Based on modifications of Fitts' Law suggested in the literature, 121 unique formulas were tested against reciprocal tapping data from 1,318 subjects (1,047 ...
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Effects of Age and Sex on Speed and Accuracy of Hand Movements: And the Refinements they Suggest for Fitts' Law George Erich Brogmus Proceedings of the Human Factors and Ergonomics Society Annual Meeting 1991 35: 208 DOI: 10.1177/154193129103500311 The online version of this article can be found at: http://pro.sagepub.com/content/35/3/208
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PROCEEDINGS of the HUMAN FACTORS SOCIETY 35th ANNUAL MEET/NG-I99I
EFFECTS OF AGE AND SEX ON SPEED AND ACCURACY OF HAND MOVEMENTS: AND THE REFINEMENTS THEY SUGGEST FOR FITTS' LAW George Erich Brogmus Human Factors Program, ISSM; Lab of Attention and Motor Performance, Gerontology University of Southern California, Los Angeles, CA
Based on modifications of Fitts' Law suggested in the literature, 121 unique formulas were tested against reciprocal tapping data from 1,318 subjects (1,047 males and 271 females) who participated in the Baltimore Longitudinal Study of Aging from 1960 to 1981 in order to determine the best formula (based on the standard error of estimate) and to examine age and sex differences using this formula. The best formula for males differed from that found for females, resulting in a set of new formulas which take into consideration age and sex and which fit the experimental data better than past formulations. While females were faster than males and young were faster than the old, a substantial portion of age and sex differences might be explained by a speed-accuracy tradeoff.
INTRODUCTION
accuracy tradeoffs that may take place with age, York and Biederman (1990) administered the Fitts' tapping task to 62 males and 84 females, 20 to 89 years of age. They found that women appear to perform better than men on the Fitts tapping task. They also found that the young men seem to favor speed over accuracy. The slopes for the lines fitted to the data using Fitts's original formula showed that women perform better on the more difficult tasks than the men and that, with age, women show less slowing. This work by York and Biederman is the first to closely examine the factors of speed, accuracy, age, and gender using the Fitts' tapping task. Most recently, Welford (1990) reviewed the current literature, including York and Biederman (1990), and concluded that the best formula for Fitts' Law is given by either Log2(AIW + 0.5) or Log2(AIW + 1). Welford also evaluated the apparent speed-accuracy tradeoff between the young and old and outlined an explanation for a shift from an emphasis on speed for the young to an emphasis on accuracy for the old.
The field of Human Factors can claim only two fundamental principles which have risen to the status of "laws": Hick-Hyman Law and Fitts' Law. The latter is the subject of this paper. Long before Fitts (1954) described the relationship between movement time, movement distance, and accuracy (target width), the qualitative nature of the relationship between these elements were well known and were documented by Woodworth (1899). Fitts, however, has been credited with consolidating the concepts into an information theory law, now known as Fitts' Law, the most frequently cited form of which is: MT =a + bLog2(2A/W)
(1)
where "a" and "b" are the empirically derived y-intercept and slope respectively, "A" is the center-to-center distance between targets, and "W" is the constructed target width. (The portion of the formula "Log2(2A/W)" is usually referred to as the index of difficulty.) Since Fitts (1954) proposed this relationship between movement time, amplitude, and target width, there have been numerous attempts to develop a formula that would better fit his original data as well as data from subsequent investigations (Bullock & Grossberg 1988; Crossman & Goodeve 1983; Howarth & Beggs 1981; Howarth, Beggs, & Bowden, 1971; MacKenzie, Martiniuk, Dugas, Liske, & Eickrneier, 1987; MacKenzie, 1989; Meyer, Abrams, Kornblum, Wright, & Smith, 1988; Meyer, Smith, & Wright, 1982; Schmidt, 1988; Schmidt, Zelazink, Hawkins, Frank, & Quinn, 1979; Wallace, Hawkins, & Mood, 1983; Welford, 1958, 1960, 1968; Welford, Norris, & Shock, 1969; Wright, & Meyer, 1983). With these modifications have come additional theoretical considerations for the information processing aspects of movement as well as methodological considerations for the design of tapping tasks. Nevertheless, Fitts' Law has been repeatedly shown to be quite robust.
Based on past research it is safe to say that a large sample size would probably be needed to clearly identify sex differences. This, combined with the desire for longitudinal research on the subject, makes it economically difficult to conduct such research. Fortunately, however, the data gathering for such a project had actually already been done. The Baltimore longitudinal study of aging (BLSA), a federally-sponsored research project, (Shock, 1984) is considered by many to be the "gold standard" of longitudinal research. The main purpose of the BLSA is to study "normal" aging. This extensive research project has been ongoing since February, 1958 and continues to conduct a multitude of tests including a battery of psychomotor performance measures on its subjects.
METHOD Welford (Welford, Norris & Shock, 1969; Shock, 1984) designed a reciprocal tapping task (similar to Fitts's original tapping task) that was administered to BLSA participants on each visit from 1960 to 1981. Only the results of analysis of the first visit data from this task are presented here. Welford's design allowed recording of each "hit" by using a pencil and paper to record the actual hits made. Initial testing of 325 males who were participating in this study was reported by Welford, Norris, and Shock (1969). In January, 1978 women began to be tested as part of the BLSA. "As of June 30, 1981, more than 300 [women] had been examined and tested at least once, 150 two or more times." (Shock, 1984, p.I) The data for the present study includes usable
Surprisingly, although much work has been done in substantiating (or attempting to refute) Fitts' Law under various conditions and for many different applications, and even though there has been some work done to improve the formula itself and to advance the psychomotor theory, there has been little work examining age and sex differences (Crossman & Goodeve, 1983; Murrell & Entwisle, 1960; Welford, 1958, 1960, 1968; Welford, Norris, & Shock, 1969). (See Brogmus, 1991, for a review of recent work on aging and gender as it relates to Fitts' Law.) Recently, with the intent to examine possible gender-related speed-
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PROCEEDINGS of the HUMAN FACTORS SOCIETY 35th ANNUAL MEETING-I99I
RESULTS AND DISCUSSION
data from 1,047 male subjects and 271 female subjects (aged 17 to 100, M=50.2; SD=16.2). Study participants were self-recruited volunteers from the Baltimore area, and therefore were neither a random sample nor a representative sample of the Baltimore population, who differ from the general population in that they are happier, healthier, and more likely to be married than the general population (Andres, 1978). Over 70 percent of the subjects were college graduates, and over 40 percent held advanced degrees.
The best formula for males differed from the best formula for females. The best formula for males turns out to be: MT = a + bLog 2(D'/W + 1)
(2)
which is of the form of Shannon's Theorem 17 (Shannon, 1948; which is presumedly where Fitts derived his original formula from) with the primary distance of measure being D' - the distance between the far edges of the scatters of hits instead of "A" - the center-to-center distance between targets. Formula 2 yields an Se= 15.43 and an r 2=0.9935 for males as compared to Formula 1 which
Each target configuration consisted of four parallel lines • two lines per target. Each line was approximately 4 1/2 inches (115 millimeters) long. Three different target widths were used (4, 11, and 32 millimeters) in conjunction with three different movement requirements (50, 142, and 402 millimeters, measured from the inside edge of one target to the center of the other target) for a total of nine target configurations. Subjects were seated at a desk and given the target configuration to be used. They were allowed to position the paper in front of them so that they were comfortable with its orientation, holding the paper with the nondominant hand and tapping back and forth from one target to the other using the dominant hand. The instructions read to the subjects included "be accurate in hitting the target and at the same time maintain maximum speed". The time in minutes for a total of 100 hits, each of the widths of both the right and left scatters of hits as well as the distance between the leftmost hit and the rightmost hit, excluding any wild deviant hits, were recorded. The nine target combinations were presented in different orders to different subjects in such a way that the serial positions both of the conditions and of the transitions from any condition to any other were appropriately balanced. One practice trial using one target configuration was given prior to the recorded trials.
resulted in an Se=23.66 and an r 2=0.98472. The best formula for females is the same as Formula 2 except D' is replaced by D - the constructed distance between the far edges of the targets: MT =
a
+ bLog2(D/W + 1)
(3)
Formula 3 resulted in an Se=21.38 and an r 2==0.98531 for females as compared to Formula 1 which resulted in an Se=27.50 and an r 2=0.97571 for females. Figure 1 shows Formula 2 fitted to the data for all subjects combined for each target configuration. 1600
~
r-;==::::c===r:::==::!==:!:==::::;---r-, l-SYf: Small Distance, Wide Target 2-81: Small Distance, Intermediate Target 3-SN: Small Distance, Narrow Target 4-MW: Medium Diatance, Wide Target 5-MI: Medium Distance, Intermediate Target 6-MN: Medium Distance, Narrow Target 7-LW: Long Distance, Wide Target 6-LI: Long Distance, Intermediate Target 9-LN: Long Distance, Narrow Target
1200
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a
In order to fairly evaluate age and sex differences, it is critically important to have a formula that provides a good fit to the data for each age group by sex. Therefore the pursuit of the "best" equation was of primary initial concern. The treatment of data can be outlined as follows: 1) first, "suitable" data was selected from the raw data, 2) next, formulas were tested using Se, the standard error of estimate, to see which one provided the best fit to the first visit data, 3) this formula was used to evaluate age and sex effects based on first visit data, 4) based on this evaluation, a new formula was created which incorporated age and sex, 5) this new formula was then tested similar to step 2 above to evaluate how well this formula fit the first visit data. One hundred and twenty one (121) unique formulas were applied to several groupings of the data to determine which formula was the best representation of the data. The 121 formulas were derived from all possible combinations of six (6) basic logarithmic expressions, five (5) different measures of movement amplitude, four (4) different measures of target width, and a formula derived by Welford (Welford, Norris, and Shock, 1969). For each of the 121 formulas, r2 (the squared coefficient of correlation, also known as the coefficient of determination) and Se were calculated for first visit data. The calculations were carried out in two ways: first, for all test conditions; second, omitting the "easiest" condition (i.e. small movement amplitude and wide target - SW) on the grounds that it does not fit the major trend of the data and instead represents a lower limit to movement time of about 200 msec (Welford, Norris and Shock, 1969, and Welford, 1990). The primary justification for the omission of this data point is that movement times of less than about 200 msec are too fast to be part of an information processing loop and thus are not indicative of the process modeled by Fitts' Law.
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INDEX OF DIFFICULTY
Figure 1. Movement time versus the index of difficulty using Formula 2 for all subjects combined. Standard error bars are smaller than the symbols and therefore are not observable. Target configuration SW (the point with the lowest index of difficulty) is not included in the regression line drawn. While it could be argued that the mean of all subjects for each target configuration is not the best baseline since it may emphasize the largest population age group, a nearly identical plot is achieved if the mean of the means of each age group are used instead. Females showed lower movement times than men for each target configuration and for every age range except those with very few subjects, but the main effects of sex were not significant (F==2.58, p==0.1083). However, there was a marginally significant interaction between sex and target configuration (F=1.85, p:::0.0625), such that females were disproportionately faster than males on the targets with a higher index of difficulty.
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PROCEEDINGS of the HUMAN FACTORS SOCIETY 35th ANNUAL MEETING-1991
With the exception of the groups with very small sample sizes, all y-intercepts are near zero and most are negative. Differences in y-intercepts between age groups were not statistically significant. Nevertheless, a trend is indicated: Young subjects tend to have a positive y-intercept, As they age this drops below zero and bottoms out around -30 ms around the 50's. It then begins to rise in the latter years. The y-intercepts for the females appear to decrease more linearly with age.
1600
~
A Males v Females
1200
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Figure 4. Y-intercepts for males and females by age using the means of the y-intercepts calculated for each subject. Formula 2 was used for males and Formula 3 was used for females.
85-94 (n=8)
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>-
-50
The consistent trend of females being faster than males for each age group and for nearly every target within each age group suggests that women may have a slight advantage in rapid hand movements that require precision. Whether this is the result of a biological advantage, performance strategy, or gender difference due to work and hobby stereotypes is open to question. Part of this difference may also be explained in terms of a speed-accuracy tradeoff. Another explanation may be related to the smaller average mass of female forearms, which might be allowing for fewer corrections to be made to the arm trajectory in order to overcome the inertia of the arm during deceleration.
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50
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INDEX OF DIFFICULTY
1600
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~n=217~ n=212
200 .----,----,---r----r---,--.-__.----.--r----, v
n=271 n=250 (n=2H) 25 (n=35)
200
5
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b. Males v Females
7
INDEX OF DIFFICULTY
Figure 3. Formula 2 fitted to each age decade's movement times for all subjects.
v 100
Age differences in movement times were significant between every age group (F::38.03, p
