.64 . . . 3.18 5.06 2.48 .00 9.97 . 10.2 .00 2.48 7.04 7.92 . .69 .00 . 1.79 1.61 . . . 8.59 . 10.8 . 8.64 6.53 2.20 . 9.76 4.83 2.71 .00 6.70 9.61 1.79 10.2 .00 . . 5.19 3.18 6.44 5.52a .00 . 7.85 3.64 . . . .69 8.28 . .00.b .00 . 2.64 . 1.10 5.68 . . 8.11 . 4.39 6.35 . 9.92c 6.38 4.74 8.10 7.67 . . .00 .00 . 9.70 . 1.95 .69 . 3.00 7.38 9.71 1.10d 3.87 5.29 9.16 11.5 .00 . 1.39 1.79 .00 12.2 11.4 4.68 9.13 .69 .00 12.1e 9.00 . . . 9.25 6.57 3.30 12.4 6.83 .00 10.6 . 6.50 . . 2.71f 4.08 11.6 4.99 . . 12.4 9.25 . . 10.4 11.6 9.03 7.36 3.85 .69 1.39 5.76 5.70g 7.33 3.56 12.4 . 1.79 . 12.7 7.73 9.03 5.33 . 12.8 9.24 6.74 3.00 10.1 11.0h 7.98 10.2 . 8.27 . 10.9 2.56 13.1 12.8 8.14 12.4 . .69 8.47 . . 11.9 7.46 11.1 3.56 13.3i .00 . 9.83 12.5 9.09 4.32 13.8 11.5 12.2 2.40 7.55 11.4 4.78 11.7 .69 6.93 7.79 11.2 . . .00j 1.10 5.36 11.4 3.50 7.61 11.0 12.2 5.61 11.4 . 8.75 7.54 3.58 7.95 11.5 13.1 11.5 9.36 2.40 1.95 11.1 . 5.46 6.81 11.3k 13.3 5.25 8.20 7.88 1.95 4.89 11.3 6.02 9.76 . 13.0 12.2 6.35 7.58 . 1.61 4.90 9.44 . 6.20 3.64 1.95 13.5 . 11.9 7.84 9.97l 7.54 9.57 12.8 6.80 9.16 10.4 10.4 11.1 11.9 12.4 14.1 3.76 2.77 2.64 3.40 . 11.7 4.23 11.4 12.8 11.6 12.0 6.60 . 8.52m 7.87 6.09 5.42 5.12 . 10.5 12.4 5.24 11.0 1.61 13.4 10.6 11.2 10.1 6.83 . 3.09 5.23 9.64 12.1 10.2 6.21 9.21 . 3.43 10.6 9.47 4.68 6.27 10.7 2.40 12.0 11.1n 6.78 11.4 8.52 4.62 3.56 12.6 12.1 11.0 9.99 .11.8 5.31 . 1.95 3.50 9.23 4.55 9.52 9.39 11.3 .00 7.66 7.30 11.2 12.4 6.54 12.5 7.75 5.91 6.64 4.89 2.08 13.9 7.05 3.26 1.95 3.00 10.4 8.60 11.0 . 9.00 13.4 7.10 6.57 12.3 11.9 4.79 3.00 9.31 11.0 1.10 7.21 8.44 8.58 6.73 10.7 12.3 5.28 8.73 10.4 11.9 .00 6.35 7.25 . 9.71 5.82 9.23 .69 1.95 12.5 . 5.09 12.9 7.68 12.0 5.65 12.4 . 11.6 9.93 11.8 11.3 10.0 .00 . 5.91 8.42 11.5 12.8 . 1.10 11.0 . 10.3 7.95 9.98 5.82 14.0 11.5 5.12 3.85 12.2 7.59 11.3 11.4 7.24 9.35 8.16 7.18 6.42 12.7 4.80 5.09 13.3 10.6 . 11.4 2.30 2.71 10.5 10.8 10.6 9.32 9.22 . 6.38 . 12.7 5.64 3.76 12.8 8.43 2.94 8.09 4.22 6.53 11.2 10.5 10.2 2.40 . 12.0 5.96 9.54 13.2 11.9 .69 3.81 9.80 3.56 3.93 10.2 13.1 12.7 2.08 4.91 4.30 9.07 5.18 8.42 3.37 9.68 9.12 13.1 6.30 1.39 7.21 8.07 .69 . 12.1 . 10.0 8.18 7.78 3.64 8.71 10.8 8.40 1.61 2.20 . 11.7 10.5 12.0 2.56 7.95 4.14 9.50 6.71 10.1 12.0 3.43 9.81 9.25 11.8 . . . 6.69 8.53 10.9 1.39 9.54 8.04 . . 3.33 11.3 10.5 10.2 12.1 5.81 2.64 1.39 10.9 7.93 . 10.6 6.95 2.30 10.9 7.36 5.84 7.46 2.56 9.58 8.38 5.42 10.7 . 10.1 8.49 12.4 7.05 4.43 3.40 13.1 4.88 .69 .69 12.1 10.7 .00 2.30 6.25 10.3 8.70 8.30 2.56 7.55 . . 11.1 9.84 . 7.75 2.89 . 1.39 1.79 Predecessor a b c d e f g h i j k l m Predecessor a b c d e f g h i j k l m 396 JONES AND MEWHORT nopqr s tuvwxyz Successor Successor Table A4 Table A3 (Continued) APPENDIX (Continued) ( received May 6, 2003; May (Manuscript received revision accepted for publication June 21, 2004.) accepted for publication revision Lowercase-by-Uppercase Bigram Frequency Bigram Lowercase-by-Uppercase z 9.41 5.86 3.69 4.73 10.1 2.56 5.00 6.32 8.93 .69 5.29 6.95 6.00 4.67 8.13 4.98 3.14 4.75 4.98 4.84 6.85 4.84 5.21 . 7.23 8.10 z ...... 1.79 . . . 1.79 . . . . 1.39 ...... abcd .00 4.09e 3.40 5.27f .00 . 3.76 7.47g 7.00 5.89 1.79h . . 3.74 . 5.43 4.83 6.55 3.30 5.12 3.81 4.77i 1.10 2.30 .00 4.91 .00 1.79 .j .00 .k . . . 2.71 4.06 . .00 6.24 . 4.48l 5.93 .00 . 2.64 .00 5.62 ...... 4.36m ...... 5.86 . 3.18 ...... 00 . . . 2.56 4.92n . . .00 3.18 .69 4.65 5.24 3.89 3.40 .69o . 4.62 . . 4.38 . 2.71 . 3.93 .00 . .00p .00 2.94 1.39 . 1.39 . 2.48 2.20q . 1.79 .00 .00 . . 1.79 .00 . . 4.53 4.78 .00 1.39 . 4.63 1.39 3.00 . 4.06r 3.93 2.83 1.10 1.61 .00 1.39 1.39 2.08 .00 2.30 .00 3.40s . . .00 . 3.66 . 3.04 ...... 1.10 4.29 . .00 3.95 ...... 2.20 .t 1.61 . 1.10 ...... 00 1.10 . . . .00 1.10 .00 .u . .00 3.50 . 1.79 . 1.10 . 4.33 .. . 1.39 . 5.43 1.95 .69 4.25 .v . . .69 2.89 ...... 2.89 .00 . 3.33w . .69 . . . 4.42 . . . . .00 . .x . 1.61 . . 2.30 .. 1.61 .. . . .00 . ... .00 3.83 .69 . . .00y 3.18 ...... 1.79 2.08 ...... 1.95 ...... 00... 3.93 .00 ...... 1.10 . 2.89 2.94 ... . .00 ...... 1.10 . . 3.30 . . ..00...... 2.30 ...... 00 .00 . .00 .00 .00 . . . .00 . .00 .69 . . .69 . . 3.53 .00 1.39 . .69 2.77 3.04 . . . . .00 . 1.10 . . .00 . . 3.30 2.20 1.79 . . . .00 . . . 2.30 . .00 . . . . .00 . . .00 . . .00 ...... 69 . . . . 1.10 .00 3.14 . . .00 . .00 . . .69 . 3.33 1.61 .00 . . 1.61 . . . . .69 . .69 . . . .00 . . . . .69 .69 . .69 ...... 00 . . . 1.95 . . . 1.39 . .00 . . .00 .69 . . . .69 . . 3.26 .00 1.10 1.79 .69 . . . . 2.48 1.61 .69 . . 1.61 . .00 . . .00 ...... 00 . .69 4.29 . .00 ...... 00 ...... 00 .00 2.89 . . . . .00 . . . .69 3.50 . . 2.20 4.01 1.10 . . . .69 . . . . .00 . .00 . . .00 . .00 ...... 00 . . . . . 1.39 ...... 69 ...... 3.78 ...... 69 . . . .00 . . .00 .00 ...... 00 . . . . opq 10.5r 10.6 11.2 12.0s 11.3 6.81 9.82 5.74 3.30t 13.0 5.81 1.95 10.6 12.3 9.43 12.8u 6.47 9.63 7.80 10.8 8.47 11.2 12.1 10.4v . 10.6 11.6 8.59 11.0 12.1 11.1 13.7 4.91 .00 12.5w 12.6 9.61 6.47 9.10 8.43 11.0 13.6 11.8 12.9 10.9 9.81 .69x 8.83 11.7 8.67 8.62 10.8 7.32 11.7 6.66 5.60 12.7 11.3 10.8 .69 13.3 6.27 5.58y 12.0 12.0 10.9 8.08 11.4 13.4 11.1 12.1 12.5 7.71 11.2 .00 .00 11.9 10.8 4.16 2.08 6.89 9.19 14.2 6.05 11.3 12.2 10.2 11.1 12.2 6.09 4.20 13.2 10.4 11.5 10.2 9.11 12.9 7.88 6.29 4.17 12.9 3.78 10.1 11.5 12.8 10.4 6.14 11.8 10.8 10.1 . 12.0 9.11 9.18 9.16 6.22 10.9 5.98 10.7 .00 6.18 8.62 3.71 8.22 6.64 12.0 8.08 1.10 9.83 4.52 9.85 11.3 11.0 .00 5.85 11.9 8.48 12.0 8.95 1.39 12.5 8.25 8.30 11.0 9.61 7.77 12.1 13.2 12.2 12.0 5.59 8.72 .00 12.1 11.4 7.33 1.10 12.2 . 11.0 8.97 6.35 8.53 1.95 .69 11.0 13.2 7.76 6.34 11.2 3.58 3.18 12.2 8.79 11.7 6.24 5.73 9.11 12.2 . 5.15 5.47 6.44 7.07 12.3 11.4 9.92 2.40 11.6 . 9.15 12.3 3.09 8.85 11.4 5.34 1.10 5.96 6.92 12.4 7.31 6.49 10.4 9.07 . .00 5.42 10.7 10.5 9.49 9.75 7.31 11.7 2.83 9.11 6.43 5.53 5.97 11.5 . 10.6 7.56 1.95 . 8.49 8.63 . 8.94 9.53 5.06 1.61 10.0 .00 7.43 4.39 8.97 7.87 10.7 2.94 .00 4.69 . 8.86 7.47 6.23 10.3 6.57 .69 6.43 5.64 4.76 2.94 3.71 8.04 . 1.39 6.76 4.55 4.42 1.10 .00 4.74 3.43 9.75 8.43 6.56 7.96 2.20 4.62 6.11 . . 5.06 1.10 6.00 1.95 10.9 .00 1.79 . 8.11 .69 1.10 . . . Predecessor a b c d e f g h i j kPredecessor A l B m C D E F G H I J K L M N O P Q R S T U V W X Y Z