Reading in a Foreign LanguageVolume 16, Number 2, October 2004 ISSN 1539-0578
Cindy Brantmeier
Through a discussion of research that examines a plethora of variables involved in second language (L2) reading comprehension, the present study attempts to examine and analyze the statistical procedures utilized in studies of this nature. A review of recent research from the past five and a half years from four leading scientific journals of reading is offered. Research questions that motivate the selection of statistical procedures are examined for each study. Results show that Analysis of Variance (ANOVA) is utilized more than Regression Models (RM) primarily because researchers are asking questions about the variation between and within groups of variables and are not predicting performance on dependent variables via independent variables. The strong resemblances and differences between ANOVA and RMs are discussed in light of the review of research, and through a detailed critique of Brantmeier's (2003) study with different research questions and additional analysis of data, the relationship between statistical procedures is further exemplified. Explanation for the use of statistical procedures in light of recent theoretical models (Bernhardt, 2003) is included.
In a discussion about the applied linguistics contribution to second language (L2) reading, Urquhart and Weir (1998) contended that there was no established body of experimental methods for applied linguists to rely on. Six years later we see that L2 reading research conducted by applied linguists continues to take many forms, but researchers who conduct experimental, quantitative investigations concerning second language reading comprehension engage in a number of similar activities. A mixture of prior investigations concerning research methods has been influential for researchers conducting studies concerning L2 reading comprehension. These experiments have examined factors involved in the creation of data collections instruments such as passage type and structure (Bernhardt, 1984; Brown, 1987; Leow, 1993; Leow, 1997; Tsang, 1987; etc.), passage content (Brantmeier, 2002; Brantmeier, 2003; Bügel and Buunk, 1996; Carrell, 1984; Hudson, 1982; Johnson, 1981; Mohammed and Swales, 1984; Pritchard, 1990; Steffenson, Joag-dev, and Anderson, 1979; Schueller, 1999; Young and Oxford, 1997, etc.), assessment tasks (Carrell, 1991; Lee, 1990; Shohamy, 1984; Wolf, 1993; etc.), language used for assessment (Lee and Ballman, 1987; Shohamy, 1982, 1984; Wolf, 1993; etc.), and procedures utilized for scoring instruments (Bernhardt, 1991). More specifically, with regard to codifying and scoring data, Bernhardt (1991) argued that collected data must be scored consistently both within the study and across L2 reading studies in order to make appropriate generalizations. In the same vein, this present study attempts to show that statistical tests should also be utilized appropriately and consistently both within and across inquiries. Researchers agree that a solid research plan for L2 reading comprehension involves a description of intended data analyses including statistical procedures. To date, no investigation has reviewed and analyzed the statistical procedures most commonly utilized in research on L2 reading comprehension. Through a synthesis of prior L2 reading research that examines comprehension, the present study attempts to do the following: 1) demonstrate which statistical procedures are currently being utilized; 2) report the research questions that motivate the choice of statistical tests; 3) discuss the strong resemblance and difference between statistical tests utilized to analyze data; and 4) exemplify the relationship between statistical procedures through a critique of a recent study. L2 reading research that examines comprehension during the last five and a half years from the following leading scientific journals of reading is reviewed:
Before moving into an examination of recent research, a brief discussion of L2 reading models and comprehension is essential. Though interactive models of L2 reading emphasize different components involved in the process, all models include and underscore the importance of comprehension (Bernhardt, 1991; Coady, 1979). Throughout the years L2 reading researchers have defined and discussed comprehension while relying heavily on Bernhardt's (1991) model (Hammadou, 1991; Lee and VanPatten, 1995; Wolf, 1993; Young, 2000), and they all agree that comprehension is obviously a critical part of the multifarious interplay of mechanisms involved in L2 reading. It is not new news that different comprehension assessment tasks may be testing different abilities. Measures of comprehension consist of a variety of assessment tasks including free written and oral recalls, summaries, multiple choice, true/false, close-deletion items, open-ended questions, and sentence completions. Dating back to the 80's and up to the present day, L2 reading researchers have utilized a mixture of comprehension assessment tasks. For example, Block (1986) utilized verbal retellings and a written multiple choice test; Anderson (1991) echoed Block's comprehension measures, but he reversed the order; Sarig (1987) utilized verbal reports of main ideas and the overall messages of the passages; Barnett (1989) used a written recall and participants also chose the most appropriate continuation of the story; Carrell (1989) only used written multiple-choice questions to assess comprehension. More recently, researchers continue to utilize a variety of assessment tasks. Bügel and Buunk (1996) utilized multiple choice questions from a standardized exam; Young and Oxford (1997) utilized oral recalls; Schueller (1999) used both multiple-choice and open-ended questions; and Brantmeier (2002; 2003) utilized both multiple-choice questions and written recall. Discussions of varied comprehension assessment tasks across studies are not enough. The diversity in measurement tasks leads to the following questions: What statistical tests are utilized to analyze data in investigations that examine L2 reading comprehension? Are there variations across studies? Which procedures are appropriate for the research questions? How much confidence can we place in results and conclusions? The present study hopes to answer these questions and more. Bernhardt's (2000; 2003) model of L2 reading illustrates that 50% of L2 reading is accounted for by L1 literacy (20%) and L2 knowledge (30%), and she contends that more research is needed to examine the remaining 50% of variance that is unexplained. Current studies with appropriate research questions and corresponding statistical tests may contribute to the unexplained variance, and in addition, recent research may possibly examine which of the many interacting variables in L2 reading models best predicts successful comprehension.
Figure 1 lists the investigations in the aforementioned academic journals that examine L2 reading comprehension with adults and children, and it also reports research questions, statistical procedures utilized to analyze data, and findings. Figure 1: Literature review on L2 reading comprehension
JLR = Journal of Literacy ResearchRFL = Reading in a Foreign LanguageRM = The Reading MatrixRRQ = Reading Research Quarterly
As demonstrated in the review of studies about L2 reading comprehension, Analysis of Variance (ANOVA) is the most widely used statistical procedure in this type of research. This is because, as depicted by the research questions, L2 reading researchers often investigate the relationship of many different independent variables with dependent variables and are concerned about the variation between and within groups of variables. For example, the following research questions guided Carrell (2001): Is there an interaction between purpose and task? In other words, will purpose for reading relate to the specific task which conforms to that purpose? And if so, what is the nature of that interaction? Given these inquiries, Carrell selected the appropriate statistical test (ANOVA) to answer her questions. Only two of the 18 studies used a regression model (RM) to analyze data, and some studies utilized both ANOVA and multiple regression MR (e.g., Wilkinson, 1998; Tweissi, 1998). For instance, Wilkinson (1998) asked: What school and classroom factors moderate gender and home language gaps in reading achievement? Wilkinson selected a variety of statistical tests including RM to answer this question because he was interested in predicting which variable (e.g., gender and home language) best predicts reading achievement. To further exemplify choice of statistical tests, a detailed discussion of ANOVA and RM follows.
The general assumptions underlying the use of ANOVA are the following: 1) data are score or ordinal scale data that are continuous; 2) data are independent. The comparison is between groups; 3) there is a normal distribution of scores in each group; 4) there are equal variances of scores in each group; 5) there is a minimum of five observations per cell; and 6) the F statistics allow the rejection or acceptance of the null hypothesis (Hatch and Lazarton, 1991). The general assumptions underlying the use of RM are the following: 1) the variables are interval or truly continuous and the relationship is linear; 2) correlation values are accurate; 3) the variables entered in the regression formula should not be highly intercorrelated; 4) the more variables there are in the regression equation, the larger the N size for the study must be; and 5) if the procedure is used for inferential purposes then the sample must be drawn at random, normal distribution and equal variances must be found (Hatch and Lazarton, 1991).
The most common way for L2 reading researchers to find out if there are significant differences between the means of more than two groups is with the ANOVA procedure, which is actually a t-test that is appropriate to use with three or more groups. ANOVA examines the variation both within and between each of the groups. Technically, ANOVA compares two different estimates of the same variance under the null hypothesis. One variance estimate is based on the within-group variation of scores around group means (error variance). In the experimental designs in Figure 1 that utilized ANOVA tests, all of the people within a group are expected to be the same, except for random variations, because they have all been treated the same. This variance estimate is the denominator of the F test. The other variance estimate is based on the variation of group means around the grand mean and is the numerator of the F test. This variation can be due to two sources: a) random variation and b) systematic variation due to an experimental treatment. But, under the null hypothesis, the second source is assumed to be zero and so the F ratio will tend to be 1.00 if the null hypothesis is true. To the extent that the null hypothesis is false, the F ratio exceeds 1.00, and if it exceeds 1.00 enough, the null hypothesis is rejected (Hatch and Lazarton, 1991). There are several types of ANOVA tests. In the One-Way ANOVA there is exactly one dependent variable (always continuous) and exactly one independent variable (always categorical) (e.g., Tweisse, 1998; Mori and Nagy, 1999; Sharp, 1999). A Two-Way ANOVA procedure attempts to discover whether the interaction of two independent variables has an effect on the dependent variable (e.g., Carrell, 2001; Brantmeier, 2003). An Analysis of Covariance is a variation of ANOVA where the researcher adjusts mean scores on the dependent variable for each group to compensate for the initial differences between groups on another variable, which is the covariate (e.g., Stakhnevich, 2002). A Multivariate Analysis of Variance (MANOVA) uses two or more dependent variables in the same analysis, and this is used when the researchers believe that correlations exist among the dependent variables. (e.g., Fraenkel and Wallen, 1996). In the MANOVA, there may be multiple dependent variables and multiple independent variables (e.g., Droop and Verhoeven, 2003). Finally, if significant differences are found among the means in the ANOVA procedures, then the researcher calculates post hoc comparisons (two-tailed tests) to identify more specifically where the difference lies.
Simply stated, regression is used to predict performance on the dependent variable via one or more independent variables (e.g., Tweisse, 1998; Wilkinson, 1998). In simple regression, researchers predict scores on one variable on the basis of scores on the second. In MR, the possible sources of prediction are expanded and tested to see which of many variables and which combination of variables allows the researcher to make the best prediction (Hatch and Lazarton, 1991). In other words, MR is a technique used to determine a correlation between a criterion variable and the best combination of two or more predictor variables. MR is the extension of a simple linear regression. In second language reading research, simple regression has been used when researchers need to predict scores on a test on the basis of another test. According to Hatch and Lazarton (1991), MR is used when researchers want to know how much "weight" to give to a number of possible independent variables that relate to performance on the dependent variable. For example, prior research that examines a comprehension assessment test for L2 reading may have shown that success on the test is related to factors such as topic familiarity levels, gender, type of assessment task, etc. By using a MR model researchers can determine which of the variables best predicts achievement. A combination of these variables or which variables do not predict achievement can also be predicted. In MR analysis, the amount of explained variation is often contrasted with residual, which is unexplained variation. MR takes correlations among the predictors into account, and thus gives estimates of the unique variance accounted for in the outcome by the predictors.
An ANOVA identifies whether the mean of one group differs significantly from the mean of another group or groups. Regressions identify whether two or more variables are significantly related to each other. Hatch and Lazarton (1991) offer a discussion about the resemblance between ANOVA and Regression. They contend that in ANOVA researchers account for the variance in a DV on the basis of two major components: the variance between groups (including the treatment effect and error) and the variance within groups (error only). In regression analysis, researchers can conceive of the sum of squares for the predicted value of Y as the sum of squares regression (the predicted variation) and the leftover variation as sum of squares residual (which is the variance left unaccounted for). In MR researchers need as many non-redundant predictors as they have degrees of freedom for the main effect (or any effect for that matter). In ANOVA it is customary to have one source of variation for each main effect and one source of variation for each interaction, perhaps because ANOVA is really a special case of MR. Aiken and West (1996) carefully address the difference between ANOVA and MR in usual practice. They state: In ANOVA with multiple levels of a factor and the use of usual approaches to variance partitioning, any curvilinear variation is automatically subsumed in the variance partitions. In contrast, in MR the analyst specifically decides which terms need to be included: Terms to represent curvilinear relationships must be built systematically into the equation (Aiken and West, 1996: 71). In other words, with ANOVA the multiple degrees of freedom for any multiple-degree-of-freedom effect are combined and tested together. In MR, each single degree of freedom is usually tested individually. The authors continue to discuss how ANOVA and MR do not differ mathematically. What they contend is that the conventional partitions of variance operationalized in common statistical packages for ANOVA are structured so that all components of an effect are subsumed in the omnibus term for that effect. In MR the structuring of the components of each effect is left to the analyst (Aiken and West, 1996: 71). What all this means to the second language reading researcher is that both ANOVA and Regression are dealing with variance in the DV, and they account for as much variance as possible as an "effect of" (ANOVA) or "accounted for by" (regression) various independent variables (Hatch and Lazarton, 1991: 486).
Brantmeier (2003) employed ANOVA in analyzing data for a study on L2 reading comprehension. More specifically, Brantmeier's study examined the effects of readers' gender and passage content on L2 reading comprehension with participants from the intermediate level of language instruction. Seventy-eight participants read two different authentic passages, and two different measures were used to assess comprehension: written recall and multiple choice questions. The following research questions guided the study: - Are there gender differences in learners' topic familiarity?
- Are there gender differences in learners' second language reading comprehension?
- Does the passage content of the second language reading text affect learners' comprehension?
Findings revealed significant interactions between readers' gender and passage content with comprehension on both assessment tasks. The results of the study provided evidence that subject matter familiarity has a facilitating effect on L2 reading comprehension by gender at the intermediate level of Spanish language instruction. In summary, Brantmeier's (2003) study was undertaken in order to examine the interaction effects of readers' gender and passage content on L2 readers' comprehension at the intermediate level of Spanish language instruction. In this research design, the independent variables were: 1) passage content (boxing and housewife) and 2) readers' gender. The two sets of dependent variables were: 1) comprehension (measured with the written recall protocol and multiple choice comprehension questions) and 2) topic familiarity. In order to compare several means simultaneously and to assess interaction effects, for research questions two and three data were submitted to a two-way Analysis of Variance (ANOVA). The ANOVA procedure showed the between-subject main effect (e.g., gender) and the within-subject main effect (e.g., passage content), as well as their interaction. The alpha level was set at .05 (Brantmeier, 2003: 8).
An attempt to answer the following questions about the appropriateness of statistical procedures follows: What statistical tests are utilized to analyze data in Brantmeier's (2003) study about L2 reading comprehension? Were the procedures appropriate for the data? How much confidence can we place in Brantmeier's results and conclusions? The goal of the ANOVA in Brantmeier's (2003) design was to explain the variance in the dependent variable (written recall or multiple choice) in terms of variance in the independent variables (reader's gender and passage content). The type of ANOVA (two-way) was used because more than one independent variable was involved in the separate designs. Brantmeier is careful to note that the two passages are not being compared. In other words, the effect of passage content was not considered as boxing content versus housewife content. Rather, the passages are treated and tested as separate entities in a single report. The researcher expected that there would be variability in the performance of males and females on the comprehension tests. She wanted to know what effect the gender factor had on variability in the data, as well as what effect the passage content factor had on that variability. She also wanted to know the effect of the combination of passage content and gender on variability in comprehension test performance. In other words, Brantmeier (2003) examined the following: - Effect of gender: male versus female
- Effect of passage content: boxing or housewife
- Interaction effect (gender by passage content)
The advantage of using a two-way ANOVA in this study is that the researcher was able to look not only at the effect of each independent variable but also the interaction effect in the combination of independent variables. Results of the ANOVAs showed no significant difference between mean scores for males and females on overall comprehension of the passages. There was no difference in performance by gender across passages, however, results of the ANOVAs yielded significant interactions between independent variables readers' gender and the boxing passage content as they affect dependent variables recall (F(1,76) = 8.26, p = .01, = .10) and multiple choice questions (F(1,76) = 4.20, p = .04, = .05). Likewise, the results of the ANOVAs yielded significant interactions between readers' gender and housewife passage content as they affect recall (F(1,76) = 15.90, p = .00, = .18) and multiple choice (F(1,76) = 8.67, p = .00, = .10). Brantmeier includes the following footnote supporting her choice of statistical procedures: A one-way ANOVA and a bivariate regression model with a dichotomous independent variable are precisely the same (King, 1986). The only substantive difference is that in the ANOVA case one only reports whether there exists a significant difference or not, and therefore to answer the research questions in the present study the ANOVA was calculated. In a bivariate regression the magnitude of the difference is reported, but in the present study the reported sample means by group (e.g., gender) reveal the magnitude, and the ANOVA shows whether the difference is significant or not (Brantmeier, 2003: 12). Findings revealed significant interactions between readers' gender and passage content with comprehension on both assessment tasks (written recall and multiple choice). Hatch and Lazarton (1991) and Kirk (1982) state that when interpreting results of a two-way ANOVA that the interpretation must emphasize the interaction effect when it is significant. If the interaction effects are not significant, then more powerful statements can be made about the effects of the independent variables on the dependent variables. Brantmeier's interpretation and discussion focused on the significant interaction effects. She states: The results of the present study indicated that two important interacting factors in the L2 reading process of university students of intermediate Spanish are the readers' gender and passage content. Male and female readers were able to make connections to familiar passage content, and therefore were able to understand and comprehend better as they read (Brantmeier, 2003: 12). How much confidence can we give the findings given the statistical procedures used? In Brantmeier's (2003) study, she was interested in accounting for as much variance in multiple choice and recall as possible as an "effect of" (ANOVA) the reader's gender and passage content. She was not interested in accounting for as much variance as possible in multiple choice and recall as "accounted for by" (regression) these independent variables. An example of a question that would require regression analysis for Brantmeier's (2003) study would be: How much of the variance in multiple choice and recall did gender account for? In order to show this predictive relationship among the effect of Readers' Gender on the performance of readers, data are re-examined using regression analysis. Results show that overall (both passages combined) readers' gender accounts for 14% of variance in written recall and 7% of variance in multiple choice questions. To provide further analysis, both passages are analyzed separately. Results show that for the boxing passage, readers' gender accounts for 10% of variance in written recall and 5% of variance in multiple choice questions. For the housewife passage, readers' gender accounts for 17% of variance in written recall and 10% of variance in multiple choice. These results add intriguing dimension to Brantmeier's (2003) findings. One way to interpret these results is that readers' gender accounts for greater variance in the written recall assessment measure than in the multiple choice questions. Future investigations could examine this relationship even further. Regarding Brantmeier's (2003) study, regression analysis can also show which of the IVs (readers' gender or topic familiarity) are superior (more influential) in producing higher scores on reading comprehension. Through MR a test of the difference between two regression coefficients can be derived. Results are listed in Table 1:
Table 1: Regression Analysis
As depicted on Table 1, the number R An excellent example of a study that emphasizes both the effect of independent variables as well as variance accounted for by independent variables is Tweissi (1998). This study formulated the following research questions: Does language simplification (LS) have a positive influence on reading comprehension? Does the difference or amount of LS and type of LS result in differences in the levels of reading comprehension? Which of the amounts and types of LS are superior in producing higher levels of reading comprehension? The researcher utilized a One-Way ANOVA, a Tukey Pairwise and a Regression procedure to analyze data. Tweissi (1998) states that the study investigates the influence of one independent variable with five levels (language of the text) on one dependent variable (level of comprehension) and therefore the One-Way ANOVA was used. Because the null hypothesis about the effect of simplification on reading comprehension was rejected, the researcher applied two other statistical procedures to answer the other research questions: a Post-hoc analysis using the Tukey's pairwise comparisons, and a MR analysis. The MR analysis was used to answer the following question: Which of the amounts and types of simplification are superior (e.g., more influential) in producing higher levels of reading comprehension? The MR specifically showed predictive relationships among the effects of the five versions of text on performance of readers by predicting scores based on these versions (Tweissi, 1998: 197). Findings revealed the following: "The premise that the simpler the text the more comprehensible to L2 learners is unwarranted. LS in general has a positive influence, however, increasing the amount of LS alone does not lead to greater comprehension. The type of simplification, rather than the amount, may have a higher impact on reading comprehension" (Tweissi, 1998: 201). Given Tweissi's (1998) research questions and research design, the MR was necessary, as explained previously.
As shown in the present study, the selection of appropriate statistical procedures driven by research questions is a critical part of the L2 reading research process. The summary of recent studies shows that ANOVA is the test most commonly used in experimental research of this type. The reviewed studies demonstrate that when ANOVA has been employed in analyzing data for inferential purposes, the appropriateness of the procedure for the study has been directly supported. In light of new issues about L2 reading (Bernhardt, 2003) perhaps more inquiries about L2 reading comprehension should be concerned with the amounts and types of variables that are superior, or more influential, in producing higher levels of reading comprehension. Studies that show predictive relationships among the effects of variables could contribute to the lacuna in the database concerning the 50% of unexplained variance in Bernhardt's (2001) model. Through a re-examination and further analysis of a published study, the present investigation attempts to exemplify the rationale behind ANOVA and MR. As a final point, although ANOVA and MR may be mathematically equivalent, analyses should be tailored to test specific research questions.
1. Brantmeier (2004) offers a concise review of research methods commonly utilized in L2 reading research and includes a graphic presentation to show the typical sequence in which the mechanisms are usually executed and described in a study. 2. See Chapter 11, Hatch and Lazarton (1991) for more specific details and examples. 3. The present study does not attempt to examine whether researchers have violated the underlying assumptions for the use of ANOVA and RM, but rather attempts to identify and discuss statistical tests utilized. 4. The t test is simply a special case of the same technique, when there are only two groups. In that case, F = t 5. See Kirk (1982) for a detailed description of post hoc comparisons. 6. When comparing the two passages, the Cortazar passage yielded lower comprehension scores on both multiple choice and recall, independent of gender. Text difficulty could be a limitation to the extent that it would be an intervening variable, or a variable that was not included in the present study. The author chose not to control for text difficulty because the study does not make comparisons of recall comprehension scores between the two passages, rather it examines the differences in recall comprehension scores by gender within each passage. Furthermore, to maintain authenticity, the researcher did not simplify the Cortazar text.
The author is thankful to Anthony Alvarez and Andy Levi for their assistance with research and to Mike Strube for his time spent discussing this article. The author would also like to thank the anonymous RFL reviewers for their constructive criticism and valuable feedback.
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An investigation into the relationship between L2 reading anxiety and L2 reading comprehension, and self-reported level of comprehension, topic familiarity, features of an L2 text and reading ability in the L1 and L2
Cindy Brantmeier is an Assistant Professor of Applied Linguistics and Spanish at Washington University in St. Louis. She is Program Director of Advanced Spanish and Co-Director of the Graduate Certificate in Language Instruction. She also oversees language placement and departmental assessment. Her research interests include interacting variables in second language reading, reading research methodology, language learning and technology, and language and gender. About RFL | Table of Contents | Past Issues | Subscribe | Editorial Board | Submissions | Contact RFL |