# A Conditional Probability View of the Role of Product Warranties in Reducing Perceived Financial Risk

ABSTRACT - Probability components of a conditional probability model of perceived financial risk were manipulated to create multiple product profiles for hypothetical brands of stereos. One of these component probabilities represented the likelihood that repairs would be covered by the manufacturer's warranty. The efficacy of the model was tested through rank-order correlations and through ANOVA. The correlations supported the conditional probability model. ANOVA revealed that the probability of warranty coverage significantly affected perceived risk as did the other component probabilities. The two-way and the triple interactions predicted by the conditional probability model were generally not forthcoming.

##### Citation:

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John W. Vann (1987) ,"A Conditional Probability View of the Role of Product Warranties in Reducing Perceived Financial Risk", in NA - Advances in Consumer Research Volume 14, eds. Melanie Wallendorf and Paul Anderson, Provo, UT : Association for Consumer Research, Pages: 421-425.
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Probability components of a conditional probability model of perceived financial risk were manipulated to create multiple product profiles for hypothetical brands of stereos. One of these component probabilities represented the likelihood that repairs would be covered by the manufacturer's warranty. The efficacy of the model was tested through rank-order correlations and through ANOVA. The correlations supported the conditional probability model. ANOVA revealed that the probability of warranty coverage significantly affected perceived risk as did the other component probabilities. The two-way and the triple interactions predicted by the conditional probability model were generally not forthcoming.

INTRODUCTION

A conditional probability perspective of perceived financial risk presumes that for product failure to lead to a financial loss, a series of events must take place, with each event conditional upon the occurrence of the previous events in the series. Financial risk is presumed to be a function of the probability of a significant financial loss. The probability of a significant financial loss can be represented by the following conditional probability model: "P(Significant financial loss) - P(Significant financial loss|financial loss)P(financial loss|product failure)P(product failure)" (Vann 1984, p. 73). Even though some authors have discussed perceived risk as if it resulted from a consideration of a sequence of conditional probabilities (e.g., Cunningham 1965, Roselius 1971, Deering and Jacoby 1972, Taylor 1974, Humphreys and Kenderdine 1979) and even though Vann (1984) has proposed the conditional probability formulation shown above, this model has not been tested.

While the probability of product failure should only be a reflection of product quality, product warranties can be positioned as affecting the other two probabilities within this framework. First, a warranty can be positioned as affecting the probability of a financial loss given product failure. This effect would result from the differential coverage of the particular warranty and would depend upon the proportion of expected failures which would be covered. A second way that the effect of product warranties may be represented within this framework is through their impact on the probability of significant financial loss given some financial loss. For example, a recent Ford advertisement (People October 21, 1985, p. 80) presents a warranty which provides for a maximum charge of $25 on any repair visit (i.e., P(loss > $25| some financial loss) - 0).

The effect of warranty quality on risk perception has been examined by Bearden and Shimp (1982). However, they did not position warranties within a conditional probability framework. The present study examines the validity of the conditional-probability model of perceived financial risk. In addition, it tests the impact of differential warranty coverage within this framework through the manipulation of the proportion of repairs covered by a warranty.

METHOD

This study involved the creation of eight different product profiles of hypothetical stereo brands through the manipulation of three different variables (each at two levels): the proportion of stereos which would need repair during the first 6 months, the proportion of stereo repairs which would not be covered by the warranty, and the proportion of non-covered repairs which would cost more than $100. The stereo profiles were presented to subjects in an experimental setting in a 2 x 2 x 2 x n factorial design such that each subject saw and evaluated each profile.

Stimuli

Each product profile was presented on a separate page and consisted of descriptions of hypothetical brands of stereos such as the following:

Incidence of repair records indicate that approximately 40 in 100 stereos of this brand require some repair during the first 6 months of use. The company offers a warranty that fully covers some types of repairs made during the initial 6 months (both parts and labor). About 5 of 100 repairs which occur are not covered by the warranty. Of the repairs which occur during the first 6 months of use that are not covered by the warranty, about 70 out of 100 cost more than $100.

The probability of requiring repair (P(R)) was manipulated at two levels (.4 and .02); the probability of the repair's not being covered (P(NCov)) was manipulated at two levels (.3 and .05); and the probability of noncovered repairs' costing more than $100 (P(>$100)) was also manipulated at two levels (.1 and .7). As all combinations were represented, this resulted in eight different product profiles. A tree diagram of the resultant sequential effects is shown in the Figure.

Dependent and Manipulation Check Measures

On the bottom of the each page, below the product profile, subjects were asked to respond to six questions. Three were criterion measures and three were manipulation check measures; all were nine point scales. The primary criterion measure asked subjects "How much financial risk do you think would be associated with buying this stereo brand?" and had scale endpoints labeled "NO RISK" and "EXTREME RISK. " A second criterion measure was a tic differential item for evaluating the stereo and had endpoints of "GOOD" and "BAD." The third criterion measure asked: "If you were to buy one of these stereos, how certain are you that you would have to pay a significant amount to have it repaired?" The response categories for this question had endpoints labeled "EXTREMELY CERTAIN" and "EXTREMELY UNCERTAIN." This question served as a measure of the overall probability of significant financial loss.

Manipulation check measures were provided for each of the manipulated probabilities. Each one had response category endpoints labeled "EXTREMELY LIKELY" and "EXTREMELY UNLIKELY." The first asked: "How likely do you think it is that this brand of stereo would need repair during the first 6 months of use?"; the second asked: "How likely do you think it is that any repairs that are required for this brand of stereo during the first 6 months of use would not be covered by the warranty?", and the third asked: "How likely do you think it is that any repairs not covered by the warranty during the first 6 months would cost more than $100?"

Hypotheses

It was hypothesized that each of the probabilities would have a significant main effect on all of the criterion variables -- that perceived financial risk and the perceived certainty of paying a significant amount would increase and the Good/Bad response would decrease with increasing chances of needed repair, with increasing chances of the consumer's having to pay for the repair, and with increasing chances of the cost of any noncovered repair's costing more than $100. In addition, it was hypothesized that all of the two-way interactions and the three-way interaction would be significant. Since the conditional probability model involves the multiplication of the three manipulated probabilities, the effect of any one is weighted by the other two. A change in any component probability should have little effect if the other two are small, but should have an increased effect if the other two are large. The same reasoning would apply to the weighting of the effect of one probability by either one of the others (i.e., to the two-way interactions), but the size of the two way interactions would depend upon the level of the third probability (i.e., the three-way interaction should be significant).

Application of the conditional probability model to the component probabilities of the eight profiles results in eight, unique, resultant probabilities. It was hypothesized that the rank orderings of the means of risk, certainty, and good/bad would be significantly correlated with the rank ordering of the calculated probabilities for the eight profiles.

Procedure

The experiment was conducted in a classroom setting with one undergraduate class of 31 students and one graduate class of 46 students. Students received class participation credit for their role in the experiment. Responses were completely anonymous. Identification numbers were distributed to the students for them to record on each page of their packets. Since the experimental design relied on repeated measures (i.e., it was a completely within subjects design), it was necessary to make an effort to control for carry-over effects (Keppel 1973, p. 395). Consequently, each set of eight profiles was randomly ordered. The data from subjects with incomplete responses was discarded; all analyses in the study are based on the remaining 69 sets of responses.

Analysis

Two types of analysis were conducted. First, analysis of variance was conducted to determine the success of the manipulations and to test the main effect and interaction hypotheses. Because of the use of the repeated-measures design, the error term against which each effect was tested was the interaction of subjects with the variable whose effect was being tested (Calfee 1975, p. 102). Second, the rank-order correlations of the ranks of calculated probabilities with the ranks of means for each criterion variable were examined.

RESULTS

Manipulation Checks

Each of the probabilities significantly affected its corresponding measure. P(R) significantly affected perceived likelihood of repair (F1.68 = 411.42, p < .0001, means of 6.50 and 2.73 for the high and low probability conditions respectively). Neither the three-way nor either of the two-way interactions was significant. The likelihood of repair was significantly affected by P(NCov) (F1.68 = 8.51, p - .0048); however, the effect size was much smaller than that for P(R), with means of 4.76 and 4.46 for the high and low P(NCov) respectively. This has implications for real firms, consumers may presume that if the firm is willing to provide a good warranty then the quality of the product must be good. (See Olson and Jacoby 1972 for a study which found that warranties and guarantees were influential cues to perceived brand quality for some product categories.) P(>$100) had no effect on perceived likelihood of repair.

P(NCov) significantly affected the perceived likelihood of a repair's not being covered (F1.68 = 131.48, p < .0001, with means of 5.52 and 3.41 for the high P(NCov) and low P(NCov) conditions respectively). However, P(R) also significantly affected this measure (F1.68 = 13.88, p - .0004). However, as for the inferential effect of P(NCov) on likelihood of repair, this effect was not very large relative to the intended manipulation (means of 4.78 and 4.14 for the high and low P(R) conditions respectively. This measure was unaffected by P(>$100) and none of the interaction effects was significant.

The P(>$100) manipulation successfully affected the perceived likelihood of any repairs' costing more than $100 (F1.68 = 1383.83, p < .0001, means of 7.0 and 3.83 for the high and low P(<$100) conditions respectively). This likelihood was also significantly affected by P(R) (F1.68 = 17.68, p < .0001) and by P(NCov) (F1.68 = 6.2, p - .015). However, again the sized of the effect was small compared to the intended effect (means of 5.68 and 5.14 for the high and low levels of P(R) and means of 5.58 and 5.26 for the high and low levels of P(NCov)). None of the interaction effects was significant.

Rank-Order Correlations

Table 1 presents the calculated values for the conditional probability model for each stereo profile along with the means and rank of perceived risk, certainty, and the good/bad rating for each stereo profile. In addition, the calculated value and rank for each profile using an additive model (in which the probabilities are summed rather than multiplied) are presented for comparison purposes.

The rank-ordering of certainty has a perfect correlation with the calculated ranks using the conditional probability model. This provides strong support that subjects were processing the probabilities in the fashion specified by the model in assessing their overall perceived probability that if they were to buy one of the stereos they would have to pay a significant amount to have it repaired. However, perceived risk did not translate directly from this perceived probability. The rank ordering of perceived risk contained two reversals compared to the ranks of the calculated probabilities (3++2 and 5++4). Nevertheless, the Kendall's tau rank-order correlation was .86 (p < .005) (Conover 1980, p. 256). The rank ordering of the good/bat rating means also parallels the ordering of the calculated probabilities, with a rank-order correlation of -.93, p < .005; brands are evaluated more positively for lower calculated probabilities of a significant financial loss.

An alternative to multiplying the component probabilities would be to add them. The values for an additive model and the resulting ranks are also shown in Table 1. The rank orderings are quite different from those calculated using the conditional probability model; especially since the first and last ranks must be the same (i.e., the lowest sum and the lowest product must come from the same set of three probabilities as must the highest sum and product). Since the certainty ranks were perfectly correlated with those for the values calculated using the conditional probability model, this suggests that subjects (at least on the average) were not using an additive model.

TREATMENT VALUES and CRITERION MEASURE MEANS AND RANKS BY STEREO BRAND

The correlational findings provide support for the conditional probability model of perceived risk. Certainty, risk, and the good/bad rating were all highly correlated with the values of the overall probability of a significant financial loss calculated through the use of the conditional probability model.

Analysis of Variance Findings

Risk. The main effects on risk of all of the component probabilities were significant (see Table 3). Perceived risk increased significantly with each increase in probability. As can be seen in Table 2 moving from any cell to adjacent cells of increasing probability results in an increase in the mean of perceived risk. However, only two of the two-way interactions were significant: P(R)xP(NCov) and P(NCov)xP('$100). The reader will recall that the effect of any probability was hypothesized to be greater when either of the other probabilities was high. This hypothesis was supported for the P(R)sP(NCov) interaction; improved warranty coverage hat a greater effect when the probability of a repair was higher.

CRITERION MEASURE MEANS BY CONDITION

However, the reverse was true for the P(NCov)xP(>$N 0) interaction. The effect of P(>$100) was greatest when the probability of the consumer's having to pay was low. This finding is not compatible with the conditional probability model.

Certainty. The certainty with which the subjects perceived that they would have to pay a significant amount to get the stereo fixed if they were to buy it was significantly affected by all three of the component probabilities from the conditional probability model. This certainty was higher for higher levels of each of the component probabilities. None of the two-way interactions was significant nor was the three-way interaction. While the significant main effects are supportive of the conditional probability model, the lack of significant interactions is supportive of an additive rather than a multiplicative model.

Good/Bad evaluation. The good/bad evaluation was also significantly affected by all of the component probabilities from the conditional probability model. Increases in any of the probabilities was accompanied by a decrease in the evaluation of the stereo. One of the two-way interactions was significant: P(NCov)xP(>$100). The results of this interaction paralleled the same interactive effect on perceived risk; the effect of the warranty coverage hat the greatest effect when the P(>$100) was lowest -- contrary to the prediction of the conditional probability model. The three-way interaction was not significant.

ANOVA RESULTS FOR CRITERION MEASURES

SUMMARY AND CONCLUSION

Some of the findings of this study are supportive of the conditional probability model and some are not. The rank-order correlations of the various criterion means with the calculated values from the model were supportive of the model while ranks derived from an additive model were quite different from those for the calculated values and for the mean criterion values. ANOVA results provided only weak support for the multiplicative model. Only one of the predicted two-way interactions was significant in the right direction. Two others, while significant, were opposite to the direction hypothesized. It should be recalled that while the probabilities in this experiment were manipulated orthogonally, they were not perceived orthogonally. Changes in one probability affected the perceived likelihood of other occurrences in the sequence. This is an effect that could have implications for manufacturers. The introduction of a good warranty could decrease the perceived probability of product failure.

One caveat is in order regarding the within-subjects design that was used in the study. This design has considerable statistical power Some of the effects which were detected, while statistically significant, may be of little practical significance. This would appear to be especially relevant for the effects of the probability manipulations on the perceived likelihood of other occurrences observed in the manipulation checks and for the two-way interactions observed for the criterion measures.

SUGGESTIONS FOR FUTURE RESEARCH

This study was indented as an exploratory examination of the conditional probability model of perceived risk and to assess the role of warranty quality with this conditional probability framework. However, it has several shortcomings. The number of subjects is small and the subjects were students. While the statistical effects of a small sample size are overcome by the within subjects design, this type of design creates the potential for multiple-treatment interactions, pretest-treatment interactions, and fatigue. It would probably be better to use more subjects and to have them view only one profile each. Students are probably more sophisticated than the general population at the use of statistical data. Effects observed using student subjects may not be replicated using a more heterogeneous sample. Only two levels of each variable were used in creating the product profiles used in the study. Only one product category was used. The choice of $100 as the threshold for a "significant" financial loss, while based on discussions with other researchers and possessing some face validity for this product category, was arbitrary; no manipulation check was performed to assess its validity. Framing is an issue that was not addressed in the study (Fischhoff 1983, Puto, Patton, and Ring 1985). Framing is relevant not only to reference points (e.g., $100) but also to whether alternatives are represented as gains or losses. All probabilities were expressed in terms of a the likelihood of a 1088. Differential framing results would be relevant to manufacturers who are drafting the terms of their warranty statements.

The following changes are suggested for future research regarding the conditional probability model:

1. Use more subjects,

2. use non-student subjects,

3. use more than two levels for each probability,

4. use multiple product categories,

5. specifically address framing as an issue,

6. test any threshold values used in the study or include multiple values in the design.

Perhaps such changes could eliminate some of the ambiguity of the present findings.

REFERENCES

Bearden, William O. and Terence A. Shimp (1982), "The use of Extrinsic Cues to Facilitate Product Adoption," Journal of Marketing Research, 19 (May), 229-39.

Calfee, Robert C. (1975), Human Experimental Psychology, New York, Holt. Rinehart and Winston.

Conover, W. J. (1980), Practical Nonparametric Statistics, 2nd et, New York: John Wiley & Sons.

Cunningham, Scott M. (1965), "Perceived Risk as a Factor in Product-Oriented Word-of-Mouth Behavior: A First Step," in Reflections on Progress in Marketing, Proceedings of the 1964 Educators' Conference, Chicago: American Marketing Association.

Deering, Barbara J. and Jacob Jacoby (1972), "Risk Enhancement and Risk Reduction as Strategies for Handling Perceived Risk," in Proceedings of the 3rd Annual Conference for the Association for Consumer Research, et. M. Venkatesan, Iowa City: Association for Consumer Research.

Fischhoff, Baruch (1983), "Predicting Frames," Journal of Experimental Psychology: Learning, Memory, and Cognition, 9 (1), 103-116.

Humphreys, Marie Adele and James M. Kenderdine (1979), "Perceived Risk and Consumer Decision Making: An Alternative View of Uncertainty," in Educators' Conference Proceedings, Neil Beckwith, Michael Houston, Robert Mittlestaedt, Rent B. Monroe, Scott Ward, eds., Chicago: American Marketing Association.

Keppel, Geoffrey (1973), Design and Analysis: A Re- searcher's Handbook, Englewood Cliffs: Prentice-Hall.

Olson, Jerry C. and Jacob Jacoby (1972), "Cue Utilization in the Quality Perception Process," in Proceedings of the 3rd Annual Conference for the Association for Consumer Research, et. M. Venkatesan, Iowa City: Association for Consumer Research.

People, October 21, 1985.

Puto, Christopher P., Wesley E. Patton III, and Ronald B. King (1985), "Risk Bantling Strategies in Industrial Vendor Selection Decisions," Journal of Marketing, 49 (Winter), 89-98.

Roselius, Ted (1971), "Consumer Rankings of Risk Reduction Methods," Journal of Marketing, 35 (January), 56-61

Taylor, James W. (1974), "The Role of Risk in Consumer Behavior." Journal of Marketing, 38 (April), 54-60.

Vann, John W. (1984), "The Managerial Implications of a Consequence-Chaining, Conditional Probability View of Perceived Risk," in 1984 AMA Educators' Proceedings, Russell W. Belk, Robert Peterson, Gerald Albaum, Morris B. Holbrook, Roger A. Kerin, Naresh K. Malhotra, and Peter Wright, eds., Chicago: American Marketing Association.

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##### Authors

John W. Vann, Ball State University

##### Volume

NA - Advances in Consumer Research Volume 14 | 1987

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