CONTROLLING THE BASELINE SPEED OF RESPONDENTS: AN EMPIRICAL EVALUATION OF DATA TREATMENT METHODS OF RESPONSE LATENCIES

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1 CONTROLLING THE BASELINE SPEED OF RESPONDENTS: AN EMPIRICAL EVALUATION OF DATA TREATMENT METHODS OF RESPONSE LATENCIES Jochen Mayerl 1 University of Stuttgart Response latencies answering to attitude questions can be used as a measure of chronic attitude accessibility. But depending on the theoretical interest, several determinants of response latencies have to be treated as bias effects and should be statistically controlled to adequately interpret response latencies. Main bias factors are the individual baseline speed of respondents reflecting a constant individual characteristic of mental speed of information processing, effects of the measurement instrument and situational effects. In this study using response latency data of a nation-wide German survey (CATI), four statistical transformation methods to control the individual baseline speed are empirically evaluated and compared: Z-Score, Difference Score, Ratio Index, and Rate-Amount Index. The empirical findings support the assumption of an increased data quality transforming raw reaction times into indices controlling the baseline speed. Additionally, the data quality increases if additional systematic bias effects are controlled (here: question order, effect of extremity). Key words: reaction time, attitude accessibility, attitude strength, CATI 1 INTRODUCTION In attitude theory, response latencies answering to attitude questions are regarded as an indicator of attitude strength. Defining an attitude as the association between an object and its evaluation (Fazio 1986, 1989, 1990b), the strength of an attitude is the strength of this association. Response latencies are often used to measure the chronic accessibility of attitudes. This accessibility points directly to the mental process during the activation of an attitude and is regarded as a measure of the associative strength. Therefore, an attitude is assumed to be stronger if it is easily accessible, measured by a shorter response latency, and to be weaker if it is less or not accessible, measured by a longer response latency. In recent decades, the development of modern techniques of computer assisted interviewing has made it possible to measure response latencies to attitude questions in the context of large scale survey studies (Bassili/Fletcher 1991, Bassili 1993, 1996b). In contrast to the laboratory context, the measurement of mental information processing in a relatively uncontrolled survey context is much more biased. For example, different interviewers may measure the reaction time with different accuracy (raw response latencies implicate the latency of the interviewer to press the appropriate key), or the respondent may be distracted by the presence of others or unforeseen events. Additional problems appear if the respondent fails to answer correctly if he or she has difficulties to understand the question or to generate an answer and translate it into the given categories or scale (see next chapter). 1 Correspondence concerning this article should be addressed to Jochen Mayerl, Institute for Social Sciences, Sociology and Empirical Social Research Unit, Keplerstr. 17 II, Stuttgart, Germany. Electronic mail may be sent to Jochen.Mayerl@soz.uni-stuttgart.de. 1

2 There is little but growing research in data treatment of response latencies to minimize such biasing effects. Response latencies are multidimensional, and the first decision to be made is which components of response latencies are substantially relevant, and which should be controlled (e.g. the baseline speed of respondents and interviewers). Another issue is the data treatment due to problems of statistical distribution, i.e. the treatment of the typical skewness and outliers that lead to a non-normal distribution of response latency data. In this paper, different bias effects (chapter 2) and alternatives of controlling the baseline speed of respondents and interviewers (chapter 3) will be discussed and evaluated empirically by the following six criteria (chapter 4): (1) intercorrelations between different response latency indices, (2) correlations of these operative indices with meta-judgemental indicators of attitude strength, (3) reduction of the covariance with baseline speed compared to raw reaction times, (4) power to moderate attitude-behavior relations (interpreting response latency as an indicator of attitude strength), (5) power to moderate attitudebehavioral intention relations, and (6) power to moderate the persistence of an attitude. Data treatment methods of response latencies can be distinguished into two steps, on the one hand controlling the baseline speed and other systematic bias effects, and on the other hand treating distribution problems. This paper deals with the first step only. In contrast to the statistical-technical question of distribution problems, controlling the baseline speed is a substantial question to adequately interpret response latencies. 2 DETERMINANTS OF RESPONSE LATENCIES There may be nothing scientifically less meaningful than the simple observation that subjects responded in x milliseconds. (Fazio 1990b: 89). It is the theoretical context of the usage of response latencies and the identification and control of vast numbers of determinants that lead to a meaningful usage and interpretation of response latencies. Depending on the theoretical interest, several determinants can be treated as bias effects biasing the adequate theoretical interpretation of response latencies. The relevant determinants of response latencies can be distinguished into situative effects (including the measurement instrument), and individual-personal effects of the respondent. Modelling the process to answer to a survey question as a four-stages-process (Bassili 1996b, Bassili/Scott 1996, Tourangeau 1992), these different determinants may appear in each stage: (1) In the stage of question interpretation, the response latency depends for example on the level of difficulty of the question (Bassili/Fletcher 1991, Bassili 1996b). Complicated, ambiguous, long or complex question wordings slow down response latencies (Bassili 1993, 1996b, Bassili/Krosnick 2000, Kohler/Schneider 1995, Klauer/Musch 1999, Pachella 1974). Other determinants are the context of the question (e.g. assimilation effects may speed up reaction times), and the item characteristics (state-judgements are stated faster than trait-judgements, Amelang 1994). These effects are inter-individually constant in a standardized survey and do not bias an empirical analysis of inter-individual differences within a question of a survey (apart from possible indirect individual effects of education, intelligence, etc.). Instead, these determinants are more important in comparing response latencies of different studies or comparing response latencies of different questions within a survey. (2) In the stage of the retrieval of associated information or (summary) judgements, the associative strength of the object and its evaluation is a main determinant of the reaction time (Fazio 1986, 1990a). This associative strength itself depends on the frequency of the statement of the attitude (Bassili 1996b, Smith/Lerner 1986) and on the direct experience with the attitude object (Bright/Manfredo 1995, Fazio 1986, Fazio/Williams 1986). 2

3 (3) In the stage of generating a summary judgement based on the retrieved information and evaluations, the response latency depends for example on the (in)consistency or ambivalence of the retrieved information (Bassili 1996b, Brömer 2000, Klauer/Musch 1999), on the amount of processed information (Bassili/Scott 1996, Houlihan et al. 1994), on the certainty or finality of a judgement (Bassili 1995), on the mode of automatic versus reasoned information processing and therefore on the motivation, opportunity and ability to process information in an elaborate way (Fazio 1990a, Petty/Caciappo 1986), on the question whether a summary judgement is already available or not (on-line versus memory-based judgements; Hertel/Bless 2000), and on priming effects which shorten reaction times (Tourangeau 1992). (4) In the stage of selecting the response, the response latency may vary depending on the length and complexity of the response (e.g. the reaction time extends with the given amount of response categories; Bassili 1993, Bassili 1996b, Fazio 1990b, Smith 1968, Pachella 1974), on the familiarity with the response scale (Smith 1968), and on whether the don t know category is given explicitely or implicitely the latter leads to longer reaction times of respondents trying to find an answer in the given scale to a question they cannot answer (Bassili 1996b). Additionally, an inverted u-shaped association is reported between the extremity of an answer and the response latency (Bassili 1996b, Fazio 1990b, Fazio/Williams 1986, Klauer/Musch 1999). In addition to these bias effects which influence response latencies in a specific stage of the response process, several situative and individual factors equally determine the response latency in all four stages. The situative factors include the speed-accuracy tradeoff (Fazio 1990b, Houlihan et al. 1994, Pachella 1974, Smith 1968), the baseline speed of the interviewer measuring the response latency, slowing down effects like diversion, the loss of attention of the respondent (Bassili 1996b) or situative complexity (Kail/Salthouse 1994), and speeding up effects like perceived obvious social desirability (Kohler/Schneider 1995), subjective perceived time pressure, and a good actual mood of the respondent (Fazio 1995). The individual factors relate to the physiology, personality and individual mental characteristics of the respondent, e.g. the individual baseline speed, age, education, gender, intelligence, perceived control of behavior, self-projection, impulsivity or health (Amelang 1994, Faust et al. 1999, Houlihan et al. 1994, Kail/Salthouse 1994). Considering these possible determinants and bias effects on raw reaction times, great patience and care must be taken in order to limit the possibility of serious error in their interpretation (Pachella 1974: 80). Therefore, among other bias effects, the response latencies have to be considered in relation to individual baseline speeds of the respondents (and the interviewers). The individual baseline speed reflects a constant individual characteristic of the mental speed of information processing that has to be controlled. Otherwise, one is simply identifying a continuum of generally fast versus slow responders. (Fazio 1990b: 87). 3 CONTROLLING THE BASELINE SPEED Taking the reported determinants into account, the measured response latency (RL raw ) implies components that should be controlled or held constant to interpret it theoretically correct (e.g. as decision time or attitude accessibility). A simple model of Response latency would be: RL raw = Processing Mode + Accessibility + Baseline speed + Measurement instrument (1) where Processing Mode is the mode of automatic versus reasoned information processing; Accessibility is the mental accessibility of information and evaluations of objects (e.g. 3

4 attitudes); baseline speed is the general speed of individuals in the case of surveys the general speed of the respondent and the interviewer: Baseline speed = respondents baseline + interviewers baseline (2) The term measurement instrument in equation (1) refers to other systematic and random errors that were discussed in the last chapter (e.g. question order, time pressure) including effects of the social situation of the interview. 2 In this paper, we will focus our attention on the controlling of baseline speed, mainly because there are already further developments that have not yet been evaluated and compared in a systematic way. Furthermore, it is not possible to compare and evaluate all different possible methods to control the baseline speed with all possible evaluation criteria in an exhaustive way on the contrary. Therefore, this paper is a first step to evaluate data treatments to control baseline speeds. The individual baseline speed can be computed by the mean reaction times of so called filler latencies reaction times to questions that are not connected theoretically or thematically to the interesting target latencies (Fazio 1990b). 3 But how these computed baseline speeds should be optimally transformed or connected to an unbiased measure of response latency is an open question. As a consequence, the applications of response latencies in empirical studies are inconsistent and do not usually discuss the reasons for the choice of one of the possible data treatment methods. There are several possible methods to control baseline speeds which differ in general aspects: A. Transformation of raw reaction times to continuous indices using baseline speed measures. B. Controlling the baseline speeds in a multivariate regression analysis using the baseline speed as control variable. C. Z-standardizing the reaction times for all items (first step) and for all respondents (second step). (ad A) Fazio (1990b) discusses three different variants to compute a response latency index considering the target latency ( RL raw ) and the baseline speed ( bs ): the difference score, the Z-Score, and the ratio index. Additionally, the rate-amount index proposed by Mayerl (2003) will be discussed here. All these indices transform the raw reaction time to a hopefully less biased continuous latency measure, trying to eliminate covariances with the baseline speed. The advantage of the difference score ( RL raw - bs ) is its easiness and plausibility: If the response reaction time consists of additive components (e.g. equation (1)), the subtraction of one of the bias components would lead to a latency measure without this biasing component and therefore to a more adequate measure of information processing. An underlying assumption of this method is the linearity of the association between baseline speed and the target latency which might not be true in all cases. Negative difference score values indicate that the respondents target latency is faster than the individual baseline speed. An advantage of this measure is that the scale remains within milliseconds and is still easily interpretable. A possible disadvantage of the difference score could be the fact that a 2 Of course, equation (1) is not sufficient and an error term should be added estimating this equation empirically. 3 Some researchers use the mean of measured response latencies of all items, including the target latencies (e.g. Bassili 2003). This implies a kind of tautology controlling a measure by itself. Additionally, the level of difficulty of the filler latencies is an unsolved question: should the baseline speed only be computed by response latencies of very easy questions like sociodemographical issues (Bassili 1993, Shrum/O Guinn 1993), thus controlling the general speed to access memory, or should the filler latencies imply more difficult questions or a mixture, controlling the general accessing speed and factors like education and intelligence? The answer might be, that this depends from the research questions. Empirical investigations of this topic are needed. 4

5 difference score of a given value for an individual with a slow baseline is equivalent to the same difference score for an individual with a fast baseline (Fazio 1990b: 88). In contrast, the ratio index is sensitive to these differences. By deviding the target latency by the sum of the target latency and the baseline speed ( RL raw / [RL raw +bs] ), one obtains an index with a scale of values from zero to one, where 0.5 indicates that the target latency corresponds to the baseline speed. The Z-Score transformation considers the individual mean baseline speed and its standard deviation ( [RL raw - bs] / stddev(bs) ). Following Fazio (1990b), the problem of the Z-Score is the need for many filler latencies to get an adequate and unbiased measure of the standard deviation. Another possible transformation method is the rate-amount index, proposed by Mayerl (2003), which is derived from multiplicative rate-amount models (see Faust et al. 1999). Following this approach, the measured reaction time is modeled as the ratio of the amount of information processing and the cognitive speed respectively cognitive process rate: amount of information processing RL raw = (3) cognitive process rate amount of information processing = (3.1) mean bs of all respondents individual bs The cognitive process rate in the equations (3) and (3.1) corresponds to the baseline speed (and thus contains the respondents and the interviewers baseline). 4 The amount of information processing reflects the substantially interesting part of the target response latency: the decision time, i.e. the mode of information processing and/or the attitude accessibility. 5 The difference between a mean baseline speed and a cognitive process rate is the scale and the base of these two baseline-measures: the mean baseline speed is based on different response latencies of one respondent and remains in the scale of milliseconds, whereas the process rate bases on the comparison of the mean response latency of the respondent and all respondents. The cognitive speed (i.e. process rate) can be computed as the ratio of the mean overall baseline speed and the individual baseline speed (see equation 3.1). Thus, the process rate value in equation (3) and (3.1) is 1.0 if the individual baseline speed corresponds to the mean baseline speed of all respondents. If the process rate value is lower than 1.0, the individual baseline speed is slower than the overall baseline mean; respectively, if the process rate is greater than 1.0, the individual baseline speed is faster than the overall mean. The logic of the rate-amount index is as follows: Processing the same amount of information, a respondent is double as fast as another respondent with half the baseline speed. And with the same raw reaction time, a respondent with a cognitive process rate indicating that he/she is generally half as fast as an average respondent will process half of the amount of informations compared to an average respondent. Therefore, if one is interested in the amount of information processing while controlling for cognitive process rate, the amount of information processing can be modelled by transforming equation (3): amount of information processing = RL raw process rate (4) 4 Other systematic bias effects (e.g. measurement instrument) have to be included in equation (3) respectively (3.1) as an additional error term. 5 The statistical-methodical separation of the mode of information processing and the accessibility of information/attitudes is a very important question to understand response latencies which cannot be dealt within this paper. 5

6 An unsolved question is whether the additive or the multiplicative model (equation (1) versus equations (3)) is more appropriate to model response reaction times. As noted above, both models are not sufficient and therefore must be modified by adding an error term estimating the models empirically. (ad B) The main disadvantage of controlling baseline speeds in a multivariate regression context by using baseline speed as a covariate instead of transforming raw reaction times to indices is simple but important: the measure of reaction time itself remains completely biased e.g., as a consequence, the researcher would not be able to use unbiased reaction time as a moderator or grouping variable (e.g. to group fast versus slower respondents). (ad C) The advantage of the z-standardization of reaction times along all items (control of question properties) and all respondents (control of individual differences) is that the computation of a baseline speed is avoided (Fekken/Holden 1994, Holden et al. 1993, Holden 1998). However, this is also this method s main disadvantage the substantial interesting differences between individuals and questions may also disappear. This could be the case, because this method does not allow to distinguish between the components of response latencies that were formulated in equation (1) or (3). Especially, there is no explicit control of the baseline speed, which is the main focus of this paper. Taking all these advantages and disadvantages of different methods to control baseline speeds into account, and considering the limitations of this article, the following indices will be compared and evaluated empirically: Z-Score, difference score, ratio index (all Fazio 1990b) and the rate-amount index (Mayerl 2003). A number of points must be taken into consideration concerning additional data treatment methods of reaction times. Firstly, as already discussed, there are a number of statistical methods to deal with outliers and distributional problems. These problems, while still relevant, are rather statistical than theoretical or substantial and can be applied as a second step of data treatment after controlling the baseline speed. Secondly, many researchers split reaction times at the median into two groups (fast versus slow latencies), transforming the continous scale into a dichotomous. The point here is that the control of moderation effects can be analyzed empirically in the easiest way by a multiple-group-test or by interaction effects. All the continous indices that will be analyzed here can be used in this way, dichotomizing the scale. But this dichotomization is not a disadvantage of any method to control the baseline speeds, but a way to analyze moderation effects, and therefore not in the focus of this paper. Thirdly, some biasing effects which are part of the term measurement instrument or an additional error term (see discussion above) in equation (1) or (3) can be considered, too. For instance, Fazio proposes to eliminate the covariance of response latency and extremity by computing the dichotomous variable at every scale point. This is only appropriate if one needs the dichotomous response latency variable to test moderation effects. Another way to handle this and to keep the continous scale would be the z-standardization for every scale point. We will consider this z-standardization in the following empirical analysis. 4 EMPIRICAL ANALYSIS 4.1 Method The empirical data of this paper are derived from a nation-wide German CATI study with 2000 respondents which was conducted in 1998 by the Institute for Social Sciences at University of Stuttgart under the direction of Prof. Dr. D. Urban (research grant, awarded by "Deutsche Forschungsgemeinschaft"). The response latencies were measured actively by 6

7 interviewers pressing a key to start the time-measure after reading the question and pressing again to stop the measurement when the respondent answered (Bassili/Fletcher 1991, Bassili 1996b). These response latency measurements are treated as invalid if the respondent asked a question (e.g. if he/she had problems understanding the question) instead of answering to the question in the given scale, if the respondent answered don t know (implicit category) or if the respondent refused to answer. A general attitude towards genetically modified food was measured by the item How do you evaluate genetically modified fruit or vegetables? with a 5-point scale (1=very good; 5=very bad). The following empirical analysis will focus on answers and response latencies to this attitude question. The four response latency indices Z-score, difference score, ratio index and rateamount index are computed as described in chapter 3. As shown in chapter 2, many systematic und unsystematic bias effects are still not controlled by computing these latency indices that control the baseline speed only. Two additional systematic bias effects will be considered here: the effect of question order and extremity. Due to the experimental design of the original study with two different versions of question order, the attitude question shows significant longer reaction times (raw and as latency indices) in the questionnaire version when the question is asked at a later time (χ 2 >18, df=1, p=0.000) possibly due to attention effects. Additionally, Fazio (1990b) suggests to control the covariation between reaction time and extremity. This effect is curvilinear, i.e. the middle category shows the longest reaction times (χ 2 >17, df=4, p=0.010). To control these two additional systematic bias effects, ten subgroups are generated (2 questionnaires 5 scale points) and the response latency indices are z-standardized for each of these 10 subgroups. After doing so, no significant effects of the question order (p>0.5) or the extremity (p>0.2) on reaction times remain. As a consequence, the following empirical comparison implies eight different latency measures: Z-score, difference score, ratio index and rate-amount index each non-zstandardized (four indices) and additionally z-standardized (four indices). The individual baseline speed is computed as the mean response latency of eleven items about environment and technology that do not differ significantly in their measured response time between the different questionnaire versions (6 of 17 items were skipped because of such a significant difference) Raw Response Latency And Baseline Speed Before evaluating and comparing the eight different indices concerning their power to control the baseline speed, it must be shown that controlling the baseline speed is empirically necessary: firstly, it should be examined if the baseline speed and the raw reaction time covary significantly if not, there would be no need for further investigation of methods to control the baseline speed; secondly, it should be analyzed whether the baseline speed empirically combines personal factors of cognitive speed (like age, gender, etc.) and the baseline speed of interviewers (e.g. reaction time to press the key), as argued above. This can be regarded as a test of the criterion validity of the measure of baseline speed. The Pearson s correlation of the raw reaction time with the computed baseline speed is r=0.266 (p=0.000). This is a low but nevertheless highly significant positive effect, indicating 6 The items about environment and technology are 5-point scaled each, reaching from 1 completely agree to 5 completely disagree, and include statements like The modern technological development guarantees the progress of society or Animals should have the same right to live as humans (translated wording; the original study was conducted german language). 7

8 that a relatively slow baseline speed accompanies with a relatively slow raw target latency. Consistently, there is empirical evidence for the need to control or eliminate this- covariance or, at least, to minimize the strength of this biasing effect. But is the computed measure of baseline speed valid, i.e. does it measure individual respondent effects (e.g. age, gender, etc.) and interviewer effects? To examine this question concerning criterion validity, a linear regression will be analysed, using the respondents age and gender as components of the respondents baseline and 25 interviewers (dichotomous dummy variable each) as predictors of the baseline speed (see table 1). 7 Table 1. Baseline Speed Depending On Sociodemographic Characteristics And Interviewers Unstandardized S.E. Standardized Colinearity Coefficient (B) Coefficient (Beta) Statistic (Tolerance) GENDER **.990 AGE **.977 INT INT INT INT INT *.580 INT **.825 INT INT INT INT **.723 INT INT **.643 INT **.550 INT INT **.735 INT **.761 INT **.578 INT **.568 INT **.713 INT INT **.627 INT **.808 INT INT **.804 **p 0.01; *p 0.05; N=1628; model R 2 =.157; gender: female=0, male=1 The regression analysis supports the assumption that the baseline speed combines the respondents and the interviewers baseline: The baseline speed is faster if the respondent is younger (beta=0.232; p=0.000), it is faster if the respondent is female (beta=0.060; p=0.009), and 13 of 25 interviewers show significant effects on the baseline speed. As a consequence, the measure of baseline speed used here is a valid indicator, implying the baseline speed of 7 Due to the fact that the OLS-regression assumes a normal distribution of the dependent variable and the baseline speed does not hold this assumption (skewness=2.0; kurtosis=6.1), the baseline speed will be transformed by taking the logarithm. Empirically, the reported findings do not differ substantially whether the logarithm is taken or not (the same predictors are significant and the Beta values differ maximally ± 0.005). Interviewer No. 14 is excluded due to collinearity problems. 8

9 respondents and interviewers. But it should be marked that the explained variance of the model is only 16%. This confirms that there are many other personal factors which determine the individuals baseline speed (see chapter 2). In addition, due to the fact that the baseline speed is computed out of eleven response latency measures, and these measures are biased themselves by systematic and unsystematic effects, the mean baseline speed implies these bias effects, too. Thus, 16% explained variance of the model are acceptable. In summary, firstly the raw reaction time and baseline speed covary substantially, indicating the need of controlling the baseline speed, and secondly the baseline speed depends significantly on personal characteristics of the respondents (age, gender) and on the interviewers, indicating that the used measure of baseline speed is valid in the sense of criterion validity. 4.3 Intercorrelations Of Response Latency Measures And Meta-Judgemental Indicators After confirming the need for controlling the baseline speed empirically, the next step is the test of the intercorrelation of the different response latency measures: the four unstandardized indices, the four standardized indices (standardized for each of the ten subgroups: 2 questionnaires 5 scale points) and the raw reaction time. The correlations between these measures can be seen as a first indication whether indices measure something different (low correlations) or measure nearly the same (very high correlations). As result, one might identify indices as almost equivalent and therefore interchangeable, one might find that an index is not appropriate or one might find that the indices do not differ substantially from the raw reaction times. The latter would mean that it would not be necessary to transform raw reaction times to indices. The correlations are reported in three tables: the correlations between unstandardized latency indices (table 2), the correlations between standardized latency indices (table 3), and the correlations between unstandardized and standardized latency indices (table 4). Additionally, tables 2 and 3 report the correlations between the latency indices and raw reaction time. Table 2. Correlations Between Unstandardized Response Latencies 8 Z-score diff. score ratio index raw Z-score diff. score ratio index rate-amount all values are Pearson s correlations with p 0.01; N= Because of the potential sensitivity of Pearson s R to skewed distributions, all reported correlations in this paper were computed with ln-transformed response latency indices, too. The results are identical with minimal differences (and therefore not reported). 9

10 Table 3. Correlations Between Z-standardized Response Latencies z-standardized Z-score diff. ratio raw z-standardized score index Z-score diff. score ratio index rate-amount all values are Pearson s correlations with p 0.01; N=1609 Table 4. Correlations Between Z-standardized And Unstandardized Latencies z-standardized Z-score diff. ratio rateamount unstardardized score index Z-score diff. score ratio index rate-amount all values are Pearson s correlations with p 0.01; N=1609 One empirical result is that all correlations between response latency indices reported in tables 2-4 are relatively high, in all cases higher than 0.7. Thus, no latency index steps out of line and indicates a problem of convergent validity. Looking at tables 1 and 2, some additional interesting findings can be reported: Firstly, the correlation between the Z-Score and the rate-amount index is the highest of all correlations, both in standardizing or not standardizing the indices. These correlations of about 0.94 are very high, which leads to the assumption that these two indices are almost interchangeable, although they are computed in a very different way. Secondly, the lowest correlations appear when raw reaction times are correlated with the indices. The mean of these correlations is (unstandardized) and (standardized). Thus, the latency indices seem not to be substitutable by raw reaction times. One interesting outlier appears: the difference scores and the raw reaction times correlate highly (0.893 respectively 0.784). Thirdly, both in the cases of standardized and unstandardized indices, the mean correlation of the rate-amount index with the other indices is the highest (0.878 respectively 0.884), and the mean correlation of the ratio index is the lowest (0.769 respectively 0.813). The mean correlation of the Z-Score is a little lower than the one of the rate-amount index (0.836 respectively 0.835), just as the mean correlation of the difference score (0.815 respectively 0.831). Therefore, one may argue that the ratio index would not be the best choice and that the rate-amount index would be a good choice as it covers the other indices quite well. But these correlation differences should not be used to rank the indices as many correlation differences are low and therefore statistically arbitrary. Therefore, additional criteria have to be considered (see below). Looking at table 4, the correlations from about 0.90 to 0.93 in the diagonal indicate that the standardized and unstandardized indices hardly differ. The other correlations are lower than the corresponding correlations in table 1 and 2 (but still about 0.7 or higher), as had to be expected due to the mix of standardized and unstandardized measures in table 3. 10

11 Correlation of latencies with meta-judgemental indicators Besides the test of the internal consistency and convergent validity analysing the correlations of the different response latency measures, the correlations of these latency indices (interpreted as an operative indicator of attitude strength) with meta-judgemental indicators of attitude strength can be regarded as a test of the reliability (in the sense of internal consistency) and also the convergent validity of the response latencies. Table 5 reports the correlations of the different response latency indicators with subjective knowledge and judgemental certainty (5-point scales, 1=agree... 5=disagree). The correlations are expected to be significant and negative if convergent validity and internal consistency are given. Table 5. Correlations Between Response Latency And Meta-judgemental Indicators Of Attitude Strength Meta-judgemental indicators Knowledge Certainty unstandardized response latency indices z-standardized response latency indices Z-score diff. score ** ** ratio index ** ** rate-amount * * Z-score * diff. score ** ratio index * rate-amount * raw ** ** knowledge 0.308** all values are Pearson s correlations; ** p 0.01; * p 0.05; + p 0.1; N=1609 The reported correlations between response latency measures and meta-judgemental indicators of attitude strength are very low, but nevertheless significant in most cases. In all cases, faster response latencies covary with higher knowledge and higher certainty. Interestingly, raw reaction times show significant correlations with the two meta-indicators, but not all transformed indices do so. Surprisingly, the Z-Score index is the only unstandardized index without a significant covariation (p<0.05) with knowledge or certainty. The other unstandardized indices correlate significantly with knowledge and certainty, but no higher than the raw reaction times. Further, controlling question order and extremity by z-standardization, the correlations of the indices with certainty become non-significant. This might appear because of the elimination of the covariance between response latency and extremity (as both are operative indicators of attitude strength) that may lead to a response latency indicator that measures mainly other factors than the chronic accessibility of attitudes. Therefore, it seems not advisable to control the extremity-effect if one wants to interpret response latency as an operative indicator of attitude strength at least at this stage of the analysis (see next chapter). Overall, the correlations between operative response latencies and meta-judgemental indicators of attitude strength underline the results of other studies that these two dimensions of attitude strength are very low correlated (Bassili 1996a). Nevertheless, the unstandardized indices difference score, ratio index, rate-amount index and the raw reaction times show significant negative correlations with knowledge and certainty, indicating a valid measure of the attitude accessibility as a measure of attitude strength. Additionally, the meta-judgemental indicators correlate higher (0.308) within this group in comparison to the correlations between 11

12 operative and meta-judgemental indicators, indicating discriminant validity assuming two different dimensions of attitude strength. 4.4 External Criteria To Evaluate Response Latency Measures In chapter 4.2, we saw that there is empical evidence that the baseline speed should be controlled. But which transformation index really does empirically control the baseline speed and which does it statistically better? Is there an advantage over the results of raw reaction times? To answer these questions, two evaluation criteria will be considered: A. The reduction of the correlation between the target latency and the baseline speed. B. The moderation of the predictive power and persistence of attitudes treating response latency as an indicator of attitude strength. (ad A) To evaluate response latency transformation indices, one criterion is the reduction of the biasing correlation between the target latency and the individual baseline speed. The more this correlation is reduced by using indices compared to raw reaction time, the better the controlling function of the indices (Fazio 1990b). Table 6. baseline speed Correlations Of Response Latencies With Baseline Speed Z-Score ratio Index difference score rate-amount raw z-stand. unstand. z-stand. unstand. z-stand. unstand. z-stand. unstand all values are Pearson s correlations with p<0.01; N=1609; z-stand. : z-standardized indices; unstand. : unstandardized indices Table 6 shows some important results of this evaluation step: the significant positive correlation of the raw reaction time with the baseline speed becomes a significant negative effect when transforming the raw reaction time to indices instead of the desired elimination of the effect. This phenomenon has been reported in other studies (Fazio/Williams 1986), but is nevertheless a problem: The faster a respondents baseline speed, the slower is its target latency after the transformation step. This is exactly the opposite of the original effect of the baseline speed on raw reaction times. As a consequence, the problem of raw reaction times that some respondents show fast target latencies due to their fast baseline speed returns as the opposite problem when analyzing transformation indices. As both are undesirable, the lesser disadvantageous should be used. Therefore, the strength of the correlation should be the main criterion. As desired, most indices show lower correlations with the baseline speed compared to the correlation of raw reaction times with baseline speed (0.266). But there are some important differences between the indices: a) the correlations of the four unstandardized indices are lower compared to the standardized indices, b) in the case of standardized indices, the ratio index and the difference score show correlations that are as high as the correlation of the raw reaction time, and c) both in the cases of standardized or unstandardized indices, the Z-Score and the rate-amount index show the highest reduction of the unintended correlation with the baseline speed compared to raw reaction time. Thus, using the reduction of the correlation with the baseline speed as evaluation criterion, the standardized or unstandardized Z-Score or rate-amount index should be used to control the baseline speed. The ratio index would be the worst choice this corresponds to the results of the intercorrelation analysis (chapter 4.3). Finally, the additional control of other systematic bias effects (here: question order and extremity) reduces the power of the indices 12

13 to control the baseline speed at least using the z-standardizing method. Thus, one should always check all applied data treatment methods and their consequences, even for data treatment steps that were applied before. (ad B) To evaluate and compare the different transformation indices, the analysis of the consequences of these transformations is very important, too. Thus, using the response latency as an indicator of attitude strength, the moderational power of the indices can be used as an external criterion: the moderation of the attitude-behavior relation, and the moderation of the persistence of attitudes (the relation of the same attitude measured at two different times). Therefore, two questions should be asked: do the transformation indices moderate these relations as expected, and is this moderation effect stronger compared to the moderation effect of raw reaction times? There are different possibilities to test moderation effects. The methods that will be used here are (1) the comparison of multiple groups (in our case: fast versus slow response latencies), and (2) the test of an interaction effect in regression analysis. The response latency measure of fast versus slow response latencies will be realized by a median split. 9 Due to the available data that does not contain a non-verbal measure of behavior, the moderation of the attitude-behavior relation will be tested by using a verbal measure of reported behavior (one continuous item) and a verbal measure of behavioral intentions (an index of six continuous items). The moderation of the persistence will be tested by using a second measure of the same attitude towards genetically modified fruit and vegetables that was asked some questions after the first measurement of the attitude. 10 (ad 1) Moderation test by multiple group analysis All correlations of the attitude (t 1 ) with behavior (recall), behavioral intention and the second measurement of the attitude (t 2 ) are reported in table 7, split into groups of fast versus slow response latencies of the attitude t 1. Additionally, the correlation differences between the groups of fast versus slow latencies are given. The significance level of the correlation differences is computed by Fisher s R-to-Z-transformation. As Pearson s R is a standardized correlation coefficent, it is possible that correlation differences appear as the result of variance inhomogeneity. Therefore, in the case of variance inhomogeneity of the concerning variables comparing the groups of fast versus slow respondents, the correlation difference is treated as significant at a significance level of p<0.01 only. 9 Interestingly, comparing the median split of the different response latency measures, the correspondence of the categorization in fast versus slow respondents is very high, at least in the case of the transformation indices. The median split of all four transformation indices corresponds in more than 94% of the respondents. The median split of the raw reaction times corresponds to the transformation indices in 78,7% (Difference Score) to 82,6% (Z-Score) of the respondents. 10 The question wording of the second attitude measurement is In general: What is your personal opinion about using gentechnology for the cultivation of fruit and vegetables? This is (5-point scale, 1 very good, 5 very bad ). Reported behaviour was measured by How often do you buy ecologically cultivated fruit and vegetables? (1 never, 2 rarely, 3 occational, 4 frequently, 5 always ), and behavioural intentions were measured by six items like Assuming that genetically modified fruit and vegetables would be longer nonperishable and less harmful to the environment. How certain are you that you would eat these fruit and vegetables? (5-point scale, 1 very certain that I would eat it, 5 very certain that I would not eat it ) (translated wording; the original study was conducted german language). 13

14 Table 7. Response Latency As Moderator Of The Predictive Power And Persistence Of An Attitude Z-Score ratio Index difference score rate-amount raw z-stand. unstand. z-stand. unstand. z-stand. unstand. z-stand. unstand. Attitude (t 1 ) - Behavior (recall) fast RL.285**.231**.261**.233**.258**.228** 1.267**.233**.197** slow RL.101**.117**.122**.127**.127**.131** 1.118**.127**.139** diff. fast-slow.184**.114**.139**.106*.131**.097(*).149**.106*.058 n.s. Attitude (t 1 ) - Behavioral Intention fast RL.601**.557** 1.590** 1.547** 1.611**.553** 1.594** 1.547** 1.561** 1 slow RL.489**.491** 1.497** 1.504** 1.478**.503** 1.495** 1.504** 1.494** 1 diff. fast-slow.112**.066(*).093**.043 n.s..133**.050 n.s..099**.043 n.s..067(*) Attitude (t 1 ) - Attitude (t 2 ) fast RL.749**.721**.742**.721** 1.762**.731** 1.740**.721** 1.727** slow RL.624**.618**.628**.617** 1.612**.610** 1.632**.617** 1.633** diff. fast-slow.125**.103**.114**.104**.150**.121**.108**.104**.094** all values are Pearson s correlations; ** p 0.01; * p 0.05; 1 variance inhomogeneity (Levene-test, p 0.05); z-stand. : z-standardized indices; unstand. : unstandardized indices In comparison to the unsplit correlations of the attitude with behavior (r=0.183, p<0.01), with behavorial intention (r=0.545, p<0.01), and with the second measure of the attitude (0.693, p<0.01), the correlations distinguished in fast versus slow response latencies indicate a moderate moderation effect. But, as in the empirical analysis before, there are some conspicious differences between the latency measuers. The interpretation of these differences will be divided into three steps corresponding to the three evaluation criteria. Firstly, concerning the attitude-behavior (recall) relation, the moderation effect of the unstandardized and standardized indices is stronger than the moderation effect of the raw reaction times. Stronger means that the significant differences of the correlations of fast versus slow latencies are higher, that the group of fast latencies shows higher correlations, and that the group of slow latencies shows lower correlations. The moderation effect (i.e. the correlation difference) of fast versus slow raw reaction times is not significant. In the case of the unstandardized indices that control the baseline speed only, the correlation differences are significant except for the difference score (because of variance inhomogeneity, the significance level has to reach p<0.01). Using the standardized indices instead of the unstandardized indices improves the moderational power of the indices. In this case, the correlation differences increase from (raw) to through 0.184, which makes a difference of about 0.1. Thus, the standardized indices which control baseline speed and additional bias effects should be preferred as attitude accessibility measures, applied as moderator variables of the attitude-behavior relation. Therefore, the doubts over using response latency indices controlled for the extremity-effect as an indicator of attitude strength (see chapter 4.3) seem to be unjustified. If one wants to rank the indices, it seems that the Z- Score is the best choice, both in cases of standardization or non-standardization. Additionally, these results underline the usefulness of measuring response latencies and controlling bias effects. Such as in the case of the standardized Z-Score, the attitude-behavior relation can be raised from r=0.183 (unsplit) to r=0.285 in the group of fast response latencies, which makes a significant difference (p<0.01) of about r=0.1 in contrast to the correlation of (thus a non-significant difference of 0.014, p>0.1) in the case of the raw reaction time. 14

15 Secondly, the correlations between attitude and behavioral intention split into fast versus slow latencies are somewhat surprising. The moderation effect of raw reaction times and all unstandardized response latency indices is not significant. Thus, controlling baseline speed alone does not, in this case at least, have any advantage. However, controlling baseline speed and additional bias effects (i.e. using the standardized indices) increases the power of the moderation effect as the correlation differences are significant in all cases of standardized indices. Thus, the standardized indices should be preferred (especially the standardized difference score, followed by the standardized Z-Score). Thirdly, looking at the moderation of the persistence of the attitude, the raw reaction time and the unstandardized indices show almost identical results (some minimal differences should be treated as statistically arbitrary). And again, the moderation effect increases in the case of the standardized indices, but hardly in the case of the ratio index and the rate-amount index. Thus, the standardized difference score should be preferred in this case, followed by the standardized Z-Score. Due to the empirical result that the z-standardized indices (controlling baseline speed and other bias effects) show the strongest moderation effects, it should be tested if it is sufficient to control only for question order and extremity. In table 8, correlations are reported using z-standardized raw reaction times (controlling the question order and extremity), split at the median. The relative strength of the moderation effect of these standardized raw reaction times ( raw in the sense of the lack of the control of baseline speed) varies enormously. Concerning the attitude-behavior relation, the strength of the moderation effect of the standardized raw reaction times is close to the moderation effect of the unstandardized indices, but lower than the moderation effect of the standardized indices. In the case of the attitude-intention relation, the moderation effect of the standardized raw reaction time comes close to the standardized indices and is stronger than the unstandardized indices. On the contrary, the moderation effect of the standardized raw reaction times concerning the persistence of the attitude is substantially weaker than the unstandardized and the standardized indices, and even compared to the completely raw reaction times. Table 8. Raw Response Latency As Moderator Of The Predictive Power And Persistence Of An Attitude raw raw z-standardized Attitude (t 1 ) - Behavior fast RL.197**.230** slow RL.139**.138** diff. fast-slow.058 n.s..092* Attitude (t 1 ) - Intention fast RL.561** 1.599** 1 slow RL.494** 1.487** 1 diff. fast-slow.067*.112** Attitude (t 1 ) - Attitude (t 2 ) fast RL.727**.725** 1 slow RL.633**.659** 1 diff. fast-slow.094**.066** all values are Pearson s correlations; ** p 0.01; * p 0.05; 1 variance inhomogeneity (Levine-test, p 0.05) Overall, these results show that the moderation effect of the response latency indices is in all cases substantially the strongest if the baseline speed and further systematic bias effects (like 15

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