Research Proposal: The Relationship between Customer Service and Profitability of XBXB Hot Pot

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Part 1: Research Proposal

Executive Summary

This research study proposal focuses on Xiabuxiabu HotPot’s (shortened as XBXB), a Chinese hot pot restaurant brand, strategy to enter the U.S. market. It intends to provide a strategic direction for XBXB to establish a unique position in the highly homogeneous and saturated hot pot industry to improve its competitiveness. The proposal defines XBXB’s current service model as the on-demand service model and referencing Haidilao’s service model, a hot pot restaurant brand known for its excellent service, to define the active service model. A research plan is proposed to XBXB to evaluate whether the mean profit of XBXB’s U.S. restaurants would increase by employing the active service model compared to employing the on-demand service model. A randomized controlled experiment is included in the plan to evaluate the research question. The 50 XBXB restaurants that are expected to be opened in the U.S. would be the sample of the experiment. Through random assignment, half of the restaurants would be assigned to the treatment group, which would employ the active service model; the other half of the restaurants would be assigned to the control group, which would employ the on-demand service model. After the employee training and recruitment costs are included, the total profit (EBIT) of each of the sampled restaurants in a 3-month operation period would be recorded as the dependent variable of the experiment. A two-sample, one-sided t-test would be applied to the mean profit of the two groups to examine the hypothesis of the study. The conclusion drawn from this study would be based on the p-value of the statistical test as well as the magnitude of the effect size observed. Lastly, two scenarios—no effect observed and an expected effect observed—of the proposed hypothesis were simulated to refine the research plan. The results of the simulations are included in the proposal.

Statement of the Problem

Xiabuxiabu HotPot (shortened as XBXB) is planning to expand into the U.S. market to increase profitability.

Of all the cuisines in mainland China, hot pot accounts for the largest Chinese food market share at 14.1% (Feng, 2019). Popularity also brings strong competition. According to the 2020 China Hotpot Category Special Report, the number of hot pot restaurants nationwide has exceeded 400,000 as of the first half of 2020 (Wisdom Research, 2020).

The hot pot category is highly homogeneous in the food items that the restaurants offer. Hot pot dishes are mostly animal products and fresh produce, such as beef, lamb, pork, animal organs, leafy vegetables, root vegetables, etc. Unlike other cuisines, the dishes are offered to the customers with minimal culinary processing because the customers would be cooking the dishes in a hot pot themselves while they dine. As a result, it leaves little room for hot pot restaurants to differentiate with food.

Unfortunately, American consumers rely heavily on the quality of food and service provided to evaluate Chinese restaurants (Liu & Jang, 2009; Ma et al., 2011). Since XBXB is unable to change the industry’s fate of product homogeneity, customer service is the only way for XBXB to differentiate itself. However, American consumers prefer the high-quality, responsive, and reliable service provided by restaurants, which is contrary to XBXB’s current on-demand service model (Donthu & Yoo, 1998; Furrer et al., 2000; Hofstede, 1991, Lee et al., 2015). Changing the customer service model could be a key factor for XBXB succeed in the US market.

Therefore, XBXB’s managers should explore the possibility of improving its customer service by adopting the active service model in its U.S. restaurants. This service model took reference from Haidilao Hotpot’s service model. Haidilao Hotpot, a leading brand in the hot pot category, is known for its extraordinary customer service that attracts an enormous amount of customers every day, even if they need to wait for hours before sitting in and enjoying the hot pot. Adopting the active service model in XBXB’s U.S. restaurants is likely to increase its customer satisfaction, thus leading to improvement in revenue (Sun & Kim, 2013).

However, it is unsure if adopting the active service model in XBXB’s U.S. restaurants will lead to higher profits than its current on-demand service model because of the higher costs involved (Haidilao International Holding Ltd, 2021). Therefore, this study should be conducted to understand the relationship between the two customer service models, active and on-demand, and XBXB’s profitability in the U.S. market.

The two service models are defined as follow:

• On-demand service model: Typical service only involves simple services such as offering menu, water, and food, or confirming the order and proceeding check. Additional services are provided upon customers’ request. It is the service model that XBXB’s restaurants are currently employing.
  
• Active service model: A comprehensive service is provided starting from the entrance to the restaurant. A server will be responsible for the whole service experience of a customer. However, this option is significantly more costly as it requires more employee training and more staffed employee (Haidilao International Holding Ltd, 2021).

Research Question and Hypotheses

Research Question

Relative to the on-demand service model, will the mean profit (EBIT) increase by employing the active service model in XBXB’s U.S. restaurants?

Hypotheses

H₀: The mean profit (EBIT) of the restaurants employing the active service model will not exceed the mean profit of the restaurants employing the on-demand service model. \[H_0: P_{Active} -P_{On-demand} \le 0\] H_A: The mean profit (EBIT) of the restaurants employing the active service model will exceed the mean profit of the restaurants employing the on-demand service model. \[H_A: P_{Active} -P_{On-demand} \gt 0\]

Importantce of the Study

The results of this study would be beneficial to XBXB, considering the increasing concern of service quality in Western countries and among the younger generations. The findings of this study could reveal the value and importance of service in the restaurant industry and provide a strategic direction for XBXB to improve its competitiveness by establishing a unique position in the highly homogeneous and saturated hot pot industry. Additionally, the findings could potentially suggest a viable path for XBXB to expand to the U.S. market successfully.

The risk associated with implementing this study is minimal. XBXB is already familiar with the customer’s reaction to its current on-demand service. On the other hand, implementing the active service model, for its higher service quality, would only potentially increase the customers’ satisfaction and XBXB brand image with minimal potential adverse effects on both.

In addition, this study should be conducted because there is no previous research studying the effect of on-demand service and active service on a restaurant’s profit that could be referenced to. While there are costs associated with implementing this study, the potential short-term and long-term benefits resulting from this study would outweigh its costs.

Literature Review

XBXB Hot Pot Background

XBXB is the flagship chain restaurant brand of the listed company XBXB Catering Management (China) Holdings Co., Ltd., which was established in 1998. The business model of XBXB is simple, standard, and expandable. Different from traditional hot pot, XBXB provides a one-person, one-pot dining mode. It adopts a U-shaped bar table layout (as shown in Figure 1), which brings higher seating density and space flexibility, and all its restaurants adopt standardized design and decoration (Chang, 2015). Because of these characteristics, XBXB is particularly welcomed among post-95 consumers. By the end of 2020, XBXB has opened more than 1,000 directly-operated restaurants in 22 provinces in China, serving more than 100 million customers, and has become one of China’s top ten hot pot brands. However, according to news reports, XBXB shut down nearly 200 of its restaurants due to the pandemic and market impact in 2021 (Chinanews, 2021). The parent company of XBXB indicated in the 2021 mid-year report that as consumers’ living standards improve, cost-effective food and beverage services can no longer meet their needs (Xiabu, 2021). Correspondingly, XBXB’s next year’s strategic plan is to reposition the brand by improving overall quality and customer satisfaction (Xiabu, 2021).
According to the 2021 semi-annual report of XBXB, the average cost per employee is 61601.4 RMB per year.

Figure 1: The layout of a XBXB restaurant

Haidilao International Background

Haidilao International Ltd., established in 1994 and publicly listed in 2018, has grown into a leading company in China’s domestic hot pot segment. Since its establishment, it has been continuously opening new restaurants. It expanded into the international market in 2012. Haidilao International operates over 1200 hot pot restaurants in China and 93 restaurants internationally (Decoding Markets, 2021).
As mentioned earlier, the key to Haidilao’s success comes from its service innovation. Each service process at Haidilao is defined in detail. It begins before the customers enter the restaurant (as shown in Figure 2), aiming to deliver the most delicate and personalized service by trying to satisfy as many needs of its customers as possible (Zhang & Xu 2016). Its service model is the reference of the active service model defined in this study. Haidilao’s innovative and systematic approach to customer service has established itself as the benchmark not only among hot pot restaurants but also across the restaurant industry. However, according to the 2021 semi-annual report of Haidilao, the average cost per employee is 101,942.3 RMB per year (Haidilao International Holding Ltd, 2021). It suggests that the active service model requires more training and additional expenses on employees.

On-demand Service Model

Traditional hotpot customer service can be interpreted as 6 steps: greeting, waiting, seating, ordering, eating, and checking. Additional service is not provided unless it is requested by the customer (Dahmer & Kahl, 2009).

Active Service Model

The active service model is constructed by referencing Haidilao’s service model. It can be interpreted as a 9-step process, from customers arriving at the restaurant till they leave. When customers are dining, servers would constantly provide basic services such as offering drinks and snacks, confirming orders, delivering food and plates. Also, providing additional services that are not typically provided by restaurants, such as shoe polish, nail salons, and other recreational facilities. The active service model, like the one of Haidilao, is proven to be successful as 40% of customers revisit Haidilao multiple times because of its extraordinary service (Zhang & Xu 2016).

Figure 2: The Process of Active Service

American consumers’ expectations on service quality and style from restaurants

American consumers expect high-quality, responsive, and reliable service—coinciding with the active service model defined in this proposal (Donthu & Yoo, 1998; Furrer et al., 2000; Hofstede, 1991, Lee et al., 2015). Their satisfaction level increases with the number of times servers initiate service on them. Conversely, their satisfaction level decreases with the number of times they have to request service from servers (Lee et al., 2015).

The importance of service quality in Chinese restaurants in the U.S.

Service quality is one of the most crucial attributes that customer satisfaction depends on (Kim et al., 2009; Ryu & Han, 2009). Especially for Chinese restaurants in the U.S. As American consumers have become more familiar with Chinese food, Chinese food has become less of an exotic taste for them (George, 2001; NRA, 2000). As a result, with less of an effect of the exotic factor from Chinese restaurants, American consumers rely heavily on the food quality and service quality provided to evaluate Chinese restaurants (Liu & Jang, 2009; Ma et al., 2011).

Customer satisfaction improves profitability

The level of customer satisfaction is positively correlated with businesses’ profitability (Sun & Kim, 2013). Customer loyalty is formed when they reach a high level of satisfaction with a business (Bowen & Chen, 2001). Once customers become loyal, they would repeat patronage, become less inclined to promotional offers, and share positive word-of-mouth of the businesses that they are loyal to. As a result, businesses with loyal customers can improve profitability by increasing their revenues and reducing their marketing expenses.

Research Plan

A randomized controlled experiment would be conducted to evaluate the relationship between the two customer service models, active and on-demand, and XBXB’s profitability in the U.S. market.

Population of Interest

XBXB is expected to open 50 restaurants in the United States within 5 years. The population of interest of this study is all the 50 restaurants that are expected to be opened. Since XBXB’s expansion plan in the U.S. has yet to be implemented at the time this proposal is drafted. Ideally, XBXB will consider the top 50 U.S. cities in terms of their GDP in 2020, disposable income per capita, and consumption level of the catering industry as the location of their restaurants. One restaurant in each city. Such layout lowers the density of restaurants, reducing the possibility that the same customer may go to different restaurants and experience different service styles. If the actual situation is different from what is assumed here, adjust this section as appropriate.

Sample Selection

From the 50 restaurants, 25 restaurants would be randomly assigned to employ the active service model and 25 restaurants would be randomly assigned to employ the on-demand service model. A simple random sampling method is chosen to balance the individual differences between restaurants so that the cities where the restaurants in the two samples are located would be similar in terms of the key indicators: average GDP, average per capita disposable income, and average catering consumption level. In addition, such a sampling method could also balance the potential confounding factors such as the number of customers that visit each restaurant, and the number of employees in each restaurant in a random manner.

Sample Size

Restrained by the number of restaurants that are expected to be opened in the U.S. Selecting a sample size of 50 restaurants out of all the 50 restaurants that are expected to be opened in the U.S. is intended to recruit the largest sample possible to improve the accuracy of the study’s results within the range of affordable costs. Sampling from 50 restaurants and applying treatment to 25 of them are feasible in operation and affordable in terms of cost for XBXB.

An alternative method to decide the sample size is to calculate the exact size needed by assuming the statistical power and using required parameters such as standard deviation. This method is not applicable here because XBXB has not yet expanded to the U.S., and such required parameters are currently not available. Therefore, a sample size of 50 out of 50 can best support XBXB to obtain the most accurate research results within an acceptable cost range in terms of the current situation.

Operational Procedures

Before this Research Proposal is Executed

Approval from the IRB has to be granted to this study since it involves human subjects under the definition of the Code of Federal Regulations (CFR, 2018). An approval from the IRB with the exemption from classifying this study as human-subjects research would be filed to reduce the complication in conducting this study since this study could satisfy the exemption criteria (CFR, n.d.). As this study is short in duration, harmless, painless, not physically invasive, not likely to have significant adverse lasting effects on the participants, it can be identified as benign behavioral interventions.

If this study is approved by the IRB with the exemption from classifying this study as human-subjects research, then this study could proceed as described in this proposal. If this study is not approved by the IRB with the exemption from classifying this study as human-subjects research, then modifications would have to be made to this study to satisfy the exemption and file for approval from the IRB again. If the IRB has indicated that an exemption from classifying this study as human-subjects research would not be possible for its nature, then this study could only be conducted by following the human subjects research regulations.

If this study is approved by the IRB with the exemption from classifying this study as human-subjects research, then this study could proceed as described in this proposal. If this study is not approved by the IRB with the exemption from classifying this study as human-subjects research, then modifications would have to be made to this study to satisfy the exemption and file for approval from the IRB again. If the IRB has indicated that an exemption from classifying this study as human-subjects research would not be possible for its nature, then this study could only be conducted by following the human subjects research regulations.

If this is the case, XBXB should re-evaluate if this study should be conducted because conducting this study under the human-subjects research regulations would introduce many complications. All of the restaurants’ managers and employees would have to undergo human-subjects protection training for their contacts with the human subjects, who are the customers. This would increase the costs and the time to complete this study. Also, formal consents have to be granted by the customers for their participation in the study. This would indicate that the restaurants’ managers, employees, and customers would be aware of their participation in this study. However, their awareness of their participation in this study would not be ideal because it could cause them to diverge from the normal behaviors which could introduce uncertainties to this study.

Corporate-level Coordination

Before conducting this study, XBXB should coordinate with its HR and finance & accounting departments to ensure smooth and proper execution of this study.

XBXB should coordinate with its HR department to develop a set of recruiting criteria for the service-employee candidates of the restaurants that employ the active service model to ensure that the hired candidates have the competence to deliver service according to the active service model. Also, it should coordinate with its HR department to develop a service-employee training protocol for the active service model. The training protocol should adequately prepare the employees to deliver service according to the active service model.

XBXB should coordinate with its finance & accounting department to provide the required profit data of the 50 sampled restaurants during the operation period to the research team.

Operational-level Coordination

XBXB should instruct the managers of the restaurants that employ the on-demand service model to evaluate the qualification of the candidates based on XBXB’s current candidate evaluation criteria. It should instruct the managers of the restaurants that employ the active service model to evaluate the qualification of the candidates based on the evaluation criteria developed for the active service model.

XBXB should instruct the manager of each of the participating restaurants to recruit an adequate number of employees according to the service model assigned to maintain a regular operation. XBXB should advise the managers of the restaurants that employ the active service model that additional employees could be required as they would have to deliver a more personalized service to each customer; more time would be spent in serving each customer.

The training of the employees at the restaurants that employ the on-demand service model should follow XBXB’s current employee training protocol. For the training of the employees at the restaurants that employ the active service model, it should follow the training protocol developed for the active service model. XBXB should advise the managers of the restaurants that employ the active service model that more time could be required to adequately train the employees since they would have to complete more tasks when delivering service under this model; more time would be spent in learning each task.

When the restaurants are in operation, XBXB should instruct all the managers to closely monitor if the employees at the restaurant are delivering service according to the service model assigned. They should also be instructed to take corrective actions when conducts of non-compliance to the service model assigned are observed from the employees. The importance of the employees’ close compliance to the service model assigned would be discussed in the limitations and uncertainties section in detail.

XBXB should avoid notifying the operational-level managers and employees about their participation in this study because their awareness of their participation in this study could cause them to deviate from their normal behaviors. If they perceive that the result of the study could have an adverse effect on their employment, they could behave in a way to favor their self-interest instead of adhering to instructions given to conduct the study.

Other unspecified operational and administrative processes at the restaurants should follow XBXB’s current procedures.

Operation Period

During the operation period, the restaurants employing different service models would be in operation and the variables required for this study would be recorded. The operation period could begin as XBXB prefers as long as all the participating restaurants are ready for a regular operation at the time. The start time and the end time of the operation period should be consistent across all the participating restaurants to ensure that time period-sensitive situational factors would not confound the results of the study. The operation period is intended to elapse for 3 months so it could capture the potential effects of customers loyalty and customer repeat patronage on profit from the higher service quality of the active service model (Sun & Kim, 2013; Bowen & Chen, 2001). The intended 3 months duration of the operation period could be adjusted as XBXB deems appropriate.

Brief Schedule

Time Period	Schedule
2 weeks	File for approval from the Institutional Review Boards
1 month	Coordinate with the corporate HR, Finance and Accounting departments to prepare for the study
1 month	Recruit and train employees
3 months	Operation period
1 month	Analyze the outcomes and report the results

Approximate total time to execute the proposal: 6 months

Data Collection

XBXB’s finance & accounting department would provide the total profit data (EBIT) of each of the sampled restaurants in the 3 months of the operation period. Before the data is provided, XBXB’s finance & accounting department would subtract the employee training and recruitment costs of each restaurant incurred before the 3-month operation period from the total profit that each restaurant generated during the 3-month operation period.

Data Security

Necessary measures would be implemented to ensure all the information collected for this study is kept securely. The collected information would be stored in an external hard drive that would require a passcode to access. When the hard drive is not being used, it would be kept in a secured lockbox. The hard drive would only be accessed in the same room where the lockbox is located. The hard drive would not be brought to another location. The information stored in the hard drive would not be stored on the devices being used to read and analyze the information. The devices being used to read and analyze the information would have adequate protection against computer viruses. Only the responsible researchers of this study would have the passcodes to access the devices being used to read and analyze the information, the hard drive, and the lockbox of the hard drive. After the study is completed, the information used for the study would be eliminated after 3 weeks of its completion.

Outcomes (Dependent Variables)

This study examines the mean profit of the 50 sampled restaurants that are employing different service models to conclude whether the active service model can increase the profit of XBXB’s restaurants in the U.S. After the employee training and recruitment costs of each of the sampled restaurants incurred before the 3-month operation period are included, the total profit (EBIT) of each of the sampled restaurants in the 3 months of the operation period would be the dependent variable of the study. The profit of each of the sampled restaurants would be in the currency of the US dollar.

The total profit of each of the sampled restaurants is selected as the dependent variable to measure the effect of the two service models because it captures the revenues and the costs generated by employing each of the service models. Employing the active service model is likely to generate higher revenue from improved customer satisfaction than the on-demand service model (Sun & Kim, 2013; Bowen & Chen, 2001). However, employing the active service model is also likely to generate higher costs than the on-demand service model (Haidilao International Holding Ltd, 2021; Xiabu, 2021). Therefore, examining the mean profit of each of the sampled restaurants could determine whether the additional revenues generated by employing the active service model would outweigh the additional costs.

Treatments (Independent Variables)

Since this study is intended to examine the on-demand and the active service models’ influence on the profitability of XBXB, the two service models would be independent variables of this study. After receiving the profit data of each of the 50 sampled restaurants from the finance & accounting department of XBXB, the independent variable, the on-demand or the active service model, would be coded to the corresponding restaurant in the profit data to indicate the service model that each of the restaurants had employed during the experiment.

Other Variables

Apart from the dependent and independent variables specified, other variables are not necessary to measure to examine the research question of this study.

Statistical Analysis Plan

After all the required data is gathered, a two-sample, one-sided t-test would be applied to the outcomes to evaluate the alternative hypothesis that employing the active service model would bring a significant increase in profits to XBXB’s restaurants. To evaluate this alternative hypothesis, it is assumed that employing the active service model would bring significant improvements in profitability. When applying the t-test on the outcomes, the estimated effect, and the p-value of the statistical test would be evaluated to understand the significance and the meaningfulness of the results. Also, the statistical power of the t-test would be evaluated to determine the probability of drawing a correct conclusion. If the t-test results in a p-value larger than 0.05, it could be concluded that the observed difference between the mean profit of the two groups are not significant, and such insignificant difference can be frequently observed in similar experiments. Therefore, the null hypothesis of the study would be rejected. Under this circumstance, XBXB should not employ the active service model in its restaurants in the U.S.

On the other hand, if the t-test results in a p-value lower than 0.05, it could be concluded that the difference in the mean profits of the two groups is significant. However, despite the result of the t-test indicating significance, the magnitude of the difference in the mean profits of the two groups would also be considered. According to XBXB’s expansion plan to the U.S., it is expected to have at least a 5% increase in profits among its U.S. restaurants (Xiabu, 2021). Thus, if the estimated effect is less than the expected increase of $7,914, namely the earnings before interest and tax (EBIT), such improvement would not be considered meaningful to XBXB. Therefore, the implementation of the active service model would not be suggested. Otherwise, employing the active service model in XBXB’s U.S. restaurants would be regarded as an actionable and profitable strategy for XBXB if the estimated effect is greater than $7,914.

Limitations and Uncertainties

One of the limitations of the study arises from the potential that the customers could visit XBXB restaurants that are employing different service models. Their overlapping experience could cause the study to measure the outcomes that are not intended to measure. The customers’ ​​prior experience with a XBXB restaurant that employs one service model could affect their subsequent experience with another XBXB restaurant that employs another service model. The ideal scenario for this experiment would be that every customer only experiences one single service model, otherwise the customers would notice the difference in the service model employed and behave differently. However, it is impossible to eliminate this limitation because XBXB has no control over the customers who would visit the restaurants. Nevertheless, the potential confounding caused by this limitation is mitigated through the random assignment of the control and the treatment group of the experiment.

Another limitation of the study arises from its intent-to-treat assumption. It is assumed that the service that the customers experience is the service defined in the on-demand and active service models. However, the service that the customers experience depends on the service delivered by the service employees at the restaurants. If the service delivered by the employees greatly deviates from the service model defined, it could cause the study to measure the outcomes that are not intended to measure. To mitigate this limitation, it is critical that the manager of each restaurant closely monitors if the employees are delivering service according to the service model assigned.

Also, the dependent variable of the study, the profit of each of the sampled restaurants, depends on the revenue contributed by the customers. However, there are varying factors unrelated to the service provided among each of the sampled restaurants that could affect the customers’ contribution to the restaurants’ revenue. For example, even though the dishes provided at each of the sampled restaurants are standardized, the quality of the food ingredients could vary from restaurants due to geographical factors.

Additionally, accounting mistakes and data collection mistakes could be caused by human errors. XBXB should be aware of the uncertainties caused by these mistakes and ensure that the manager of each of the sampled restaurants and the finance & accounting department are reporting the required data accurately.

Lastly, the restaurant’s managers’ and the employees’ awareness of their participation in the study could also affect the results of the study. Their awareness could cause them to deviate from their normal behaviors. If they perceive that the result of the study could have an adverse effect on their employment, they could behave in a way to favor their self-interest instead of adhering to instructions given to conduct the study. Therefore, to mitigate the effect of this uncertainty, XBXB should avoid notifying the operational-level managers and employees about their participation in this study.

Even though all the limitations and uncertainties mentioned above may not be eliminated completely, necessary measures are implemented in this study to effectively mitigate the factors that could potentially impact the results. The chance of having results that diverge vastly from the actual phenomenon due to the limitations and uncertainties is rare. The results of the study are expected to be a close representation of the reality, therefore, can be interpreted accordingly.

Part 2: Simulation of Effects

Introduction and Assumptions

The research proposal in the previous section provides a detailed plan to conduct the study. In this section, two scenarios of the proposed experiment are simulated to refine the research plan. In scenario 1, the treatment of different service models would have no significant effect on the average profit of the sampled restaurants. In scenario 2, an expected significant effect is observed.

• Scenario 1: No effect observed

• Scenario 2: An expected effect observed

Function of Experiment Analysis

Define function to conduct the simulations

# set up
n <- 50

# function for analyze experiment
analyze.experiment <- function(data) {
    require(data.table)
    setDT(data)
    the.test <- t.test(x = data[service == "on-demand", profit], 
                       y = data[service == "active", profit], 
                       alternative = "less")
    the.effect <- the.test$estimate[1] - the.test$estimate[2]
    upper.bound <- the.test$conf.int[2]
    p <- the.test$p.value
    result <- data.table(effect = the.effect, upper_ci = upper.bound, p = p)
    return(result)
}

Assumption

Assumptions about the mean profit (EBIT) of two groups, the expected effect size of two scenarios, and the standard deviation for two scenarios were set.

Basic Assumption

mean_profit_1 = 158277 # mean profit of the on-demand service group
mean_profit_2 = round(mean_profit_1 * 1.05) # mean profit of the active service group
mean_diff_1 = 100 # difference of mean profit in scenario 1
mean_diff_2 = mean_profit_2 - mean_profit_1 # difference of mean profit in scenario 2

Standard Deviation for Scenario 1

# find the standard deviation for scenario 1
sd_loop <- data.frame(number = seq(1, 10), 
                      sd = c(100, 500, 800, 1500, 3000, 5000, 8500, 9000, 11000, 15000))
power_tbl_1 <- data.table(number = seq(1,10))
for (i in sd_loop$number) {
  power <- pwr.t2n.test(n1 = 25, n2 = 25, d = mean_diff_1/sd_loop[i, 2], sig.level = 0.05, 
                        alternative = "greater")
  power_tbl_1[i, "power"] <- round(power[[5]], 4)
}
power1 <- as.numeric(power_tbl_1[number == 7, 2])
sd1 <- as.numeric(sd_loop %>% filter(number == 7) %>% select(sd))
datatable(power_tbl_1, rownames = F)

Standard Deviation for Scenario 2

# find the standard deviation for scenario 2
sd_loop_2 <- data.frame(number = seq(1, 10), 
                      sd = c(100, 500, 800, 1500, 3000, 5000, 8500, 9000, 11000, 15000))
power_tbl_2 <- data.table(number = seq(1,10))
for (i in sd_loop_2$number) {
  power <- pwr.t2n.test(n1 = 25, n2 = 25, d = mean_diff_2/sd_loop_2[i, 2], sig.level = 0.05, 
                        alternative = "greater")
  power_tbl_2[i, "power"] <- round(power[[5]], 4)
}
power2 <- as.numeric(power_tbl_2[number == 7, 2])
sd2 <- as.numeric(sd_loop_2 %>% filter(number == 7) %>% select(sd))
datatable(power_tbl_2, rownames = F)

To conduct the simulation, a sample size of 50 and make assumptions about the sample mean, effect size, statistical power and standard deviation are required. Referring to the 2021 financial report of XBXB (XBXB, 2021), the average restaurant profit before interest and tax at the end of 2020, which is $158,277, is determined as the mean profit of the control groups in both scenarios. For scenario 1, since no effect is expected, an increase of $100, which is considered not meaningful, is set for the treatment group. For scenario 2, For scenario 2, an increase of 5% in mean profit from the control group is considered meaningful. Therefore, an increase of $7914 in mean profit for the treatment group is set. Correspondingly, an effect size of 5% is assumed as it is considered meaningful. A statistical power of 90% is set for scenario 2, which is usually recognized as powerful enough. For scenario 1, as it is expected to observe no-effect, the simulation needs to control the power to be lower than 1 - power which is 10%. To find the appropriate standard deviation to achieve the expected power, the loop function below was used to experiment with standard deviation ranging from 100 to 15,000 for both scenarios. When the standard deviation is set to be 8500, scenario 1 has a power of 0.0544 and scenario 2 has a power of 0.9452, which they satisfy the expected 90% statistical power. Therefore, a standard deviation of 8500 is set for the simulation in both scenarios.

Research Question

Relative to the on-demand service model, will the mean profit (EBIT) increase by employing the active service model in XBXB’s U.S. restaurants?

Scenario 1: No Effect

Single Experiment

Simulation

set.seed(seed = 437)
RNGversion(vstr = 3.6)
# randomly create data
xbxb_1 <- data.table(service = c(rep.int(x = "on-demand", times = n/2), rep.int(x = "active", times = n/2)))
# set up profit
xbxb_1[service == "on-demand", profit := round(x = rnorm(n = .N, mean = mean_profit_1, sd = sd1), digits = 1)]
xbxb_1[service == "active", profit := round(x = rnorm(n = .N, mean = (mean_profit_1 + mean_diff_1), sd = 8500), digits = 1)]
datatable(data = xbxb_1)

Analysis

# Analyze the outcomes
single_exp_1 <- analyze.experiment(xbxb_1); single_exp_1

     effect upper_ci         p
1: -710.828 3537.537 0.3898708

pval1 <- round(single_exp_1$p, 2)

In this scenario, since the p-value is 0.39, we fail to reject the null hypothesis at a 95% confidence level. A result like this would suggest that the active service model would not generate a meaningful increase in mean profit than XBXB’s current on-demand service model. If the study observes a result same as the one in this simulated scenario, XBXB should remain in its current on-demand service model.

Repeated Experiments

Simulation

# set up
B <- 1000
set.seed(seed = 437)
RNGversion(vstr = 3.6)
experiment <- 1:B
# conduct many experiments
service <- c(rep.int(x = "on-demand", times = n/2), rep.int(x = "active", times = n/2))
xbxb_1_rep <- as.data.table(expand.grid(experiment = experiment, service = service))
setorderv(x = xbxb_1_rep, cols = c("experiment", "service"), order = c(1,1))
xbxb_1_rep[service == "on-demand", profit := round(x = rnorm(n = .N, mean = mean_profit_1, sd = sd1), digits = 1)]
xbxb_1_rep[service == "active", profit := round(x = rnorm(n = .N, mean = (mean_profit_1 + mean_diff_1), sd = sd1), digits = 1)]
dim(xbxb_1_rep)

[1] 50000     3

Analysis

# Analyze
results_1_rep <- xbxb_1_rep[, analyze.experiment(data = .SD), keyby = "experiment"]
datatable(data = round(x = results_1_rep[1:100, ], digits = 3), rownames = F)

# mean power
mean_power_1 <- results_1_rep[, mean(p < 0.05)]
# percentage of false positives
FP <- mean_power_1 * 100
# percentage of true negatives
TN <- (1 - mean_power_1) * 100
# range of observed effects
results_1_rep[, summary(effect)]

    Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
-8284.23 -1530.86   159.12    32.15  1590.76  8799.97 

mean_effect_1 <- round(results_1_rep[, mean(effect)], 2)
#range of the upper bound of the 95% confidence interval
results_1_rep[, summary(upper_ci)]

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  -4323    2479    4172    4056    5609   13342 

mean_upper_ci_1 <- round(results_1_rep[, mean(upper_ci)], 2)

In scenario 1, the treatment group has a small increase in mean profit of $32.15 compared to the control group. However, according to the 95% confidence intervals (CI), the increase in mean profit has to reach at least $4056.38 to have statistical significance. This indicates that, on average, in the 1000 repeated experiments of scenario 1 the null hypothesis would not be rejected, so it would suggest that there is no significant difference in mean profit between on-demand and active service models. At a 95% confidence level, the true negative rate for this 1000 repeated experiments is 95.4%. It indicates that this study design has a 95.4% chance of failing to reject the null hypothesis when the actual increase in mean profit is $32.15 or less, which would draw a correct conclusion.

Scenario 2: An Expected Effect

Single Experiment

Simulation

set.seed(seed = 437)
RNGversion(vstr = 3.6)
# randomly create data
xbxb_2 <- data.table(service = c(rep.int(x = "on-demand", times = n/2), rep.int(x = "active", times = n/2)))
# set up profit
xbxb_2[service == "on-demand", profit := round(x = rnorm(n = .N, mean = mean_profit_1, sd = sd2), digits = 1)]
xbxb_2[service == "active", profit := round(x = rnorm(n = .N, mean = mean_profit_2, sd = sd2), digits = 1)]
datatable(data = xbxb_2)

Analysis

# Analyze the outcomes
single_exp_2 <- analyze.experiment(xbxb_2); single_exp_2

      effect  upper_ci            p
1: -8524.828 -4276.463 0.0008019535

pval2 <- round(single_exp_2$p, 2)

In Scenario 2, the active service model is expected to have a meaningful increase in mean profit compared to the control group. Since it has determined that 5% increase in mean profit is meaningful to XBXB, the mean profit from the treatment group is set to be 5% higher than the one of the control group. In a single experiment, the p-value is 0, it provides statistically significant evidence to reject the null hypothesis at a 95% confidence level. To understand the statistical power of the study design in the scenario, this then repeated for 1000 times.

Repeated Experiments

Simulation

# conduct many experiments
set.seed(seed = 437)
RNGversion(vstr = 3.6)
service <- c(rep.int(x = "on-demand", times = n/2), rep.int(x = "active", times = n/2))
xbxb_2_rep <- as.data.table(expand.grid(experiment = experiment, service = service))
setorderv(x = xbxb_2_rep, cols = c("experiment", "service"), order = c(1,1))
xbxb_2_rep[service == "on-demand", profit := round(x = rnorm(n = .N, mean = mean_profit_1, sd = sd2), digits = 1)]
xbxb_2_rep[service == "active", profit := round(x = rnorm(n = .N, mean = mean_profit_2, sd = sd2), digits = 1)]
dim(xbxb_2_rep)

[1] 50000     3

Analysis

results_2_rep <- xbxb_2_rep[, analyze.experiment(data = .SD), keyby = "experiment"]
datatable(data = round(x = results_2_rep[1:100, ], digits = 3), rownames = F)

# mean power
mean_power_2 <- results_2_rep[, mean(p < 0.05)]; mean_power_2

[1] 0.947

# percentage of true positives
TP <- mean_power_2 * 100
# percentage of false negatives
FN <- (1 - mean_power_2) * 100
# range of observed effects
results_2_rep[, summary(-effect)]

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   -986    6223    7655    7782    9345   16098 

mean_effect_2 <- round(results_2_rep[, mean(-effect)], 2)
#range of the upper bound of the 95% confidence interval
results_2_rep[, summary(-upper_ci)]

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  -5528    2205    3642    3758    5335   12137 

mean_upper_ci_2 <- round(results_2_rep[, mean(-upper_ci)], 2)

In Scenario 2, the treatment group generates $7781.85 more than the control group in mean profit, which is far greater than the 95% confidence interval of the mean effect (3757.62). At a 95% confidence level, it provides statistically significant evidence to reject the null hypothesis to suggest that XBXB would generate higher mean profit per restaurant when employing the active service model compared to its current on-demand service model.

If the actual active service model generates at least 5% higher in mean profit than the on demand service model, this study design would have a 94.7% chance to reject the null hypothesis, which would draw a correct conclusion. On the other hand, under the same effect size, this study design would have a 5.3% chance of failing to reject the null hypothesis, which would draw an incorrect correct conclusion.

With about 95% chance of drawing a correct conclusion and about 5% chance of drawing an incorrect conclusion, this study design should give XBXB’s decision makers reasonable confidence to rely on the study’s result to make decision on the restaurant’s service model.

Results

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