WORD LENGTH, PROSE DIFFICULTY, AND READING RATE a

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1 WORD LENGTH, PROSE DFFCULTY, AND READNG RATE a Ronald P. Carver b University of Missouri-Kansas City Abstract. n Study 1, the functional relationship between word length and passage difficulty was determined to be linear from Grade 1 to Grade 17 difficulty levels. A total of 360 passages were studied; the passages were sampled from curriculum materials used in all school levels ranging from Grade 1 to graduate school. Average word length was measured in both character spaces per word and letters per word. The newly developed Rauding Scale was used to estimate passage difficulty. n Study 2, the reading rate of college students was found to decrease from about 315 to 200 words per min. as difficulty increased from about Grade 2 to about Grade 17. However, when measured in standard length words per min. reading rate was approximately constant at about words per min. as difficulty increased from about Grade 5 to about Grade 14. These data were interpreted as providing no support for certain current theory relating redundancy to reading rate and eye movements. ntuitively, one would expect reading rate to go down as prose material becomes more difficult and to go up as prose material becomes less difficult. ndeed, the idea that a flexible reader adjusts his rate to the difficulty of the prose complements this intuition. Yet, the intuition appears to be mostly wrong. Studies by Carver (1972), Klare (1963), Miller and Coleman (1972) and Pitcher (1953) have helped to clarify the relationship between rate and difficulty. These studies verify that rate in words per minute does decrease as difficulty increases. However, as prose becomes less difficult the average word length becomes smaller, i.e., there is a high correlation between average word length and prose difficulty (Bormuth, 1969; Carver, 1974c; Coleman, 1971). Thus, if the physical length of the prose is controlled, e.g., in letters per second or standard length words per minute, it is clear that reading rate is not highly correlated with prose difficulty. n fact, the data presented by Carver (1972) and Miller & Coleman (1972) indicate that reading rate is relatively constant throughout a wide range of difficulty. Thus, a The preparation of this paper was supported in part by the U.S. Office of Naval Research, Personnel and Training Research Programs, Contract No. O C-O240. b Reprints may be requested from the author, School of Education, University of Missouri- Kansas City, Missouri,

2 194 Journal of Reading Behavior 1976 V, 2 the idea that readers increase their rate when material gets easier does not seem to be true. Yet, it is true that the actual number of words read per minute does increase, because the words tend to get shorter as material becomes easier. The purpose of this article is to further clarify and quantify the interrelationships among word length, reading rate, and prose difficulty. Data from two studies, Study 1 and Study 2, will be presented. n both studies, a new and highly valid method for measuring prose difficulty will be employed. n Study 1, the nature of the relationship between word length and prose difficulty will be determined, using two different methods for measuring word length. n Study 2, the relationship between reading rate and prose difficulty will be further investigated using two methods of measuring reading rate. The new method that will be used for measuring difficulty, or readability, is the Rauding Scale of Prose Difficulty (Carver 1975). Unlike traditional readability formulas, this method employs a group of qualified experts to rate passages according to the complexity of the ideas contained in those passages. The Rauding Scale provides grade difficulty units (G d ) from Grade 1 to Grade 18, and this scale may also be converted into a level scale (L d ) from Level 1 to Level 6 with each level consisting of three grades, e.g., Level 4 consists of Grades 10, 11, and 12. Thus, word length and reading rate may be related to the grade difficulty or the level difficulty of prose using the Rauding Scale. STUDY 1 NTRODUCTON The purpose of this study was to investigate the functional relationship between word length and passage difficulty. As noted earlier, it is known that word length is correlated with passage difficulty but the precise nature of this relationship has not been determined throughout the range of prose difficulty. Word length was measured two ways, character spaces per word (cpw) and letters per word (lpw). Passages Two sets of passages were studied. One set consisted of the 330, 100-word passages that Bormuth (1969) sampled from curriculum materials used in Grades 1-12 and college. The other set of materials consisted of 30 passages that Carver (1974c) sampled from graduate school reading material. The second sample was combined with the first sample so as to be able to extend the range of prose difficulty.

3 Carver 195 Passage Difficulty The Rauding Scale grade difficulties of the 360 passages were determined as part of another study reported elsewhere (Carver, 1975). Briefly summarized, the passages were rated for difficulty using the following standard procedures: (a) the Rauding Scale Qualification Test (Carver, 1974b) was administered, (b) three raters who had passed the test were paid to rate each of the 360 passages, and (c) the mean of their three ratings was used to determine the final G d value for each passage. Word Length Character spaces per word, cpw, was determined by counting the total number of character spaces in each passage and dividing by the total number of words in the passage. Character spaces correspond to line length on a regular typewriter, e.g., each alphabetical character in a word counts as a character space as well as each space between words and each punctuation mark, etc. Words were defined as what is contained between two blank spaces. Letters per word, lpw, were counted using the rules derived for using the RDE Scale as a measure of prose difficulty (Carver, 1975). This procedure, explained in detail elsewhere (Carver, 1974c), requires that certain atypical segments be deleted prior to counting words and letters. Numbers, abbreviations, and capitalized words are deleted. n general, what falls between two blank spaces is counted as a word and the number of character spaces between the two blank spaces counts as a letter. This method for counting letters per word eliminates a certain amount of unrepresentativeness associated with some passages, e.g., those that include a large number of single digits or a large number of references to a person with a long name such as "Elizabeth". RESULTS AND DSCUSSON Fig. 1 contains the median character spaces per word, cpw, and letters per word, lpw, values for all the passages at each grade difficulty, G d. t may be noted that there is a linear relationship between word length and passage difficulty, no matter which method, cpw or lpw, is used for measuring word length. Furthermore, the two relationships are almost perfectly parallel. t may be noted that there are approximately 3.9 letters per word, lpw, in Grade 1 material and approximately 5.2 letters per word, lpw, in Grade 17 material. For Grade 1 material, there are approximately 5.2 character spaces per word, cpw, while for Grade 17 material there are approximately 6.4 character spaces per word, cpw. A least squares straight line was fit to these data and these lines and their equations are also presented in Fig. 1. The equation for predicting character spaces

4 196 Journal of Reading Behavior 1976 V, CHARACTER SPACES PER WORD (cpw) _ cpw =.0753 G d t 5.5 O o rr o LETTERS PER WORD (lpw) lpw G d flfil PASSAGE DFFCULTY, G d Figure 1. Word length as a function of passage difficulty (G d ), using character spaces per word (cpw) and letters per word (lpw) as indicants of word length. per word, cpw, from grade difficulty, G d, may be transformed to predict G d from cpw, i.e., G d = cpw (1) The equation for letters per word, lpw, also may be transformed to predict grade difficulty, G d, i.e., G d = lpw (2) Equation 2 may be subtracted from Equation 1 to develop an equation which expresses character spaces per word, cpw, in terms of letters per word, lpw, i.e.,

5 Carver 197 cpw =.957 lpw (3) When any one of the three values G d, cpw, or lpw is known, Equations 1,2, and 3 may be used to make a rough estimate of the other two values. These estimates are not likely to be highly accurate for a single passage, but should be relatively accurate for a set of passages. Equation 2 may be used to estimate that an average word in a passage at Grade 18 difficulty (5.28 lpw) is approximately 34 percent longer than an average word in a passage at Grade 1 difficulty (3.94 lpw). t appears that average word length is indeed a significant variable that tends to co-vary linearly with passage difficulty. t may also be estimated from Equation 1 that a passage that has an average word length equal to a standard length word, i.e., 6 character spaces (see Carver, 1972, or Carver, 1974a), has an estimated difficulty of Grade 12.8, i.e., G d = 12.8 when cpw = 6. Thus, passages of Grade 12 difficulty and lower may be estimated to have an average word length less than the standard length word while passages of Grade 13 difficulty or higher may be estimated to have an average word length greater than the standard length word. This means that when reading rate is measured in actual words per minute, such estimates will tend to overestimate rate when the reading material is Grade 12 difficulty or less, and will tend to underestimate rate when the reading material is Grade 13 difficulty or greater. These data suggest that any investigation of reading rate which purports to be precise should control for word length, especially when the material is at different grade difficulties. n the interest of standardization, reading rate could be measured in character spaces per minute (cpm) and converted into standard length words per minute (Wpm) dividing by 6, i.e., & (4) n certain reports of reading rate, the actual words per minute (wpm) may be given as well as the grade difficulty of the material. n these situations, Wpm c may be estimated using the following equation: Wpm = wpm X 2^. (5) An estimate of characters per word, cpw, may be obtained using Equation 1 when the grade difficulty, G d, of the material is known. n some reports of reading rate, the number of letters read per second (ps) may be given. f the grade difficulty of the material, G d, is given, then rate in standard length words per min.,wpm,may be estimated using the following equation: c Notice that standard length words per min. is designated by an upper case "W" in Wpm, while actual words per min. is designated by the traditional lower case "w" in wpm.

6 198 Journal of Reading Behavior 1976 V, (6) The values of character spaces per word, cpw, and letters per word, lpw, may be solved for in Equations 1 and 2, respectively. As one example of how Equations 5 and 6 may be used, suppose a study of reading flexibility found that college students read Grade 5 material at 300 wpm and Grade 11 material at 276 wpm. The Grade 5 and 11 rates expressed in wpm may be entered into Equation 1 and solved for cpw, i.e., 5.41 cpw and 5.87 cpw, respectively. These values may be entered into Equation 5 to give Wpm values of 270 and 270 respectively. Thus, it may be seen that such a study might report that fifth grade material was read almost 10 percent faster than eleventh grade material but the difference in the rates would actually have been closer to 0 percent if the rates had been measured in standard length words per minute, Wpm. The following study demonstrates more dramatically the consequences of measuring rate in Wpm rather than the traditional wpm when the reading material is at varying levels of passage difficulty. STUDY 2 NTRODUCTON The purpose of Study 2 was to investigate how reading rate, measured in actual words per minute, wpm, and standard words per minute, Wpm, differed as a function of level difficulty, L d, as measured by the Rauding Scale. Passages The prose materials were the 36, Miller and Coleman (1967) passages that have been published by Aquino (1969). Passage Difficulty As in Study 1, the Rauding Scale of Prose Difficulty was used to estimate the grade difficulties, G d, of the 36 passages. The standard procedures were used for the Rauding Scale. As for time limits and passage instruction, each of the three raters was asked to: (a) read the entire passage and to try to understand the passage as they read it, (b) take as much time as they wanted in making their ratings, (c) wait until one minute had expired, as noted by a special timing device explained elsewhere (Carver, 1975), until they proceeded to the next passage. After the grade difficulty, G d, values had been obtained from the above procedures, all the passages at each level of difficulty, L d, were combined. The number of passages at each level of difficulty, L d, was as follows: Level 1, N = 6; Level 2, N = 14; Level 3, N = 7; Level 4, N = 2; Level 5, n = 5; and Level 6, N = 2.

7 Carver 199 Reading Rate The mean reading rates for each passage was that found by Miller and Coleman (1972). Each of 83 college students read a set of 9 passages so that each mean reading rate score represented 83 5s but not necessarily the same 83 Ss were represented in each mean. For each of the 36 passages, Miller and Coleman reported their data both in words per minute, wpm, and letters per second, lps. For the set of the passages at each level of difficulty, L d, a mean value for both wpm and lps was calculated. 11 The wpm mean values were then substituted into Equation 5 to get one estimate of standard words per minute (WpmO; the cpw values for Equation 5 were estimated from Equation 1 using the middle G d value for each L d, e.g., when L d = 3, G d = 8, and cpw = The mean lps values were substituted into Equation 6 to get a second estimate of standard words per minute (Wpni2 ); the cpw and lps values were determined in a manner similar to that described for Wprrii, e.g., when L d = 2, G d = 5, cpw = 5.41, and lpw = RESULTS AND DSCUSSON Fig. 2 contains the relationship between reading rate and passage difficulty when rate is measured in both wpm and Wpm. Wpm is given for both the estimate based upon wpm, Wpmi, and the estimate based upon lps, Wpm 2. Notice that the reading rate in actual words per min., wpm, decreases with each successive increase in the level of prose difficulty, going from 315 wpm at Level 1 (Grades 1-3 difficulty) to 202 wpm at Level 6 (Grades difficulty). This result is no doubt the type of result that has contributed to the idea that individuals are flexible in their reading, i.e., the most difficult level of prose difficulty was read at a rate 56 percent slower that the least difficult level. Stated differently, materials of graduate school difficulty were read 56 percent slower than materials at the beginning reading level. Rate, as measured in standard words per minute, Wpm, appears to be quite different, however. There is little difference in the rate at which Levels 2-5 are read, either for Wpmi or Wpm 2. The range is only from 248 Wpm to 262 Wpm, a 14 Wpm difference. On a percentage scale this range is only about 5 percent, a very small amount of deviation for a wide range of material, i.e., from about Grade 5 to about Grade 14 in difficulty. The easiest materials, i.e., about Grade 2 difficulty, seem to read slightly faster, around 270 Wpm. The most difficult materials, i.e., about Grade 17 difficulty, are read somewhat slower, i.e., about 220 Wpm. The data in Fig. 2 may appear to add very little to the results already published by Carver (1972) and Miller and Coleman (1972). One advancement d The cooperation of G. R. Miller and E. B. Coleman in providing their data for reanalysis is gratefully acknowledged.

8 200 Journal of Reading Behavior 1976 V, < 260 cc O o.w 240 c Wpm (N-6) (N-14) (N-7) (N-2) (N-5) (N-2) ' PASSAGE DFFCULTY Figure 2. Reading rate as a function passage difficulty (G d and L d ), using actual words per min. (wpm) and standard words per min. (Wpm) as indicants of rate. represented in Fig. 2 is that the big difference between rate measured in wpm and Wpm, noted by Carver, has been replicated using the data collected by Miller and Coleman. Perhaps the biggest advantage represented by the Fig. 2 analysis is the measurement of difficulty along an absolute scale rather than the relative difficulty scales used in the two earlier studies. The measurement of difficulty along a grade difficulty, G d, and level difficulty, L d, scale allows rate to be analyzed in terms of specific difficulty levels. Also, the interaction between rate, difficulty level, and ability levels may be noted. Since these subjects were college students, it may be assumed that their mean level of reading ability was college level, i.e., approximately Level 5, or Grade 14, ability. Thus, the data suggest that Level 5 individuals, i.e., college-level students,

9 Carver 201 tend to read all material equal to and below their own level of ability, i.e., Levels 1-5, at approximately the same rate. The data also suggest that rate drops when the level of material difficulty exceeds the level of individual ability, e.g., when college level readers are reading graduate school materials. As Miller and Coleman (1972) have pointed out, however, it would be best if these data were replicated using different passages. Yet, even Miller and Coleman seem to agree that it was not unreasonable to suggest that individuals might lower their rate when they encounter material that is highly difficult to understand. On the other hand, under certain reading situations it would also seem reasonable that individuals might skip over material at a rate faster than their normal rate if they found it extremely difficult to understand. Probably, the most likely event to occur when individuals are presented highly difficult material would be high variability in rate, i.e., both between- and within-individuals. n any event, reading rate for materials above the reader's own level of ability does not seem highly important because most individuals tend not to read material that is above their own ability level (see Carver, 1974a). t seems much more important to be able to understand and predict reading rate for materials equal to and below an individual's own level of ability. These data have implications for reading theory that relates rate to redundancy. Smith (1971) has argued that individuals can take advantage of the redundancy in prose and thereby read faster because less visual information is required in order to get the meaning. Smith presents no prose reading data to support this theory but it does seem to be a plausible one. Yet, the data in Fig. 2 suggests that college individuals tend to throw their eyes down a line of print in a manner that has little or nothing to do with the redundancy of the material. Redundancy was not measured directly in Study 2, but it could be assumed that Level 2 materials are more redundant than Level 3, 4, and 5 materials at least redundancy as measured by the degree to which individuals could accurately predict succeeding words. Rather than simply assume the type of redundancy described above, the relationship between passage difficulty and redundancy was investigated. The mean cloze scores for all the passages of each difficulty level were calculated using the data published by Aquino (1969). These data are presented in Fig. 3. t may be noted that redundancy does decrease as the difficulty level of the reading material increases, going from about.68 at Level 1 to about.28 at Level 6. Of course, the proportion of cloze blanks correctly completed is only one way to estimate the semantic redundancy of prose. Another way would be to have individuals guess at each successive word in a prose passage. Miller and Coleman also did this and these data (from Aquino, 1969) plotted as a function of difficulty level, L d, are also presented in Fig. 3. Again, redundancy decreased in an almost perfectly linear fashion as the difficulty of the prose increased. There appears to be no question but that redundancy decreases as passage difficulty measured by the Rauding Scale increases. Therefore, the Wpm data in Fig. 2 do not support the theoretical

10 202 Journal of Reading Behavior 1976 V, o o.60 CLOZE UJ SUCCESSVE WORD GUESSNG (N«6) (N-14) (N-7) (N-2) (N-5) (N-2) L d G d» PASSAGE DFFCULTY Figure 3. Redundancy as a function of passage difficulty (G d and L d ), using cloze and successive word guessing as indicants of redundancy. mechanism outlined by Smith. College level individuals tend to read the same number of character spaces per minute no matter what the redundancy, at least for material that is equal to or below their own reading level. The data in Fig. 2 also do not appear to support the cognitive search guidance (CSG) mechanism suggested by Hochberg (1970). According to Hochberg, an individual uses his knowledge of what he has seen so far to predict where the eyes should move to obtain further information, and this mechanism is termed CSG. f CSG accurately describes eye movements during reading, then it would seem that Level 2 material should be read faster than Level 5 material. This is because it should be easier to predict where the words or phrases are which carry the most information in material which contains a high proportion of semantically redundant words and phrases. t appears that these empirically collected data relating passage difficulty to reading rate do not support the theoretical ideas of Smith and Hochberg. nstead, they seem to support an eye movement mechanism that ordinarily is little affected by the redundancy of prose. Before revising or completely rejecting any of the theory involved, it would seem best to collect more and better reading rate data which relates this variable to both prose difficulty and individual ability.

11 Carver 203 REFERENCES AQUNO, M. R. The validity of the Miller-Coleman readability scale. Reading Research Quarterly, 1969, 4, 352, 357. BORMUTH, JOHN R. Development of Readability analyses. U.S. Office of Education Final Report, Proj. No , Contract No. OEC , University of Chicago, March, CARVER, RONALD P. Evidence for the invalidity of the Miller-Coleman Readability Scale. Journal of Reading Behavior, 1972, 4 (3), CARVER, RONALD P. Toward a comprehensive theory of reading and prose rauding. Paper presented at the annual meeting of the American Educational Research Association. Chicago, April (a) CARVER, RONALD P. Manual for the Rauding Scale Qualification Test. Silver Spring, Md.: Revrac Publications, (b) CARVER, RONALD P. mproving reading comprehension; Measuring readability. Washington, D.C.: American nstitutes for Research, FNAL REPORT, R74-2, May (c) CARVER, RONALD P. Measuring prose difficulty using the Rauding Scale. Unpublished manuscript, COLEMAN, EDMUND B. Developing a technology of written instruction: Some determiners of the complexity of prose. n E. A. Rothkopf and P. E. Johnson (Eds.) Verbal learning research and the technology of written instruction. New York: Teachers College Press, [Pp ] HOCHBERG, JULAN Components of literacy: Speculations and exploratory research. n H. Levin and J. P. Williams (Eds.) Basic studies on reading. New York: Basic Books, [Pp ]. KLARE, GEORGE R. The measurement of readability. Ames, owa: owa State University Press, MLLER, GERALD R. & COLEMAN, EDMUND B. A set of thirty-six passages calibrated for complexity. Journal of Verbal Learning and Verbal Behavior, 1967, 6, MLLER, GERALD R. & COLEMAN, EDMUND B. The measurement of reading speed and the obligation to generalize to a population of reading materials. Journal of Reading Behavior, 1972, 4 (3), PTCHER, R. W. An experimental investigation of the validity of the Flesch Readability Formula as related to adult materials. Unpublished doctoral dissertation, University of Michigan, SMTH, FRANK Understanding reading. New York: Holt, Rinehart, and Winston, nc., 1971.