國立臺灣自兩範大學教育心理與輔導學系 教育心理學報，民 91 ' 34 卷， 1 期， 123-138 頁
SexDi質erences
in Statistical Reasoning
HUI-JU C. LIU
Dep位組lentof English LanguageDa-Yeh University
JOAN
B.
GARFIELD
Department of Educational Psychology University of Minnesota
Despite considerable research having been done in the area of sex dífferences ín mathematícal ability, statístícal ability has rarely been the subject of a major research effort. This study focuses on the question of whether there are sex differences in statistíca1 reasoníng for college students. Participants included 245 college students in Taiwan and 267 American college students. The Statística1 Reasoníng Assessment (SRA) was used in this cross-cultural study to assess students' statistical reasoning ability. Whíle the origína1 version of the test was administered to students in the United S闊的，a Chínese version of the instrument was administered to p紅白ipantsin Taiwan. Statistícal methods were used to ascert位nwhether there were mean differences between males and fema1es and whether there was equa1ity between the correlation matrices for males and females. Al1 the analyses are based on both the correct reasoning scores and the mísconception scores obtained from the SRA ínstrument. Results tend to support the general research findíngs that when sex differences appe缸， they are in the direction favoring males, p紅ticularlyin hígher cognitive tasks such as mathematical reasoning. Analysis of the correlation matrices suggest 曲的 there are no differences in statistical reasoning between males and fema1es for both countries. However, it should be noted that the results may be due to low item intercorrelations.
KEY WORDS: sex differences, statistical reasoning, misconception, correlation matrix
There has been considerable research on people's reasoning about probability over 也epast few decades. A wide variety of research studies in 也is area has focused on the errors made in probabilistic reasoning by children of all ages, college students and adults ( Lecout間， 1992; Kahneman & Tvers旬， 1972, 1973; Konold, 1989; Konold, Pollats恤，Well, Lohmeier, & Lipson, 1993; Tversky & Kahneman, 1971, 1974). Both mathematics educators and psychologists have contributed to the research in statistical reasoning. Psychologists are primarily concemed with the difficulties people have with reasoning about probability and statistics or even about everyday life problems under the situation of uncertainty. Mathematics and statistics educators are interested in the effect of instruction on helping students confront and correct their conceptual misunderstandings.
statistical reasoning have rarely been reported as major research findings. In the area of mathematical learning, however, sex di旺'erences have been the subject of research over many decades. Approximately 10% of the articles published in one major mathematics education joumal, the Joumal for Research in Mathematics Education, during the twelve-year period
1978-1990, had a gender theme ( Leder, 1992 )..甘lepresent study intends to ascertain whether there are differences in reasoning about probability and statistics between males and females in two countries, Taiwan and the United States.
The research on statistical reasoning has been greatly influenced by the work of Daniel Kahneman and Amos Tversky since the early 1970s. Research studies by Kahneman and Tversky via the “heuristics and biases" approach have shown 曲的 peopleemploy a limited number of heuristics when making predictions and judgments about probability under uncertainty ( Kahneman & Tversky, 1973; Tversky & Kahnem帥， 1974). These heuristic principles help people reduce the comple刃tyof tasks involving assessing probabilities and often result in quick and reasonable judgments, but sometimes 也eymay lead to
“
se\ ~re and systematic errors" 出at 缸e at odds wi也 probability the。可﹒ Tversky and Kahneman ( 1971 ) suggested that even people with statistical training are proneωthe same heuristics and biases as naive subjects. They believe that these heuristics are also prevalent in our reallife situations when making numerous decisions based on the likelihood of uncertain events ( Kahneman & Tvers旬， 1972).Researchers such as Nisbett, Krantz, Jepson, and Kunda ( 1983 ), who have extensively explored the effects of statistical training on subjects, found that people apply statistical heuristics in reasoning about everyday life problems. They suggested that the important determinants for people to apply statistical heuristics 紅e(1) clarity of the sampling process and the sample space,
(2) presence of the role of chance factors in producing events, and (3) cultural prescriptions to reason statistically. Konold ( 1989 ) argued that some people did not reason probabilistically through judgment heuristics or via formal probability theory, but according to an outcome approach. He suggested that outcome-oriented people perceive each trial in an experiment as an individual event and their task is to successfully predict the outcome of th
Although there is considerable research on statistical reasoning, sex differences in statistical reasoning have rarely been analyzed in previous research. The literature revealed considerable research on mathematical ability, typically showing sex differences favoring males ( Benbow & Stanley, 1980, 1983; Dye & Ve句， 1968; Hilton & Berglund, 1974; Maccoby & Jacldin, 1974; Very, 1967; Very & Iacono, 1970). However, it is important to note 也at sex differences may depend on the portion of the distribution 也atis being studied, including age of the subjects and the complexity of the tasks tested. Most researchers suggest that there are no significant sex di証erences in mathematical learning before the seventh or eighth grades ( Maccoby
&
Jacklin, 1974; Fennema, 1977). Differences start to appear after the elementary school years, but they do not a1ways appe也 Ageneral consensus is that if differences appe缸，fema1es tend to score higher than males on tasks that involve less cognitive complexity, such as rote memo旬， arithmeticcomputation, and verba1 tasks. Males, on the other hand, tend to outperform females in tasks involving higher cognitive complexity, such as mathematical reasoning, problem solving, and tasks that require visual-spatia1 ability. Researchers such as Benbow and Stanley ( 1980, 1983 ) and Stevenson, Hale, Klein, and Miller ( 1968 ) found that sex di叮叮ences a1so depend on the ability level of the subjects. In Benbow and Stanley's large-sca1e study of intellectually talented youth, sex differences in mathematical reasoning are found p紅ticularly noticeable for students who are at the higher end of the ability distribution. Other factors that are associated with sex differences include cognitive (i.e. verbal ability, spatial ability), affective (í.e. attitudes toward math, stereotyping math as a male domain, achievement motivation in math) and educational variables (i.e. course taking, teachers, school organizations). The question of sex differences is of multi-faced nature, broad and complex.
Traditional assessment of statistical knowledge rarely provides information about how students apply their probabilíty and statistics knowledge to reason and solve problems ( G訂field， 1998). The Statistical Reasoning Assessment (SRA) used in the present study is the first instrument developed to measure students' reasoning skills and misconceptions of st姐姐cs and probability. Ite
Method
Subjects
Samples of this study inc1uded 94 males (38.4%) and 151 females (61.6%) from two universities in Taiwan, and 152 males (56.9%) and 115 females (43.1 %) from one large midwestem university in the United States. The 245 students in Taiwan were majoring either in
Information Management or Intemational Trade at the time of the test. They were mostly sophomores. The majority of the 267 students in the United States were either freshmen or sophomores majoring in business. All the subjects were at the end of an introductory business statistics course when the test was administered in the 1995-1996 academic year.
The Instrument
甘leinstrument used in the study is the Statistical Reasoning Assessment (SRA; Liu, 1998), a 20 multiple-choice test. It was the fIrst paper-and-pencil instrument developed to assess students' statistical reasoning, which students do not usually learn from the traditional curriculum. A test-retest reliability of .70 for correct reasoning items and .75 for misconception items of the instrument was obtained. 百leonly evidence in suppo此 ofvalidity of 也isinstrument is content validi旬，which is mainly based on su吋e呵呵 judgmentsfrom expe此s. Factor analysis of the item intercorrelations failed to provide evidence of content validity for 也is ìnstrument due to small inter-relationships of the iterns. There is also a lack of criterion-related validity for the instrument since no other measure of the same construct has been found to correlate with the test scores.
Items from the instrument were designed to measure students' correct reasoning skills and misconseptions respectively in eight di旺erent areas. For each item, there may be one single correct response or multiple correct responses. An item may measure one or more than one correct reasoning skill or misconception. For instance, there are three altematives for item 12. Altemative A measures misconception involving law of small numbers. Altemative B measures whether examinees correct1y understand the importance of large samples. Altemative C measures outcome orientation misconception. Thus, three item scores, one for the correct conception (12b) and two for different misconceptions (12a and 12c), are derived from item 12. It should be noted that not all the items measures both correct reasoning skiU and mísconception. Item 7 only measures misconception when altemative B or C is selected. No altemative was designed to measure correct reasoning skill for item 7.
Rather than obtaining 20 individual item scores and a total composite score depending on whether an examinee responds correctly
,
each examinee therefore has 19 item scores,
eight subscale scores and one total composite score for his correct reasoning，組d21 item scores, eightsubscale scores and one total composite score for his misconceptions. Table 1 shows the eight correct reasoning scales and eight misconception scales and the corresponding items and altematives designed to measure each conception and misconception.
Table 1 Correct Reasoning Skills and Misconceptions Measured by the SRA and the Corresponding Items and Alternatives for Measuring Each Conception and Misconception
Con習ctReasoning Skills
1. Correctly interprets prob咽bilities
2. Understands how to select an appropriate average 3. Correctly computes probability
4. Understands independence 5. Understands sampling variability
6. Distinguishes between co叮elationand causation 7. Correctly interprets two-way tables
8. Understands importance of 1位.gesamples
AI/isco呵ceptions
1. Miscon血"泌的involving averages 2. Outcome orientation misconcep啦。n
3. Good sam抖的 haveto represent a high percentage 'Of the popula討on
4. Law of small numbers
5. Representativeness misconc皂:ption 6. Correlati'On implies causati'On
7. Equiprobability bias
8. Groups can 'Only be ∞mpared if 也eyare the same size
C.orrespondin:g ltems and A/tematives
2d,3d ld,4ab,17c 8c, 13a, 18b, 19a, 20b 知，IOdf, lle 14b, 15d 16c 51d* 6b, 12b la, 17e, lc, 15b~ 17a 誨， 3泊，l1 a恤，12c, 13b 7bc,16ad 12a,l4c h恤， 1缸，l1c 16be 13c, 18a, 19d, 20d 6a
*Note: F'Or item 5, subjects have t'O cho'Ose from two 'Opti'Ons bef'Ore they can make further selecti'On 台omf'Our
altematives under each opti'On. Altemative D under opti'On 1 f'Or item 5 measures whether examinees
c'Orrectly interpret two-way tables.
Data Analysis
To ascertaìn whether there were mean differences in statistica1 reasoning between the sexes for college students, both the differences in the total correct reasoning scores and the total misconception scores for males versus fema1es were tested using two-way analysis of variance (ANOVA). A two-way ANOVA of the total scores by sex and coun甘y was used to study the effects of sex, coun旬，and the interaction between sex and coun句﹒
Equa1i句 betweenthe correlation matrices for ma1es and fema1es were a1so ana1yzed. Pearson product-moment correlation matrices based on the correct reasoning item scores and misconception item scores are respectively obtained for each sex and split-sex group. The purpose of splitting each sex group in half is to examine discrepancies within a group. These wi也ingroup discrepancies give some idea of the amount of expected sampling error and serve as a basis for interpreting differences between the sexes.
To ascertain the equality between the correlation matrices for males and femal郎， two descriptive indices were obtained. One was the root-mean-squ訂'e error term (RMSE) for the difference in two correlation matrices ( Rock, Werts, & Flaugher, 1978). The RMSE va1ue is
defined as the square root of the mean of the squ訂'eddiscrepancies of the corresponding elements of the two correlation matrices. If the two correlation matrices being compared are simil缸，也e
RMSE values will be small. The other was the percentage of discrepancies that falls below certain levels (i.e. .05, .10, .15, etc.) for the absolute difference of each corresponding value in the two correlation matrices (Lei & Skinner, 1982). A higher proportion ofthe discrepancies will be small if the two correlation matrices being comp紅edare similar.
Results
Analysis ofMean D{加rences
The results for the two-way analysis of variance on the total correct reasoning scores by
coun虹yandsex are presented in Table 3. Cou":'缸yeffect appears to be highly significant (p<.Ol). Students in Taiwan have higher correct reasoning scores than their counterp紅的 inthe United States. Both the sex effect and the interaction effect between coun釘yand sex are not significant.
However, both the effects are on the margin of being significant at the .05 level.
Table 2 Cell Means of Total Correct Reasoning Scores for Males and Females in Each Country
Taiwan ρLVE
ea-、 .J 、自'， 啥叫“ -hyoo uτ35 s-44 1-(( e-576 .吋且 -zJE3r3
h-aao
YL-勻，“勻，街勻，- '，'，令 3 叫一 4.fz mm 一訕訕訕 Male Female Tota! 22.90 (4.83) 21.38 (4.80) 21.97Note: Numbers in ( ) are standard deviations.
Table 3 Analysis of 、可IlrianceResult for the Total Correct Reasoning Scores by Country and Sex Source of Variation SS Country 307.27 Sex 69.05 Country x Sex 73.03 E叮or 11193.60
**
p< .01 df MS F F-prob 307.27 13.95 <.∞ 1 料 69.05 3.13 077 73.03 3.31 .069 22.04 508The ANOVA result for the total misconception scores by coun甘y and sex is presented in Table 5. Both coun甘y and sex effects appe位 significant (p < .01). Students in Taiwan have significantly lower misconception scores than students in the United States. Also, males show significantly lower misconception scores 由antheir female counterparts.
Taiwan
Table 4 Cell Means of Total Misconception Scores for Males and Females in Each Country
Mal Female Tota1 11.28 (4.42) 12.81 (3.53) 12.26 CSE 戶uv-、 BF 、‘ F U 一αu s-44
M-U
叭叭叮
m h-z31 , •• 、-•. ι •• 蠱， •• a Total 12.22 13.09 12.68Note: Numbers in ( ) are standard deviations.
df
Table 5 Analysis of Variance Result for the Misconception Total Scores by Country and Sex
F-prob Source of Variation SS Country 145.42 Sex 129.70 Coun住yx Sex 31.26 E叮or 8095.∞
**
p < .01 508 E 弓， hnu' 。 A 且可 s-AY29 4H-59l.-3 FaMU 劃 HL -句 3AaTζU F 一 119 -hyo 。 .I .003**
.005**
.162Although it is also the interest of the study to invesúgate sex differences within each culture, no further test was conducted in the flfst phase of the data analysis due to lack of significance for the interaction effect.
Analysis of the Equality of Correlation Matrices
Problems occur when creating correlation matric自由的 inc1udeitems with extreme p-values since correlation depends on covariation. When there is no variability, there is no covariation and hence no correlation. ltems with extremely low or high p-values were therefore removed from the analyses. Items deleted include five correct reasoning items (ld，詞，祉，鈍， and 12b) and seven misconception items (1 前，缸， 9a恤， 10e, 12a, 1缸， 16ad).
The root-mean-square error term (RMSE) and the cumulative propo此ions of absolute discrepancies for the correlation matrices based on the correct reasoning scores 訂epresented in Table 6. It is expected that the average intrasex RMSE value should be lower than the corresponding average intersex value for the split-sex groups, and there should be higher proportion of discrepancies for the within-sex groups than the between-sex groups below the same level since there should be more correspondence for the correlation matrices within sex than between the sexes. As shown in Table 6, the RMSE value for the Male-Female (0.143) is lower than the within split-sex values for the Malel-Male2 (0.195) and Femalel-Female2 (0.161) of Taiwan samples. The increase in the RMSE values for these within-sex comparisons may result from 也edecrease in the sample size and the stability of the correlation matrices for the split-sex groups. The average RMSE value for the wit甘h出h趾1茵in-s鉛ex di缸e缸renc臼es i誌s0.178 (the average ofO.195 for Ma叫le划el
more comparable s叩pI訕it-s間ex groups iβs 0.1凹94 (the average of 0.209 for Ma叫lel-Fema叫alel ， 0.188 br Malel-Female2, 0.195 for Male2-Femalel, and 0.183 for Male2-Female2). Comparison of these
two average RMSE values (0.178 vs. 0.194) shows that there is a 9% increase in the between-sex RMSE value relative to the within-sex RMSE value. The comparison also shows more homogeneity within sex, as expected.
Table 6 Descriptive Indices for Discrepancy Between the Corr可elationMatrices for Males and Females in Taiwan and the United States ßased on Correct Reasoning Scores
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< -1111111-1111111的一∞們鄉"賄的判哪一∞阿斯
mmm
酬
的一捌卿卿蜘卿卿卿一棚蜘如州州卿卿
拍一棚的咧咧叩怖的一捌絢捌叮叮側捌蜘
如一側向仰的行的前一個叫
η仰加向前
的一切仰的的似的的一郁的到翩翩翩翩
m一判刑制訂喲
mm-mm
仰的州州那
5 一個訕訕的泊的“一行目的 MMW 師詞 。一 2221222-2222 E 一-M 心一的 M叫“ ω 間好的 -M 布加 ηMmhH R 』 -t 且， itA 勻，.，且，且， -A-t 且， AtAtA 勻旬，且 -A N-mF
抑自
mu叩們必一
AF
祕凹的叭
mm
叩
HM 附叫刊州州悶悶一的恥闊別叫 MMMThe cumulative proportions of absolute discrepancies less than O.的 to0.5 are given in steps of 0.05. M and F respectively represents the full sex samples for ma1es and females. Ml, M2, Fl, and F2 represent the split-sex groups for males and females respectively.
The distribution of cumulative proportions of absolute discrepancies shows 血atan average of 87.9 percent of the discrepancies in the corresponding correlations for the between-sex groups (83.5% for Malel-Femalel, 90.1 % for Malel-Female2, 86.8% for Male2-Femalel, and 89% for Male2-Female2) are less than 0.30，的 comparedwith an average of 92.9 percent of the within-sex discrepancies (92.3% for Malel-Male2 and 93.4% for Femalel-Female2). There is only a 5.5
percent decrease for the between-sex discrepancies relative to the corresponding value within sex. The discrepancies between the sexes are very small as contrasted with the intrasex di紅erences.
Sirnilarly, for students in the United States, there is only a 4% increase in the intersex RMSE value (0.187) 的 contrastedwith the RMSE value within sex (0.180). Comparison of these s;>lit-sex groups show that within 0.30, there is only 0.8% decrease in the proportion of the between-sex discrepancies (89.3%) relative to the within-sex value (90.1%).
Table 7 Descriptive Indices for Discrepancy Between tbe Correlation Matrices for Males and Females in Taiwan and tbe United States 8ased on Misconception Scores
RMSE <.05 <.10 <.15 <.20 <.25 <‘30 <.35 <.40 <.45 <.50 TAIWAN M-F .142 .308 .571 .736 .835 .890 .956 .989 .989 .989 1.α)() MI-M2 .217 .165 .429 .538 .670 .769 .824 .857 .912 .956 1.做沁 FI-F2 .148 253 .473 .736 .835 .901 .945 .978 .978 1.α)() 1.“)() MI-Fl .223 .143 .363 .527 .681 .758 .824 .879 .923 .934 1α沁 MI-F2 .217 .198 385 .560 .659 .758 .824 .868 .934 .956 1.α)() M2-Fl .161 .308 .462 .670 .791 .879 .945 .967 .989 .989 1.“沁 M2-F2 .165 .242 .462 .670 .791 .879 .945 .967 .967 .978 1.α)() USA M-F .127 .286 .538 .769 .879 .956 .978 .989 1.∞o 1.∞o 1.α)() MI-M2 .187 .176 .473 .648 .802 .846 .890 .923 .956 .967 1.α沁 FI-F2 .178 .198 .341 571 703 .835 .879 .978 1.α)() 1.α)() 1.α沁 MI-Fl .182 .198 .473 .582 .725 .868 .912 .934 .956 .978 1.α)() MI-F2 .190 .253 .473 .604 .725 .813 .857 .879 .945 .989 1.α沁 M2-Fl .184 .165 .429 .582 .736 .824 .846 .945 .967 1.∞o 1.α)() M2-F2 .164 .319 .484 637 .725 .868 .923 .989 .989 .989 1.α)()
The cumulative proportions of absolute discrepancies less than 0.05 to 0.5 are given in steps of 0.05. M and F respectively represents the full sex samples for males and females. M1. M2, Fl, and F2 represent the spJit-sex groups for males and females respectively.
Table 7 shows the RMSE and the cumulative proportions of absolute discrepancies in the correspondmg correlations of the misconcepnon scores. For the Taiwan s剖nples ， there 15 a 5~ incrc..t!:>e in the between-sex RMSE value (0.192) as compared with the within-sex value (0.183). For the samples in the United States, there is an unexpected 2% decrease m the between-sex
RMSE valu 巴 (0.180) in contrast to the corresponding within-sex RMSE value (0.183).
Cumparisons of these split-sex groups within 0.30 show that equal proportions of intersex discrepancies and intrasex discrepancies (88.5%) are obtained for s組nplesin both countries.
If the two correlation matrices being compared are similar, there wíll be low RMSE values and higher proportion of small discrepancies of the corresponding values for pairs of matrices. The results show that the intersex RMSE values for the split-sex samples as contrasted with the corresponding intrasex RMSE values were either small or unexpectedly decreased. Also, decreases in the proportions of the intersex discrepancies for the split-sex s缸nples are relatively sma11 in contrast to the corresponding intrasex di叮叮encesless than 0.30. There were even equa1
propo此ions of discrepancies between the sexes below 0.30 relative to the corresponding within split-sex values. These findings indicate 也atthere are no differences in the correlation matrices between males and females for botb countries.
Summary and Con
cI
usion
Thepu中oseof the present study is to ascertain whether there are sex differences in statistical reasoning. All the test results are based on examinees' correct reasoning scores and misconception scores obtained from the Statistical Reasoning Assessment (SRA), an instrument developed to assess students' understanding of probabílity and statistics concepts and reasoning skills.
The two-way analysis of variance test resuUs based on both the correct reasoning scores and the misconception scores show 也at coun缸y effect is highly significant. Students in Taiwan have significantly higher correct reasoning scores and significantly lower misconception scores than students in the United States. Results also show 曲的 bothsex effect and interaction effect between country and sex are nonsignificant when the t。但1correct reasoning score is used as the dependent variable in the ANOVA test. However, both effects are on the margin of being significant at the .05 level. Plotting the ceH means of the total correct reasoning scores for each sex by two countries shows 也atthe línes for males and females are not parallel. The lines should be parallel if there is no interaction e釘'ect. The results suggest the strong possibility of interaction effect between country and sex. Males tend to have higher correct reasoning scores than females, while males and females in the United States have approximately equal performance on the same test items. When the total misconception score is used 品 thedependent variable, sex e在'ectbecomes highly significant. Males have lower total misconception scores than their female counterparts.
These results provide evidence in support of the general sex differences fmdings that when differences between the sexes appe缸，出ey tend to favor males, particularly on tasks involving higher level cognitive skills such as mathematical reasoning and problem solving. However, it is essential to understand that sex differences are a function of a combination of di証erentialfactors,
induding cognitive, affective and educational factors, rather than a function of simple factors. Sex differences cannot be c<?nsidered as inferiority of either sex. Various socialization factors as well as biological factors may be involved in determining the differences between males and females. The stereotyping of mathematics as a male domain, the perceived attitudes of significant others,
the United States in their perforrnance on the SRA test, not much confidence can be placed in 也e generalizabi1ity of the findings. It is recommended that the study be replicated by selecting more schools throughout the two countries to enhance generalizability of the results in the future. Different colleges in Taiwan may have different admission standards. Researchers suggest that sex differences are likely to exist depending on the portion of the population 也at IS being studied ( Benbow & S怯nley， 1983). Thus, more schools should be selected to represent the variability of the whole population of males and females in both cultures. It will be interesting to see if replications of 也isstudy will yield similar results. It is also of interest to investigate whether sex differences 紅econsistent across the countries in future studies.
Further, considerable efforts were made in the process of test translation. Items with problems associated with translation were identified either by using the back translation technique or by having different people in both the United States and Taiwan review the translated version of the instrument. However, researchers such as Hambleton and Bollwark ( 1991 ) suggested that, to test the equivalence of source and target versions, a combination of judgmental methods and empirical methods should be used. Errors missed by one method may be identified by another method. Statistical technique is also needed to verify translation quality. It is therefore recommended that in future studi郎， the schedule and budget of a cross-cultural study should provide for the time and money necess訂Yto deal with the issue of scale comparability. Statístical analyses such as examination of the mean score differences, correlation coefficients, and equivalence of the factor structures of the two language forms should be used in combinatíon with judgmental methods in the future to establish item equivalence.
Lastly, results based on the comparisons of the RMSE values and correlation discrepancies for the split-sex groups suggest that there are no sex differences in the correlation matrices for males and females in both countries. As foretold, if there is similarity between the correlatíon matrices for males and females, bo也 theRMSE value and a higher proportion of the discrepancies will be smalL Findings show that when there are increases in the between-sex RMSE values and decreases in the proportion of
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收稿日期 :2∞ 1 年 6 月 12 日 接受刊登日期: 2∞2 年 6 月 18 日
Bulletin of Educational Psychology, 2∞2， 34(1), 123-138 National Taiwan Normal Universi吟，Taipei, Taiwan, R.O.C.
統計推理的性別差異
劉慧如 大葉大學 英美語文學系 摘 要 JOANB.
GARFIELD 明尼蘇達大學 教育心理學系過去，在數學能力方面的性別差異 (sex differences in mathematical abihty )或在統計推理
(statistical reasoning) 兩個重要領域，都分別有過許多不同的研究，但是，卻不會有人以統計推理方
面的性別差異 (sexdifferences in statistical reasoning) 做為研究主題。本研究主要在探討大學男女生
在統計推理方面是否有性別差異。研究樣本包括 245 位台灣的大學生，以及 267 位美國的大學生。研
究使用的問卷是統計推理測量 (the Statistical Reasoning Assessment ' SRA) ，在美國施測所使用的是
英文原版問卷，在台灣施測時則使用翻譯成中文的版本。 本跨國研究使用不同的統計方法研討下列兩個主要問題(1)男主生在統計推理方面是否有平 均數的差異? (2)男玄生之間的相關矩陣 (correlation matrices) 是否有所差異?所有的統計分析都 是根據學生在回答問卷之後所得到的兩個分數:正確推理 (correct reasonmg) 所得的分數及對於機率 與統計不正確酌觀念(misconception )所得的分數。針對第一個問題，研究結果偏向支持一般性別差 異研究的發現:當男女生有性別差異時，尤其在較高層次認知的運用如數學推理方面，男生表現比女 生優異。針對第二個研究問題所作的統計分析，結果顯示男生與女生的相關矩陣沒有差異。值得注意 的是針對第二問題所得到的研究結果極可能導因於問卷 (SRA) 題目之間的相關係數 (即 關躍詞:性別差異、統計推理、迷思概念、相關矩陣
