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Verbal Materials for Adult Aphasics in a Letter-Prediction Task
VERBAL MATERIALS FOR ADULT APHASICS IN A LETTER-PREDICTION TASK' John W. Black (The Ohio State University)
The predicting of successive typewritten spaces was used by Shannon (1951) to determine the amount of information vs. redundancy in written language. (Garner's case for "uncertainty" instead of "information," 1962, is convincing). Shannon generalized from single predictors, viewing the subject's guesses longitudinally throughout a sustained passage. In the present procedure the agreement of 10 predictors on a single space was used as a basis for generalization. Specifically, agreement by 10 normal users of the language was accepted as a criterion for redundancy for a particular letter. Ten paragraphs of approximately 70 words were predicted space-by-space by 10 university students and the letters that were uniformly predicted correctly were treated as redundant. Two important and confounded assumptions were put to test. The first was an assumption that the redundant spaces were equally probable to be predicted correctly or at least that inequalities would average out over a paragraph. The second was that this equality in probability would be demonstrated in the predictions of aphasic individuals. Here, an explanation is in order. The normal-speaking adult who has lost his use of oral language through a cardio-vascular accident is not a child. He is an adult who behaves in some manners as he is expected to behave. In these instances the rules of probability , This research was supported jointly by Research Grant no. RD-1184-S from the Division of Research and Demonstration Grants, Social and Rehabilitation Service, Department of Health, Education, and Welfare, and a contract between The Ohio State University Speech Department and the Ohio Department of Health, Division of Chronic Diseases.
176
John W. Black
in normal behavior carryover to post-stroke behavior: stance, gait, affirmation and denial, smiling, and the like. It might follow that the more probable events of common language usage would also carry over into the post-stroke behavior. This is where the two assumptions under consideration become a confounded issue. The materials might be of equal probability, letter-by-Ietter for a normal group of experimental predictors (and this would be an expected and relevant observation) or for an abnormal group of predictors. This is the instance that was carried out in the study reported here. Both of the foregoing assumptions may be tested for a long time to come. Meanwhile, for practical purposes it may be feasible to collapse the two preceding assumptions into a single topic of the predictability of selected material by aphasic adult persons.
PROCEDURES AND RESULTS
Twenty adult aphasic individuals who were at least six months post-stroke served as experimental subjects. Both physicians and speech pathologists agreed that they were ready for systematic language therapy. Each subject responded to the paragraphs two times, a total of 20 experiences over at least as many days. The paragraphs were completed in a rotational order with each subject, through 10, beginning with a different paragraph. Some assumptions were, (a) spaces that have been found redundant by university students are of equal difficulty in a letter-prediction task for aphasic individuals, and (b) spaces that are predictable for university students tend to be predictable for aphasic individuals, this being evidence that adult aphasics are somewhat familiar with the statistics, vocabulary and syntax of their language. Only the first of these was tested directly.
Hypothesis I. There is no difference in the apparent level of difficulty of the 10 paragraphs as measured by percent-correct scores. It was an assumption that a redundant space is a redundant space, always, for everyone for whom the language is vernacular and that the identically programmed paragraphs would be of equal difficulty. The mean proportion of correct responses was determined paragraph-byparagraph and trial-by-trial. Paragraph 1 designates a partie-glar passage
Verbal material in a letter-prediction task
177
irrespective of the order of presentation. The data were cast into a matrix in which columns represented paragraphs, sub-columns the two trials, and rows subjects. The data were treated by a triple analysis of variance. The analysis is summarized and the relevant mean values are enumerated in Table I-A. Clearly the paragraphs were unequal in difficulty and the hypothesis was rejected.'
TABLE I
A. Mean Percent Correct Responses of 20 Aphasic Subjects to 10 Paragraphs Throughout Two Trials Paragraph
Trial I Trial II Mean
1
2
3
4
5
6
7
8
9
10
Mean
66.8 72.0 69.4
70.9 77.3 74.1
64.0 70.7 67.4
76.3 81.3 78.8
67.4 72.3 69.9
66.9 75.0 71.0
70.0 78.5 74.3
70.9 75.1 73.0
67.2 72.6 69.9
63.2 71.5 67.4
68.4 74.6
Any difference between two row and column means of 3.2 significant at the .05 level of confidence. B. Analysis of Variance Source of variation A (Paragraphs) B (Trials) S (Subjects) AB AS BS ABS Total
d.f.
Sum of squares
Mean square
F
9 1 19 9 171 20 171 400
4533.2 3959.6 71344.6 299.1 12203.5 3622.6 8820.1 104712.7
503.7 3959.6
7.05* 21.86"
25.4 71.4 181.1 51.6
.49
* Significant beyond the .05 level of confidence.
Hypothesis II. There is no difference in the mean uncertainty (information) of the successive "redundant spaces" of the paragraphs. , A separate study with vastly different material yielded similar results (Wild, Hooker and Black, 1969). Paragraphs were taken from three levels of encyclopedias, children's, intermediate, and adults'. Redundant spaces were determined as in this study. Aphasic individuals made highest scores on the children's material and lowest scores on the adult paragraphs. The differences were statistically significant.
178
John W. Black
This provided a test of a different aspect of the same assumption that was tested above. In testing this hypothesis the tallies of the responses to a single paragraph typically extended across 14 pages of 20 column paper. Under an assumption of equally probable events the uncertainty within a column varied from 0 to 4.333 bits as the subjects gave from o to 20 different responses. The obtained uncertainty associated with the 20 responses to a single redundant space was computed in the conventional manner. However, not all of the data were used. Nineteen equally spaced columns among the redundant spaces of each paragraph were selected. An analogy provides the rationale. One might imagine that one race course is a mile long, another is a kilometer, and that one wishes to compare performance or achievement at an equal number of points in the two courses. An experimenter might divide each length by 20 - or any convenient number - and thereby select the same number of data points in the two courses. In the present instance, the measures of uncertainty of the 19 equally distant data points (columns of the ledger paper) were cast into a matrix that accommodated a triple analysis of variance with 19 columns representing the selected spaces of the paragraphs, two sub-columns trials, and 10 rows paragraphs. The analysis is summarized and the relevant mean values of uncertainty expressed in bits are enumerated in Table II A and B. Consistent with the results reported above, there was a significant difference between trials. This reflected greater agreement of the predictions on the second trial. There was no difference in the uncertainty among the 19 spaces. Thus, the "redundant letters" that occurred late in the paragraphs were not different in uncertainty from the earlier ones. The data suggested some observations. First, 10 paragraphs written about a single topic would be expected to contain a number of repeated substantive words both within a paragraph and from one paragraph to another. Seven occurred more than five times in one paragraph, occurred in more than one paragraph, and contained four or more letters: vote, people, elect, good, country, citizens, government. Scores were computed for the subjects, word by word, on Trial I and Trial II, and experience by experience. There was significant improvement in the spelling of the words on the basis of (a) sequential occurrences within a trial, either Trial I or Trial II, and (b) for Trial II over Trial I (t). Second, aphasic individuals predicting redundant spaces of a series of paragraphs might be expected to err in manners predictable
Verbal material in a letter-prediction task
179
TABLE II
A. Mean Uncertainty Measures (Bits) of Selected Spaces for Each Paragraph, Trial I and Trial II
Paragraph* 1
Trial I Trial II
2
3
1.510 1.464 1.403 1.363 1.008 1.092
4
5
6
7
8
9
10
Mean
.989 1.178 1.491 1.312 1.247 1.553 1.627 .795 1.014 1.157 1.243 1.173 1.283 ·1.205
1.3774 1.1333
* The differences between the means of the two rows exceeds .2 and is therefore significant beyond the .05 level. B. Analysis of Variance -~~--
Source of variation A (Spaces) B (Trials) C (Paragraphs) AB AC BC ABC Total "
d.£. 18 1 9 18 162 9 162 379
Sum of squares 9.2 5.7 9.5 1.5
134.7 1.6 15.6 177.8
Mean square
.5 5.7 1.1 .1 .8
F .62 31.97* .88
.2
.1
Significant beyond the .05 level of confidence.
to persons familiar with the language disorders of aphasia and the accompanying visual problems. Eight categories of errors were established a priori and given arbitrary definitions: 1. anticipatory response - an error which precedes a correct response by no more than two letters of spaces (eX'ample, govnrment); 2. perseveration response - a repeated letter within two spaces after a correct response (example, governmmnt); 3. a phonetically reasonable response (examples, sitizen, stats); 4. another word (examples, goodrnment or in for is); 5. C011l11lon mispronunciation (example, govermment); 6. an error that is the next letter in the alphabetic sequence after a correct response (example, goversment); 7. nonsense and carelessness; and 8. "other and explanation."
180
John W. Black
Five staff members, all familiar with aphasic patients, worked independently in categorizing the errors that occurred two of more times in the equally-distant data points used in testing Hypothesis II. The errors were copied to five sets of ledger sheets for them, one set per judge. The errors were studied within the context of otherwise correctly spelled words, independent of other errors within the same words. The judges were urged to try to use the first seven explanations (a-g) but, if the error did not fit one of the seven categories, to try to describe it and explain it. Three hundred seventy-six of the 421 errors were unanimously judged as being in one of the eight categories. Only 45 errors did not yield a clear majority of judgments. In both Trials I and II, categories 1, 4 and 7 were used most frequently. Category 4 occurred 79 times in Trial I and category 7 occurred 63 times in Trial II. Categories 3, 5, 6 and 8 occurred fewer than seven times each throughout both trials. SUMMARY
The principal assumption under test was that redundant spaces, as determined by unanimity of correct responses by 10 normal adults, are equally simple for aphasic persons to predict. This is not the case. Paragraphs may be predicted in the same manner and be unequal in difficulty as measured by correct responses. This difference is not revealed by pooling the relative uncertainty of equally spaced data points in different paragraphs and using uncertainty or diversity among the 20 responses per data point as the criterion. This is not inconsistent with the earlier finding. If the spaces are unequal in ease of prediction, then they would probably be unequal in the diversity of the results, space by space. As these inequalities are pooled the unsystematic differences would tend to cancel each other. The basic fact is that a redundant space, based on 10 normal predictors, is not a tenable generalization, at least when extended to aphasic predictors. This does not alter the usefulness of the material for repeated measures and for comparisons with counter balanced stimuli. REFERENCES GARNER, W. R. (1962) Uncertainty and Structure as Psychological Concepts, Wiley, New York. SHANNON, E. E. (1951) Prediction and entropy of printed English, "Bell System Techn. J.," 30, 50-64. WILD, ,so D., HOOKER, E. H., and BLACK, J. W. (1969) A study of aphasic individuals predicting letters of graded material, "J. Communicat. Disord.," 2, 336-339. John W. Black, The Ohio State University, Department of Speech, 154 North Oval Drive, Columbus, Ohio 43210, U.S.A.
The predicting of successive typewritten spaces was used by Shannon (1951) to determine the amount of information vs. redundancy in written language. (Garner's case for "uncertainty" instead of "information," 1962, is convincing). Shannon generalized from single predictors, viewing the subject's guesses longitudinally throughout a sustained passage. In the present procedure the agreement of 10 predictors on a single space was used as a basis for generalization. Specifically, agreement by 10 normal users of the language was accepted as a criterion for redundancy for a particular letter. Ten paragraphs of approximately 70 words were predicted space-by-space by 10 university students and the letters that were uniformly predicted correctly were treated as redundant. Two important and confounded assumptions were put to test. The first was an assumption that the redundant spaces were equally probable to be predicted correctly or at least that inequalities would average out over a paragraph. The second was that this equality in probability would be demonstrated in the predictions of aphasic individuals. Here, an explanation is in order. The normal-speaking adult who has lost his use of oral language through a cardio-vascular accident is not a child. He is an adult who behaves in some manners as he is expected to behave. In these instances the rules of probability , This research was supported jointly by Research Grant no. RD-1184-S from the Division of Research and Demonstration Grants, Social and Rehabilitation Service, Department of Health, Education, and Welfare, and a contract between The Ohio State University Speech Department and the Ohio Department of Health, Division of Chronic Diseases.
176
John W. Black
in normal behavior carryover to post-stroke behavior: stance, gait, affirmation and denial, smiling, and the like. It might follow that the more probable events of common language usage would also carry over into the post-stroke behavior. This is where the two assumptions under consideration become a confounded issue. The materials might be of equal probability, letter-by-Ietter for a normal group of experimental predictors (and this would be an expected and relevant observation) or for an abnormal group of predictors. This is the instance that was carried out in the study reported here. Both of the foregoing assumptions may be tested for a long time to come. Meanwhile, for practical purposes it may be feasible to collapse the two preceding assumptions into a single topic of the predictability of selected material by aphasic adult persons.
PROCEDURES AND RESULTS
Twenty adult aphasic individuals who were at least six months post-stroke served as experimental subjects. Both physicians and speech pathologists agreed that they were ready for systematic language therapy. Each subject responded to the paragraphs two times, a total of 20 experiences over at least as many days. The paragraphs were completed in a rotational order with each subject, through 10, beginning with a different paragraph. Some assumptions were, (a) spaces that have been found redundant by university students are of equal difficulty in a letter-prediction task for aphasic individuals, and (b) spaces that are predictable for university students tend to be predictable for aphasic individuals, this being evidence that adult aphasics are somewhat familiar with the statistics, vocabulary and syntax of their language. Only the first of these was tested directly.
Hypothesis I. There is no difference in the apparent level of difficulty of the 10 paragraphs as measured by percent-correct scores. It was an assumption that a redundant space is a redundant space, always, for everyone for whom the language is vernacular and that the identically programmed paragraphs would be of equal difficulty. The mean proportion of correct responses was determined paragraph-byparagraph and trial-by-trial. Paragraph 1 designates a partie-glar passage
Verbal material in a letter-prediction task
177
irrespective of the order of presentation. The data were cast into a matrix in which columns represented paragraphs, sub-columns the two trials, and rows subjects. The data were treated by a triple analysis of variance. The analysis is summarized and the relevant mean values are enumerated in Table I-A. Clearly the paragraphs were unequal in difficulty and the hypothesis was rejected.'
TABLE I
A. Mean Percent Correct Responses of 20 Aphasic Subjects to 10 Paragraphs Throughout Two Trials Paragraph
Trial I Trial II Mean
1
2
3
4
5
6
7
8
9
10
Mean
66.8 72.0 69.4
70.9 77.3 74.1
64.0 70.7 67.4
76.3 81.3 78.8
67.4 72.3 69.9
66.9 75.0 71.0
70.0 78.5 74.3
70.9 75.1 73.0
67.2 72.6 69.9
63.2 71.5 67.4
68.4 74.6
Any difference between two row and column means of 3.2 significant at the .05 level of confidence. B. Analysis of Variance Source of variation A (Paragraphs) B (Trials) S (Subjects) AB AS BS ABS Total
d.f.
Sum of squares
Mean square
F
9 1 19 9 171 20 171 400
4533.2 3959.6 71344.6 299.1 12203.5 3622.6 8820.1 104712.7
503.7 3959.6
7.05* 21.86"
25.4 71.4 181.1 51.6
.49
* Significant beyond the .05 level of confidence.
Hypothesis II. There is no difference in the mean uncertainty (information) of the successive "redundant spaces" of the paragraphs. , A separate study with vastly different material yielded similar results (Wild, Hooker and Black, 1969). Paragraphs were taken from three levels of encyclopedias, children's, intermediate, and adults'. Redundant spaces were determined as in this study. Aphasic individuals made highest scores on the children's material and lowest scores on the adult paragraphs. The differences were statistically significant.
178
John W. Black
This provided a test of a different aspect of the same assumption that was tested above. In testing this hypothesis the tallies of the responses to a single paragraph typically extended across 14 pages of 20 column paper. Under an assumption of equally probable events the uncertainty within a column varied from 0 to 4.333 bits as the subjects gave from o to 20 different responses. The obtained uncertainty associated with the 20 responses to a single redundant space was computed in the conventional manner. However, not all of the data were used. Nineteen equally spaced columns among the redundant spaces of each paragraph were selected. An analogy provides the rationale. One might imagine that one race course is a mile long, another is a kilometer, and that one wishes to compare performance or achievement at an equal number of points in the two courses. An experimenter might divide each length by 20 - or any convenient number - and thereby select the same number of data points in the two courses. In the present instance, the measures of uncertainty of the 19 equally distant data points (columns of the ledger paper) were cast into a matrix that accommodated a triple analysis of variance with 19 columns representing the selected spaces of the paragraphs, two sub-columns trials, and 10 rows paragraphs. The analysis is summarized and the relevant mean values of uncertainty expressed in bits are enumerated in Table II A and B. Consistent with the results reported above, there was a significant difference between trials. This reflected greater agreement of the predictions on the second trial. There was no difference in the uncertainty among the 19 spaces. Thus, the "redundant letters" that occurred late in the paragraphs were not different in uncertainty from the earlier ones. The data suggested some observations. First, 10 paragraphs written about a single topic would be expected to contain a number of repeated substantive words both within a paragraph and from one paragraph to another. Seven occurred more than five times in one paragraph, occurred in more than one paragraph, and contained four or more letters: vote, people, elect, good, country, citizens, government. Scores were computed for the subjects, word by word, on Trial I and Trial II, and experience by experience. There was significant improvement in the spelling of the words on the basis of (a) sequential occurrences within a trial, either Trial I or Trial II, and (b) for Trial II over Trial I (t). Second, aphasic individuals predicting redundant spaces of a series of paragraphs might be expected to err in manners predictable
Verbal material in a letter-prediction task
179
TABLE II
A. Mean Uncertainty Measures (Bits) of Selected Spaces for Each Paragraph, Trial I and Trial II
Paragraph* 1
Trial I Trial II
2
3
1.510 1.464 1.403 1.363 1.008 1.092
4
5
6
7
8
9
10
Mean
.989 1.178 1.491 1.312 1.247 1.553 1.627 .795 1.014 1.157 1.243 1.173 1.283 ·1.205
1.3774 1.1333
* The differences between the means of the two rows exceeds .2 and is therefore significant beyond the .05 level. B. Analysis of Variance -~~--
Source of variation A (Spaces) B (Trials) C (Paragraphs) AB AC BC ABC Total "
d.£. 18 1 9 18 162 9 162 379
Sum of squares 9.2 5.7 9.5 1.5
134.7 1.6 15.6 177.8
Mean square
.5 5.7 1.1 .1 .8
F .62 31.97* .88
.2
.1
Significant beyond the .05 level of confidence.
to persons familiar with the language disorders of aphasia and the accompanying visual problems. Eight categories of errors were established a priori and given arbitrary definitions: 1. anticipatory response - an error which precedes a correct response by no more than two letters of spaces (eX'ample, govnrment); 2. perseveration response - a repeated letter within two spaces after a correct response (example, governmmnt); 3. a phonetically reasonable response (examples, sitizen, stats); 4. another word (examples, goodrnment or in for is); 5. C011l11lon mispronunciation (example, govermment); 6. an error that is the next letter in the alphabetic sequence after a correct response (example, goversment); 7. nonsense and carelessness; and 8. "other and explanation."
180
John W. Black
Five staff members, all familiar with aphasic patients, worked independently in categorizing the errors that occurred two of more times in the equally-distant data points used in testing Hypothesis II. The errors were copied to five sets of ledger sheets for them, one set per judge. The errors were studied within the context of otherwise correctly spelled words, independent of other errors within the same words. The judges were urged to try to use the first seven explanations (a-g) but, if the error did not fit one of the seven categories, to try to describe it and explain it. Three hundred seventy-six of the 421 errors were unanimously judged as being in one of the eight categories. Only 45 errors did not yield a clear majority of judgments. In both Trials I and II, categories 1, 4 and 7 were used most frequently. Category 4 occurred 79 times in Trial I and category 7 occurred 63 times in Trial II. Categories 3, 5, 6 and 8 occurred fewer than seven times each throughout both trials. SUMMARY
The principal assumption under test was that redundant spaces, as determined by unanimity of correct responses by 10 normal adults, are equally simple for aphasic persons to predict. This is not the case. Paragraphs may be predicted in the same manner and be unequal in difficulty as measured by correct responses. This difference is not revealed by pooling the relative uncertainty of equally spaced data points in different paragraphs and using uncertainty or diversity among the 20 responses per data point as the criterion. This is not inconsistent with the earlier finding. If the spaces are unequal in ease of prediction, then they would probably be unequal in the diversity of the results, space by space. As these inequalities are pooled the unsystematic differences would tend to cancel each other. The basic fact is that a redundant space, based on 10 normal predictors, is not a tenable generalization, at least when extended to aphasic predictors. This does not alter the usefulness of the material for repeated measures and for comparisons with counter balanced stimuli. REFERENCES GARNER, W. R. (1962) Uncertainty and Structure as Psychological Concepts, Wiley, New York. SHANNON, E. E. (1951) Prediction and entropy of printed English, "Bell System Techn. J.," 30, 50-64. WILD, ,so D., HOOKER, E. H., and BLACK, J. W. (1969) A study of aphasic individuals predicting letters of graded material, "J. Communicat. Disord.," 2, 336-339. John W. Black, The Ohio State University, Department of Speech, 154 North Oval Drive, Columbus, Ohio 43210, U.S.A.