About the anchoring effect in Willingness to Pay studies
with mobile fNIRS
Wantenaar, J.J. 11339055
Supervisor: Van Der Leij, A.
Abstract:
An interesting new way of researching neuronal activity in real life situations is functional near-infrared spectroscopy (fNIRS). The development of this technique has allowed for research to move itself towards the Point of Sale (PoS). Also, the technique is relatively cheap. This has increased the interest of neuromarketing companies in fNIRS. One thing neuromarketing companies are interested in is measuring the Willingness To Pay (WTP) for different products. This study tries to build a price classifying model using logistic regression and verify this model by measuring an anchoring effect. A model was found which could distinguish between best price and oddball category, the greatest possible difference in WTP found in this experiment. Furthermore, this study has found an anchoring effect in behavioural data elicited by the price shown in the previous trial. This effect had not yet been found and other researchers had wrongly thought that randomisation would cancel out the anchoring bias in such research design. The initial plan of this study, to verify the WTP model by trying if it would be sensitive to anchoring effects, was not conducted because of time limitations. Future studies could try to find this effect, with ultimately becoming a step closer to build a fNIRS pricing model available for the market.
1. Introduction
Neuromarketing is the application of imaging techniques to study consumer and market behaviour (Lee, Broderick and Chamberlain, 2007). In recent years, neuromarketing has gained popularity amongst scholars as well as business owners. However, whether the hype is going to result into a well-respected marketing strategy remains to be seen (Ariely and Berns, 2010). For this to happen, neuroimaging should develop into one of several ways. Firstly, it could be faster or cheaper than conventional ways. Secondly, it could reveal information not obtainable by conventional marketing research methods.
In order to do both, recent research has begun the use of mobile functional Near-Infrared Spectroscopy (fNIRS) (Krampe et al., 2018; Kawabata Duncan et al., 2019). Mobile fNIRS is a technique that is cheaper than more conventional neuroimaging techniques such as fMRI. Also, it can be used in situations that are more ecologically representative for consumer research, namely the point of sale (PoS). For example, as Kawabata Duncan et al. (2019) showed, it allows for researchers to investigate consumers’ willingness to pay (WTP) as they are using an item of interest. Furthermore, Krampe et al. (2018) proved that mobile fNIRS is applicable in investigating WTP of consumers while browsing a store. These studies both use a right dorsolateral prefrontal cortex (rDLPFC) and
orbitofrontal cortex (OFC) model for measuring WTP, first described by Plassman et al. (2007). These areas are part of a network which is correlated with aversive and appetitive goal values (Plassmann, O’Doherty and Rangel, 2010). Aversive and appetitive goal values are values that are assigned to stimuli at time of decision making. When a stimulusis presented, the OFC functions as a hub that adds all aversive and appetitive signals from the senses the brain receives. The role of the rDLPFC is most likely to compute the goal value signal, since its activity is positively correlated with appetitive signals and negatively correlated with aversive signals, possibly because this is where the prediction error is encoded (Plassmann, O’Doherty and Rangel, 2010). The prediction error is the difference between the expected signal and the received signal. This signal is crucial in research into decision making.
WTP research is a field of research that ultimately falls into the field of human judgment and decision making. Human choices are always affected by several cognitive heuristics, of which one is the anchoring effect. The anchoring effect is one of the most robust cognitive heuristics and has been found in several previous WTP studies (Furnham and Boo, 2011). It was first discovered by Tversky and Kahneman (1974). It tells us that when people have no clear answer to a certain question, they are prone to use available statistics as an anchor for their answer, even if this statistic is unrelated to the question at hand. For example, when people are asked to guess the percentage of African nations in the UN, they are influenced by what happened just before. If you let them spin a rigged wheel of fortune, which always lands at 10 or 65, and asked them to write the number down, they would be influenced by the number that they just wrote down. The group that wrote down the high number estimated the percentage to be higher than the group with the low number. Since then, the effect has proven to be a very robust one, occurring in a multitude of studies in several domains (Epley and Gilovich, 2001; Ariely, Loewenstein and Prelec, 2003; Englich and Soder, 2009).
It is believed that the anchoring effect stems from both semantic priming as well as
hypothesis-consistent testing (Mussweiler and Strack, 1999). This means participants are inclined to believe a hypothesis is right rather than wrong. This is thought to be explained by a selective
accessibility model of the working memory. The anchor ensures that anchor-consistent information is more readily available, therefore skewing the absolute judgment towards the anchor, even if there is no relation between the anchor and the field of judgment. The effect is especially strong when the
available information is limited. Self-generation of information therefore enhances the anchoring effect.
A brain region closely related to the retrieval from the working memory is the DLPFC (Li et al., 2017). This incentivized researchers to investigate the relation between the anchoring effect and stimulation of the DLPFC in WTP experiments. They used anodal transcranial current direct current stimulation (tDCS) to increase excitability of the rDLPFC and used kathodal tDCS to decrease its excitability. Activity in the rDLPFC was found to negatively correlate with the anchoring effect, therefore confirming the link between the rDLPFC and the anchoring effect.
All of the previously discussed rDLPFC WTP models come from open bid designs.
Nevertheless, once researchers start applying fNIRS to real life situations, such as stores, people don’t have the opportunity to place their own bets. This is because most stores offer products at a set price and the customer can decide whether to buy or not buy. Because of this, a model based on a closed-end dichotomous choice design might be more relevant for these type of situations (Herriges and Shogren, 1996). A closed-end design is a design in which the participant can only opt to buy not buy for a specific price, much like in a real life store. however, this type of design is known to be affected by anchoring effects (Araña and León, 2007). In these experiments, the second closed-ended question always elicit a significant lower WTP than in the first question, if the initial price was asked with a low price. Also, if the initial question was asked with a higher price, a positive anchoring effect can be observed (Bateman et al., 2001; Bollino, 2009).
However, how and if the anchoring effect represents itself in randomised WTP dichotomous choice studies has not yet been investigated. This study will try to investigate whether this anchoring effect is present in these type of studies and if it might influence a rDLPFC model for WTP. Normally, anchoring effects in these studies are said to be mitigated by randomisation of the first price shown in the experiment (Herbes et al., 2015). However, the anchor investigated in this design will be the price shown in the previous trial. If the price in the current trial is lower, there is a positive anchor and vice versa. We expect to find higher explicit WTP values when this anchor is positive, reflected in a higher probability of buying the item for the same price.
Furthermore, we try to build a pricing classification model of fNIRS beta weights. These beta weights are achieved by making a predictor for the best price and the oddball prices in the
experiment. Best price category will be deducted from the behavioural data, and is defined as the price at which the buying probability is 0.5 (Wang and Hu, 2019). This is because buying behaviour is expected to follow an s-curve, as shown in figure 1. If the WTP is higher for an item the curve is expected to shift to the right. The best price is therefore the price that is furthest away from the highest and the lowest prices in the experiment, called the oddballs. The classifier is expected to be able to accurately distinguish between best prices and oddballs. Also, to verify our model, we would expect our fNIRS model to classify higher prices as best prices in trials were there is a positive anchor if such an effect was found in the behavioural data.
Figure 1. Expectations of the probability of buying behaviour with increasing price for an item. Prices for which the WTP is higher are
expected to have the curve shifted to the right, while prices for which the WTP is lower the curve is expected to be more to the left. The best price condition is defined as being at the 0.5 buying probability.
2. Methods
2.1 Participants
A total of 100 participants conducted the experiment. Several were excluded because of a data leak caused by the Bluetooth setup, which resulted in a total of 67 participants. 12 participants were excluded because they did not buy any items, resulting in a total of 45 participants ultimately. Participants mean age was 24.6 yrs (sd=9.8) and were predominantly female (75%). Participants were screened for possible allergies for any of the items. No participants needed to be excluded for of this, because of the different categories. All categories had a similar distribution of gender and age.
2.2 Stimuli
Participants were given one of four categories of fast moving consumer goods. The categories were beer, shower gel, chocolate and toothpaste. For each of the four categories there were four products, summing to a total of sixteen products. Each of the product were controlled for specifications. The beers were all six-packs of 0.33 cl bottles. The shower gel were all bottles of 250 ml. The chocolate bars were all hazelnut milk chocolate bars of 200 grams each. Lastly, the
toothpastes were all whitening toothpaste tubes containing 75 ml. Items were shown on the computer in high resolution (720p). Each category contained a premium brand, an environmentally aware brand, a cheap brand and a middle of the road brand. All stimuli are included in the appendix.
All items were shown with a price. Prices were specific for a certain category. Some of the categories were characterized by a big difference in prices, in others the prices were closer. We tried to implement this by choosing the prices for the categories carefully. To counteract the diminishing sensitivity for higher prices as predicted by the Prospect Theory, we decided to let the price
differences increase exponentially (Kahneman and Tversky, 1979). For all categories, the median and standard deviation of all the retail prices for the separate items within the category were calculated. Then, the LOG of the medians and standard deviations were used to measure the different prices. For each category, we added and subtracted 0.5, 1 and 3.5 times the standard deviation to the median to
give categories where retail prices were closer to each other smaller price ranges. After this we calculated the values back to normal prices. Lastly, we rounded the prices to the nearest second decimal 9. For example, 4.47 would become 4.49. This is because the way in which these prices are presented can have influence on sale figures and therefore willingness to pay (Schindler and Kibarian, 1996). Sadly, due to financial limitations, the upper cap for the prices was 20 euros. This led to the prices shown in table 1. Because all prices were set up in the same way, they were comparable over categories with the corresponding price index for each price.
Table 1. An overview of the prices used within the different categories in euros. The horizontal header shows the amount of log standard
deviations that were added to the log of the median.
Prices -3.5 sd -1 sd -0.5 sd Median +0.5 sd +1 sd +3.5 sd Price Index 1 2 3 4 5 6 7 Beer 1.79 3.09 3.49 3.89 4.39 4.99 8.79 Shower gel 0.09 1.39 2.49 4.49 7.99 14.29 19.99 Chocolate 0.39 0.99 1.29 1.59 1.89 2.39 6.49 Toothpaste 0.19 1.49 2.29 3.49 5.39 8.19 19.99
2.3 Procedure
Participants all were informed about the experiment and signed an informed consent. Then, they were presented with four cards. They were told the cards contained the different categories from which they could choose. Without seeing the cards, they picked one and looked what their category would be. Then the items within the category were all presented to the participant. They were instructed to investigate the items and form an opinion about them, because they would only see a picture of them in the experiment. Next the budget, which was identical to the highest price for the category, was handed to them. It was made clear that this money was theirs now and they could use it to buy the items in the auction in the experiment. They were also carefully explained that the ideal strategy was to buy whenever they thought the item was worth the presented price. When conducting the auction, participants had already participated in another experiment for 45 minutes.
During the auction, participants were situated 50 cm from the screen in a dimly lit room. Stimuli were presented using EventIDE (Okazolab, Delft, Netherlands) on a grey background with BGR values of 127 for all three colours. Participants conducted seven practice trials to familiarize
themselves with the paradigm. Firstly, only the item and price were shown. 3 seconds after, the BUY and DO NOT BUY buttons were added to the screen. Participants answered using the ‘M’ and ‘Z’ keys on the keyboard for the right and the left answer on the screen, respectively. The side in which the keys were presented was altered randomly to control for a motor bias in the data. Participants had a total of 2.5 seconds to respond to the offer, after which the item plus the price disappeared from the screen. There was an ISI with a duration different for each trial, so to complement the total duration of a trial to a randomized duration between 7 and 9 seconds to be able to have a rapid event related design (Burock et al., 1998). Only three items of each category were shown to increase the amount of repetitions per participant. Every item was shown with every price once each block, with a total of 4 blocks. Between blocks there was a self-imposed break. Attention was monitored during the
Figure 2. A schematic overview of a single trial in the paradigm. First only the item and the price were shown, followed by the
screen in which the buy and don’t buy buttons were assigned to either button ‘m’ or ‘z’. Lastly, a grey ISI was shown.
2.4 Data acquisition
Participants wore a neoprene cap holding a fNIRS system (Artinis BV., Netherlands, 50 Hz) with 10 transmitters and 8 receivers at two near infra-red wavelengths (760nm and 850nm) and a 12 channel OpenBCI EEG system (OpenBCI, America, 125 Hz). The EEG was not used for this research. However, it did mean that all fNIRS data was resampled to 125 Hz. The fNIRS was positioned in 2*12 channel template with 30 mm distance between each transmitter and receiver. The midpoints between transmitters and receivers were defined as channels. Only the channels between receiver 1 and transmitter 2 (Rx1-Tx2) and receiver 5 and transmitter 7 (Rx5-Tx7) were too far apart to yield reliable data resulting in 44 functional channels spreading across multiple frontal brain areas. These areas include both the rDLPFC and the OFC. Transmitter 5 and 10 were placed at FP2 and FP1, respectively. The system measured both the Oxy-HB and the deoxy-HB time series using the modified Beer-Lambert law in units of millimolar * millimetre. Furthermore, explicit data and reaction times were recorded in EventIDE. However, only the Oxy-HB data would be used in this research, since the activity found in these channels more closely resemble the canonical hemodynamic response function(cHRF) (Nishiyori, 2016).
A.
B.
Figure 3A. A picture of the Neoprene cap with the holders for the fNIRS transmitters (t) and receivers (r). The yellow lines are the locations of the channels. Tx10 and Tx5 are located at FP1 and FP2, respectively. The yellow lines are the points of measurement. The red line was recorded in Oxysoft, but was unusable because of the distance between Tx2-Rx1 and Tx7-Rx5 being too great. In figure B. it is visible where point FP2 and FP1 are located on the skull.
2.5 Data Analysis
Data analysis in this experiment was twofold, as both behavioural data as well as fNIRS data had to be analysed. Behavioural data was analysed using Rstudio (RStudio Team (2015). RStudio: Integrated Development for R. RStudio, Inc., Boston, MA URL http://www.rstudio.com/). First, all participants were checked for buying the items for a price that was higher than the low-oddball. If they bought none, they were excluded from further analysis, because they were not part of the costumers group of the presented items. Also, if they only bought one of the items, they would be analysed for only that item. Prices were converted to an index to allow for inter-category testing. The
low oddball would get index number one and the high oddball index number seven. All the other prices would be the numbers in between. For every item, every price was shown four times. The best price for that item was defined as the highest price at which they bought the items two times. The best price was further used in the analysis of the fNIRS data.
To find an anchoring effect, all behavioural data for the first block was analysed. In this block, there were still shifts in the participants behaviour of buying. Every trial was marked dependent on its price and the price of the trial before. If the current price was lower than the price before, the trial was marked as being a positive anchoring trial and vice versa this would be called a negative anchoring trial. If the current price was the same as the price before or if it was the first trial in the experiment, the trial was marked as neutral anchoring. This way, the low oddball could never be a negative anchoring trial and the high oddball never a positive anchoring trial, so these were excluded for further analysis. Also, the neutral trials were excluded because these were too little in numbers. Lastly, the amount of buying at prices where buying behaviour was above 20% were compared using a chi-squared test (McHugh, 2012).
FNIRS data was pre-processed using Matlab 2007b (The Mathwork, inc. Matwick, USA). Raw fNIRS signals were smoothed by applying a 5th order cubic Savitzky-Golay filter with a framelength of
12 seconds. Next, the smoothed signal was filtered with a Chebyshev Type 1 lowpass filter (passband freq 2 Hz, stopband freq 5 Hz, passband ripple 1 dB, stopband attenuation 20 dB).
Next, the remaining data was further analysed by convolving a stickmodel time series of predictors and the hemodynamic response function (Friston et al., 1998). Predictors in the
experiment were the best price deducted from the behavioural data and the oddballs. The resulting model was regressed against the standardized and mean-centered timeseries using a glmfit. From this, we could get a β value per channel per predictor per subject, resulting in a total of 3960 beta scores. Data was checked for normality and proved to be not normally distributed for both category oddball (p=9.0627e-12) and the best price category(p=1.3386e-16). Quantile-Quantile (QQ) plots showed the data to be overly dispersed, containing a total of 107 outliers. Outliers were defined as 1.5 times the Inter-Quartile-Range (IQR) added to the third quartile, or 1.5 time the IQR subtracted from the first quartile. Therefore, difference in mean beta weights between condition were compared using a non-parametric Yuen-test, which does not take the outer 10 percent of the distributions in its assessment for the difference in means (Yuen, 1974).
For further analysis of the data via logistic regression, outliers had to be dealt with. First, the outliers above the third quartile were reduced to the third quartile and the outliers below the first quartile were increased to the first quartile for each subject, to keep between subject variation intact whilst also not decreasing the IQR. The second transformation done was to z-score all beta’s per subject, to further normalise the data while keeping inter-subject variation intact (Pereira, Mitchell and Botvinick, 2009). In the final data the null hypothesis for normality in the oddball category could be rejected (p= 0.01), while the p-value for the best category was not significant (p= 0.24). This was reflected in the QQ-plots.
Figure 4. QQ-plots for the raw data (left) and the processed data (right). The processing increased p-values from 9.06e-12 to 0.01 for and
1.34e-16 to 0.24 for the oddball and best category, respectively.
In order to run the logistic LASSO regression, the dataset was split up in using 70% training set and 30% test set. This was done randomly for 30 times per lambda. Using the glmnet package in rstudio, a model was made to separate the two categories between subjects using a logit link function (Friedman, Hastie and Tibshirani, 2009; Pereira, Mitchell and Botvinick, 2009). The model was used to predict the test set. An average percentage of correctly classified subjects was computed for each lambda. Next, a difference between the correctly classified percentage for the model was compared to classifying at chance using a t-test to test for a difference in mean correct classification between chance and the model. Lastly, A coefficient test was run to see what channels were predictors in the model. No further analysis was done on these channels, since the goal of this study was not to find where the activity was coming from, but solely whether activity contains enough information to distinguish between the two categories.
3.1 Results
The behavioural data showed an overall buying probability of 0.37 for the lowest price after the low oddball. The third price index had a probability of 0.20 of buying behaviour. The fourth price was with a probability of 0.19 no longer assessed in further analysis. A mean probability of buying of 0.39 and 0.31 was found for the positive and negative anchoring group at the second price index, respectively. For the third price index this was 0.26 for the positive anchoring group and 0.09 for the negative anchoring group. Using a chi-squared test, a significant difference was found between negative and positive anchoring at the third price index (p=0.037). No difference was found at the second price index (p=0.567).
Figure 5. An overview of buying behaviour at different prices. Negative group is where the price in the previous trial was lower than in the
negative trial and vice versa. A difference in buying behaviour between groups was found at the third price index (p=0.037) using a Chi-squared test for goodness of fit. Achieved with LOESS smoothing, span=1.
For fNIRS data a non-paramatric Yuen test was conducted to assess differences in mean beta values. No significance difference was found between categories’ mean (p=0.409). Next, data was tested using a logistic LASSO regression using only O2HB, because these channels were expected to have a response more like the cHRF response fitted in the GLM (Nishiyori, 2016). Data was split up into a testing set (30%) and a training set (70%). Different lambda were tried to find the best model and every lambda was used in thirty different permutations of splitting the test set and train set. The best lambda was found to be 0.014, with a resulting model classifying the corresponding category correctly in 61.5% of the cases. A t-test was conducted to assess the difference between the average correct classification rate and classification at chance and resulted in a significant result (p= < 2.2e-16). A coefficients analysis showed all channels contributing to the model, except for channels 5,6,7,16,20 and 22. Channels contributing the most were channels 15,19 and 21. See appendix for exact locations of these channels.
Figure 6. Percentage correctly classified trials for model made with different lambda’s. Every point is an average of 30 models made with the
same lambda. The higher the lambda, the less coefficients are taken into consideration for the model. When lamda was 0.016 the model yielded the best results, classifying at correctly at a rate of 61.5%. on average. The classification performed above chance (p=< 2.2e-16).
3.2 Discussion
From these results, we can conclude that an anchoring effect is present in this study even when the order in which prices are presented is random. This effect only presents itself at prices were there is enough buying behaviour, although not at the second price index. This might be due to the confidence intervals in the negative anchoring group being too large to yield significant results, which is because the sample size is very small. More statistical power is needed to confidently draw
conclusions about this price range. So far, the effect has only been found for one price range. However, it should be noted that these results are from the first block only, because the early blocks are most prone to anchoring effect as stated in the introduction. How the effect develops over time in such a design remains to be seen.
The findings for the third price range were surprising, as other researcher have used randomisation of prices in a similar setup to exclude a bias from the anchoring effect (Herbes et al., 2015). In contrast, our results suggest that prices where there is some buying behaviour and there are enough anchor both positively and negatively see bias from the anchoring effect. Low prices are therefore anchored to be bought even more than high prices, because of their greater chance of being positively anchored in a random presentation of prices. This means that results of buying behaviour are biased in random setups and that this needs to be controlled using a pseudorandom setup, so that every price has an equal amount of negative and positive anchors if you want to fully exclude an anchoring effect from your dataset.
Figure 7. Chances of positive and negative anchor in a randomised design with 21 trials and 7 prices. Chances for negative anchors are lower
for low prices which biases the amount of buying at these prices. Chances do not add up to 1 because of the chance of neutral anchor trials.
Analysis for the fNIRS data resulted in no difference found between mean beta weights. However, we were able to build a classifier that could predict price categories based of fNIRS data in the testing set. This implies that there is information about the category found in the fNIRS data, in line with earlier research on this topic. The way the categories were chosen made sure that the model was not just detecting whether a price was high or low, but that is was predictive of the whole s-curve as expected in the introduction. Therefore, fNIRS would be a feasible technique to base a WTP model on. However, if fNIRS is able to detect differences in trials that are anchored positively and negatively, as expected by behavioural data, remains to be seen. Due to time limitations this paper will not be able to answer this question.
So, future studies could try to validate the model proposed in this study by assessing if the model is sensitive for robust psychological findings, such as the anchoring effect found in this study. Also, the accuracy of the model should be increased. However, as shown is this experiment, all future repeated measures WTP studies should be wary of the bias the previous trial imposes on the current trial. If you want to counter this bias, studies should not be randomised, but account for the
difference in chances to be positively and negatively anchored for different prices.
The findings of this study also look very promising for future ventures of fNIRS into the field of neuromarketing. As mentioned before, its lower costs and superior manoeuvrability compared to more conventional neural techniques such as fMRI and EEG make it an interesting option for
neuromarketeers looking to move their research to the PoS. Now that we have found that fNIRS is able to detect where prices are on buying behaviour s-curve, companies might be interested in finding a more refined model which could lead to a prediction of revenues when a price is sold for a certain price. This could make neuromarketing able to detect information not yet obtainable by
conventional methods, especially if this fNIRS model is combined with already existing EEG models ((Herbes et al., 2015).
This also leads to the most important limitation of the current study. Because of it’s crude way of contrasting between the predictors, it is difficult to predict the prices in between those predictors. A more elegant way of modelling the fNIRS data used in this experiment would be to compute a distance towards the oddballs, instead of labelling the price that is the farthest away with the help of behavioural data. This way you would get a data driven model instead of a behaviourally driven data, which is important if you want to defend the point that the future of neuromarketing is obtain information unobtainable via conventional methods.
Furthermore, another limitation of the current setup is that participants would often deviate from the s-curve for buying behaviour in the expectations. This factor made it so that often times participants would only partake in the experiment for which they showed such an s-curve in buying behaviour, causing a loss of data. Also, for toothpastes especially, people started buying the product less at low prices, an effect common for Veblen Goods (Trigg, 2001). These goods were not accounted for in the current way of researching and could therefore have decreased accuracy of classifying. So a model that doesn’t rely on the expectation of a buying behaviour s-curve would be a step forward and could potentially increase the accuracy of the model.
All in all has this study shown that differences in price perception are detectable by fNIRS. This study has also produced a model being able to detect these differences. Furthermore, we have found an anchoring effect in a randomised design contrary to common believe. These findings could be combined in the future to allow for a prove of concept for a pricing model that could make it to the market. However, yet still a large amount of work needs to be done before these first findings can be put to actual use.
Literature:
Araña, J. E. and León, C. J. (2007) ‘Repeated dichotomous choice formats for elicitation of willingness to pay: Simultaneous estimation and anchoring effect’, Environmental and Resource Economics, 36(4), pp. 475–497. doi: 10.1007/s10640-006-9038-7.
Ariely, D. and Berns, G. S. (2010) ‘Neuromarketing: The hope and hype of neuroimaging in business’,
Nature Reviews Neuroscience, pp. 284–292. doi: 10.1038/nrn2795.
Ariely, D., Loewenstein, G. and Prelec, D. (2003) ‘“Coherent Arbitrariness”: Stable Demand Curves Without Stable Preferences’, The Quarterly Journal of Economics, 118(1), pp. 73–106. doi:
10.1162/00335530360535153.
Bateman, I. J. et al. (2001) ‘Bound and path effects in double and choice contingent valuation’,
Resource and Energy Economics, 23(3), pp. 191–213. doi: 10.1016/S0928-7655(00)00044-0.
Bollino, C. A. (2009) ‘The willingness to pay for renewable energy sources: The case of italy with socio-demographic determinants’, Energy Journal, 30(2), pp. 81–96. doi: 10.5547/issn0195-6574-ej-vol30-no2-4.
Burock, M. A. et al. (no date) Randomized event-related experimental designs allow for extr... :
NeuroReport. Available at:
https://journals.lww.com/neuroreport/fulltext/1998/11160/randomized_event_related_experimenta l_designs.30.aspx (Accessed: 12 December 2019).
Englich, B. and Soder, K. (2009) Moody experts-How mood and expertise influence judgmental
anchoring, Judgment and Decision Making.
Epley, N. and Gilovich, T. (2001) ‘Putting adjustment back in the anchoring and adjustment heuristic: Differential Processing of Self-Generated and Experimenter-Provided Anchors’, Psychological Science, 12(5), pp. 391–396. doi: 10.1111/1467-9280.00372.
Friedman, J., Hastie, T. and Tibshirani, R. (2009) Regularization Paths for Generalized Linear Models
via Coordinate Descent.
Friston, K. J. et al. (1998) ‘Event-related fMRI: Characterizing differential responses’, NeuroImage. Academic Press Inc., 7(1), pp. 30–40. doi: 10.1006/nimg.1997.0306.
Furnham, A. and Boo, H. C. (2011) ‘A literature review of the anchoring effect’, Journal of
Socio-Economics, 40(1), pp. 35–42. doi: 10.1016/j.socec.2010.10.008.
Herbes, C. et al. (2015) ‘Willingness to pay lip service? Applying a neuroscience-based method to WTP for green electricity’, Energy Policy. Elsevier Ltd, 87, pp. 562–572. doi:
10.1016/j.enpol.2015.10.001.
Herriges, J. A. and Shogren, J. F. (1996) ‘Starting point bias in dichotomous choice valuation with follow-up questioning’, Journal of Environmental Economics and Management. Academic Press Inc., 30(1), pp. 112–131. doi: 10.1006/jeem.1996.0008.
Kahneman, D. and Tversky’, A. (no date) E C O N OMETRICA I C I VOLUME 47 MARCH, 1979 NUMBER
2 PROSPECT THEORY: AN ANALYSIS OF DECISION UNDER RISK.
Kawabata Duncan, K. et al. (2019) ‘Willingness-to-pay-associated right prefrontal activation during a single, real use of cosmetics as revealed by functional near-infrared spectroscopy’, Frontiers in
Human Neuroscience. Frontiers Media S.A., 13. doi: 10.3389/fnhum.2019.00016.
Krampe, C. et al. (2018) ‘The application of mobile fNIRS to “shopper neuroscience” – first insights from a merchandising communication study’, European Journal of Marketing. Emerald Group Publishing Ltd., 52(1–2), pp. 244–259. doi: 10.1108/EJM-12-2016-0727.
Lee, N., Broderick, A. J. and Chamberlain, L. (2007) ‘What is “neuromarketing”? A discussion and agenda for future research’, International Journal of Psychophysiology. Elsevier, 63(2), pp. 199–204. doi: 10.1016/J.IJPSYCHO.2006.03.007.
Li, J. et al. (2017) ‘Controlling the Anchoring Effect through Transcranial Direct Current Stimulation (tDCS) to the Right Dorsolateral Prefrontal Cortex’, Frontiers in Psychology, 8. doi:
10.3389/fpsyg.2017.01079.
McHugh, M. L. (2012) ‘The Chi-square test of independence’, Biochemia Medica, 23(2), pp. 143–149. doi: 10.11613/BM.2013.018.
Mussweiler, T. and Strack, F. (1999) ‘Hypothesis-Consistent Testing and Semantic Priming in the Anchoring Paradigm: A Selective Accessibility Model’, Journal of Experimental Social Psychology, 35(2), pp. 136–164. doi: 10.1006/jesp.1998.1364.
Nishiyori, R. (2016) ‘fNIRS: An Emergent Method to Document Functional Cortical Activity during Infant Movements’, Frontiers in Psychology, 7. doi: 10.3389/fpsyg.2016.00533.
Pereira, F., Mitchell, T. and Botvinick, M. (2009) ‘Machine learning classifiers and fMRI: a tutorial overview.’, NeuroImage, 45(1 Suppl). doi: 10.1016/j.neuroimage.2008.11.007.
Plassmann, H., O’Doherty, J. P. and Rangel, A. (2010) ‘Appetitive and aversive goal values are encoded in the medial orbitofrontal cortex at the time of decision making’, Journal of Neuroscience, 30(32), pp. 10799–10808. doi: 10.1523/JNEUROSCI.0788-10.2010.
Schindler, R. M. and Kibarian, T. M. (1996) Increased Consumer Sales Response Though Use of
W-Ending Prices.
Trigg, A. B. (2001) ‘Veblen, Bourdieu, and conspicuous consumption’, Journal of Economic Issues. Association for Evolutionary Economics, 35(1), pp. 99–115. doi: 10.1080/00213624.2001.11506342. Wang, T. and Hu, M. Y. (2019) ‘Differential pricing with consumers’ valuation uncertainty by a monopoly’, Journal of Revenue and Pricing Management. Palgrave Macmillan Ltd., 18(3), pp. 247– 255. doi: 10.1057/s41272-018-00166-2.
YUEN, K. K. (1974) ‘The two-sample trimmed t for unequal population variances’, Biometrika, 61(1), pp. 165–170. doi: 10.1093/biomet/61.1.165.
Appendix:
A. Location of fNIRS channels:
fNIRS Channel Channel Location
1 Rx1-Tx1 2 Rx1-Tx3 3 Rx2-Tx1 4 Rx2-Tx3 5 Rx2-Tx4 6 Rx3-Tx2 7 Rx3-Tx3 8 Rx4-Tx3 9 Rx4-Tx4 10 Rx3-Tx5 11 Rx4-Tx5 12 Rx5-Tx6 13 Rx5-Tx8 14 Rx7-Tx7 15 Rx7-Tx8 16 Rx7-Tx10 17 Rx6-Tx6 18 Rx6-Tx8 19 Rx8-Tx8 20 Rx8-Tx10 21 Rx6-Tx9 22 Rx8-Tx9
B. Stimuli used in the experiment: Showergels:
