# Best practice to handle double negatives when using the expectancy-value model?

My question is regarding the multiplicative combination rule in the Expectancy-value model developed by Fishbein and Ajzen, and the issues regarding the expectancy value-muddle, or the case of "double negatives," in the multiplicative combination.

For my master thesis, I conducted a questionnaire toward a sample of people and asked questions about their attitudes toward a hospitality company. My intention is to derive their attitudes with the help from the expectancy-value model:

$$\ a=\sum_{i=1}^{n}b_{i}e_{i}$$

a is one respondent's attitude towards the object. $$\ b_i$$ is the belief that the object has the attribute i. $$\ e_i$$ is the evaluation of the attribute.

a is one respondent's attitude toward the object. $b_i$ is the belief that the object has the attribute i. $e_i$ is the evaluation of the attribute i.

The first question (e) accesses the respondent's opinion of the importance of attribute i (e.g. central location), and the second question (b) accesses the respondent's belief that the hospitality company will deliver attribute i. I also have a direct attitude variable, which is not in the scope of this problem unless it is, of course, a part of the solution.

The respondents choose one alternative on a bipolar semantic differential scale with the extremes between "unimportant - important" (e) and "unlikely - likely" (b) for every attribute with a coded scale between -3 to +3.

The attitude points are compared with various hypothesis t-test. One independent t-test between the experimental group and the control group. And one dependent t-test to investigate a difference within the groups.

It's beyond the scope of the examination to carry out a focus group to elicit the attributes from a representative sample of the population (hospitality company customers). Thus, the reason to use a bipolar scale to "permit" a negative response e.g. "unlikely" instead of "slightly likely" on the lower scale:

"For example, when - as part of belief elicitation - a person indicates 'my drinking alcohol makes me nauseous,' it is reasonable to use, for that person a unipolar scale to assess the strength of this belief. However, when the same statement is presented to an individual who did not personally emit it, the individual may well judge it to be highly unlikely or false. To permit this kind of response, a bipolar belief scale should be used, such as a seven-point scale ranging from unlikely to likely or fall to true." (Fishbein & Ajzen, 2010, p.106)

A problematic issue, the expectancy-value muddle or the case of the double negative, occurs when the respondents answer with a negative evaluation and belief. Newton et al. (2011, p.3) claim that the phenomenon "expectancy-value muddle" occurs since the b*e "computation are uninterpretable":

"if both responses were coded on bipolar scales, then the individual would receive the highest score possible due to the multiplication of the two negative terms (-3*-3=9). Thus, the ranking of scores in the expectancy-value framework becomes contingent upon the method of scaling used. Hence, the rankings of expectancy-value scores are dependent on item scaling can have important implications for the analysis and interpretation of results." (Newton et al., 2011, p.2-3)

Fishbein and Ajzen have also dealt with this problem; French and Hankins (2003) explain the 'psychology of the double negative', which was originally presented by Ajzen and Fishbein (1980):

"The rationale given by Fishbein and Ajzen for the scoring system adopted is based on what they term the ‘psychology of the double negative’. For instance, if an ‘expectancy’ belief and its associated evaluation were both scored from - 3 to + 3, as recommended by Ajzen and Fishbein (1980), an individual who indicated that (s)he thought an outcome was both likely and good would score the maximum possible (+ 3 * + 3 = + 9), as would an individual who thought the outcome was both unlikely and bad (-3 * -3 = + 9). That is, a negatively valued consequence with a perceived low probability of occurring is thought to be as much a reason for inferring a positive attitude as a positively valued consequence with a perceived high probability of occurring. Note that, according to this viewpoint, the distant positions have led to the same numerical outcome." (French & Hankins, 2003, p.39)

Fishbein and Ajzen thus state that bipolar scaling is the best choice:

"In sum, evidence available to date indicates that bipolar scoring is generally superior to unipolar scoring of behavioral beliefs." (Fishbein & Ajzen, 2008, p.2231)

And they have also stated that the multiplicative combination is correct:

"We thus conclude that the multiplication of belief strength and outcome evaluation, which is at the core of the expectancy-value model, is a reasonable and well-supported assumption." (Fishbein & Ajzen, 2010, p.118)

What puzzles me is that Fishbein and Ajzen, both in 2008 and 2010, have suggested to convert from a bipolar to a unipolar scale after the data has been collected:

"Even though the shift from unipolar to bipolar scoring involves a simple linear transformation (i.e., subtraction by 4), it results in a nonlinear transformation of the product term (be). This can be seen in the following computation where the original values of b are transformed by the addition of a constant B, and the values of e by a constant E. For simplicity, only one behavioral belief is entered into the expectancy–value equation:

$$\ A_{B}\propto(b+B)(e+E)\propto be+Eb+Be+BE$$

In practice, however, the impact of a linear transformation is often relatively small as a result of a restricted range of belief strength or outcome evaluation scores. In the limiting condition in which scores on either variable are the same for all participants, a linear transformation of that variable will result in a linear transformation of the b * e product, thus having no effect on correlations with external criteria." (Fishbein & Ajzen, 2008, p.2226-2226)

To conclude, both French and Hankins (2003) and Newton et al. (2011) problematize the multiplicative combination because of the double negatives, also called the expectancy-value muddle. They do suggest various solutions but recommend two other models developed by Schmidt (1973) and Haddock and Zanna (1998), the "expectancy-valence model" and "open-ended measures of attitudinal components," respectively.

These models, however, are not applicable to my problem. I have already carried out questionnaires that do have double negatives in the resulting data.

I'm considering to either use the suggestion by Fishbein and Ajzen (2008) or to accept this issue as a "psychology of the double negative" presented by the same authors (1980).

But I'm not sure, and that's why I'm reaching out to this community to ask: What is the best and common practice to overcome this issue with double negatives when using the expectancy-value model?

Bibliography

• Ajzen, I., & Fishbein, M. (2008). Scaling and Testing Multiplicative Combinations in the Expectancy–Value Model of Attitudes. Journal of Applied Social Psychology, 38(9), 2222–2247. doi:10.1111/j.1559-1816.2008.00389.x
• Ajzen, I., & Fishbein, M. (1980). Understanding attitudes and predicting social behavior. Prentice-Hall.
• Fishbein, M., & Ajzen, I. (2010). Predicting and Changing Behavior: The Reasoned Action Approach. Taylor & Francis Group.
• French, D. P., & Hankins, M. (2003). The expectancy-value muddle in the theory of planned behaviour — and some proposed solutions. British Journal of Health Psychology, 8(1), 37–55. doi:10.1348/135910703762879192
• Haddock, G., & Zanna, M. P. (1998). On the use of open-ended measures to assess attitudinal components. British Journal of Social Psychology, 37(2), 129–149. doi:10.1111/j.2044-8309.1998.tb01161.x
• Newton, J. D., Ewing, M. T., Burney, S., & Hay, M. (2011). Resolving the theory of planned behaviour’s “expectancy-value muddle” using dimensional salience. Psychology & Health, 27(5), 588–602. doi:10.1080/08870446.2011.611244
• Schmidt, F. L. (1973). Implications of a measurement problem for expectancy theory research. Organizational Behavior and Human Performance, 10(2), 243–251. doi:10.1016/0030-5073(73)90016-0
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You could simply "shift" the scale of one of the variables. Instead of going from -3 to 3, go from 0 to 7. I would recommend converting the bi-polar "expectancy" variable to a percentage. – Mew Jan 2 '13 at 15:21
@Chris The $\ e_i$ is the evaluation of attribute i according to the expectancy-value model (see for example p.97, Ajzen & Fishbein 2010). – socialli Jan 2 '13 at 20:41

Fishbein, M., Middlestadt, S. (1995) Noncognitive Effects on Attitude Formation and Change: Fact or Artifact? Journal of Consumer Psychology, 4(2),181-202. [DOI]

Direct quote from page 187:

Note that the psychology of the double negative is an essential part of an expectancy-value formulation (Ajzen & Fishbein, 1980; Fishbein, 1967; Fish- bein & Ajzen, 1975). From the perspective of an expectancy-value theory, and consistent with Heider's (1958) balance theory, believing that an object does not have a negative characteristic or that performing a behavior will prevent a negative outcome should contribute positively (rather than negatively) to the attitude toward that object or behavior. For example, if a student does not believe (i.e., if he or she disbelieves) that "my professor is a capricious grader," this belief should, according to an expectancy-value formulation, contribute positively (not negatively) to his or her attitude toward my professor.

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The problem is fundamentally due to the level of likelihood you allocate to an event, that is variable $e_i$, should not be measured using a bi-polar scale. Instead, likelihoods should be associated with a percentage, between 0 and 100%. This is a more natural unit, as a "low likelihood" result usually means that the respondent thinks the probability of the occurance to be low, e.g. 20%. I could easily convert a bipolar scale to a percentage scale by using simple arithmetic. E.g. if the scale is -3, -2, -1, 0, 1, 2, 3, then I would convert these numbers to percentages as 0, 16.6, 33.3, 50, 66.6, 83.3, 100. This avoids the double negative problem, and is a more natural measurement of certainty than the bi-polar scale.

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Could you please link to relevant literature that is related to the solution? Also, the $\ e_i$ variable is the evaluation of how important an attribute i is (Ajzen & Fishbein, 2010) and is not related to any likelihood since the scale is unimportant - important. I'll make that more clear in the question. – socialli Jan 2 '13 at 20:25
I meant b not e in my response sorry. – Mew Jan 3 '13 at 5:34
Is there any evidence that this solution will not break the model? Is there any documented empirical support that one could refer to for the conversion of the bipolar likelihood scale when using the expectancy-value model? – socialli Jan 3 '13 at 15:41