library(data.table)
library(DT)
library(purrr)Since COVID-19’s patient zero was identified in the United States in February 2020, the disease has spread at a rapid rate worldwide, resulting in a global pandemic. This has had a colossal influence on almost every industry resulting in numerous unprecedented pressures requiring rapid and everchanging response, and the fashion industry is no exception. The apparel industry is known as one of the world’s most prominent fiscal heavyweights with a current value of 1.5 trillion U.S. dollars and a projected growth of 2.25 trillion dollars by 2025. (Statista, 2021) Even though current clothing sales trends have dropped by 34%, major retailers such as Gap and H&M, have made an effort to maintain a revenue stream through quick reaction to current trends following a lifestyle shift across the world. With approximately 51% of the United States working population working from home, these retails have seen a white space opportunity in casual clothing which has had an increase of 70% in sales. (BBC, 2020) Our research team believes that Macy’s Inc. needs to react quickly to changing trends and capitalize on the opportunity of casualwear with a product line offering more relaxed and informal pieces of clothing or footwear, which for men includes: casual fitting jeans, t-shirts, sweaters, short sleeve or open front button-down shirts and tennis sneakers.
Furthermore, with the aforementioned shift to casual wear, occurred a shift of accepted clothing in the workplace. Investment bankers have largely indulged in expensive suits to project authority and influence on Wall Street. Recently, a rather surprising shift occurred when workers at a large multinational investment bank were encouraged to embrace more flexible and casual attire. As a result of this increased trend, we would like to propose a research study to explore the shifts in perception of appropriate workplace attire. Through those insights, the company can decide whether to invest in a new line of casual clothing. The study objective will be based on two research questions interpreting whether there is a difference in desirability to wear casual clothing between employees who work on-site and employees who work remotely as well as, determining whether there is a difference in acceptability of wearing casual clothing between employees who work on-site and employees who work remotely. The population of interest will be males between ages 25 and 35 who are investment banking professionals at an associate level.
For the past few decades, a clear status quo existed for acceptable clothing in the workplace. For investment bankers, “expensive suits have projected power on Wall Street, almost like a piece of “armor,” said Susan Scafidi, academic director of the Fashion Law Institute at Fordham University.” (The Washington Post) However, in early 2019, a rather surprising shift occurred when Goldman Sachs, an “American multinational investment bank and financial services company headquartered in New York City” (Goldman Sachs), released a company memo encouraging their employees to embrace more flexible and casual attire. For this leading financial service company, the shift from business formal clothing to a more casual dress code was to address a shift in the work environment to be more “people” focused rather than management and business focused.
The shift from business formal to an increasingly casual and flexible dress code has been further cemented by the current working conditions in the United States. During the peak of the SARS-CoV-19 pandemic, 51% of the United States working population was working from home (Gallup News). Furthermore, in a survey by Gallup News, two-thirds of newly remote workers stated that they would like to continue working from home. As a result of this increase in remote work, Macy’s Inc., a clothing retailer, would like to perform a research study to explore whether there has been a shift in the perception of appropriate workplace attire. Macy’s can use insights gained from this research to decide whether or not to produce a new line of casual clothing catering to this newly flexible workplace environment.
Research Question 1: Is there a difference in desirability to wear casual clothing between employees who work on-site and employees who work remotely?
Null Hypothesis: Proportion of employees who desire to wear casual clothing on-site = proportion of employees who desire to wear casual clothing remotely
Alternative Hypothesis: Proportion of employees who desire to wear casual clothing on-site < proportion of employees who desire to wear casual clothing remotely
Research Question 2: Is there a difference in the perception of acceptability of wearing casual clothing between employees who work on-site and employees who work remotely?
Null Hypothesis: Proportion of employees who believe it is acceptable to wear casual clothing on-site = Proportion of employees who believe it is acceptable to wear casual clothing remotely
Alternative Hypothesis: Proportion of employees who believe it is acceptable to wear casual clothing on-site < Proportion of employees who believe it is acceptable to wear casual clothing remotely
The findings of this study will redound Macy’s Inc. to achieve an increase in sales and revenue. The data produced will show whether there is opportunity for the organization to maximize profitability in a niche market of casualwear. Based on the findings, the company can conclude if there should be an investment in a fashion line of casual clothing for men. This study will search as a white space analysis to fill a gap that customers are responding to in order to scale Macy’s revenue with this new brand launch. If we reject the Null Hypotheses that there is no correlation between desirability and acceptability of wearing casual clothing on-site and remotely, the company can confidently invest in a new production team and clothing line that will allot for successful sales.
Workplace dress codes allow for a professional standard that serves two purposes – providing employees with guidelines as to what is appropriate to wear and providing a common personal identity that enables sophistication and competent professionalism. There is evidence of pros and cons to both casual and more formal dress codes; an organization’s selection depends on the kind of culture they want to embrace and the type of workers they employ. In a study performed by Haefner, 41% of employers surveyed said that employees who dress more formally have a higher chance of being promoted. This figure jumps to 55% in financial services (Haefner, 2008). Research respondents have also been found to consider the hierarchical positions of both themselves and of those they were planning to interact with to decide on the formality of their work outfits (Rafaeli and Dutton 1997). Another study’s results showed that employees felt more productive and more trustworthy in formal attire than in casual attire, while they felt more friendly and more creative in casual attire than formal attire (Peluchette and Karl, 2007). In contrast, a study performed by Alonzo in 1996 found evidence of casual dress improving productivity as well as employee morale (Alonzo 1996). In a more casual environment, employees report that they feel more like an integral part of an organization (Yates & Jones, 1998) Furthermore, a 2020 study found that almost 80% of previous formal dressers have felt more productive working in casual wear versus professional attire (SHRM, 2020) rather than simply a small part of an organizational hierarchy.
Upon further research, some studies found a middle ground on the topic. According to a study performed in 2001, preferred work attire for men is slacks with long sleeved button up shirts or short sleeve collared knit shirts (Fisherpub, 2001). The hypothesis of this study conjectured that casual dress policies could be related to more positive attitudes in the workplace and sought to determine whether casual dress policies would positively or negatively impact measures of performance and perception. However, the results concluded that there was no significant relationship between preferences of dress code and job satisfaction, performance and perception (Fisherpub, 2001).
These conflicting findings and ever-changing trends make producing appropriate attire for the workplace an ongoing challenge for clothing retailers. In today’s work landscape, the adage of “dress for success” is being challenged due to COVID and the personal need for comfort (NCBI, 2014). As a result, workplace attire is quickly evolving under the new work from home norm. In our research study, we will expand on this investigation and study the effects of the shift of remote work on dress trends in the workplace. The goal of this study is to inform Macy’s on whether or not it should further invest in developing casual dress-wear products.
The inclusion criteria for our population of interest are: males, between the age of 25 and 35, that work as investment bankers, in an associate level role. This would exclude females and all individuals under 25 or over 35 years of age. Additionally, it would exclude individuals who do not work at an investment banking firm or that are below or above an associate level role within an investment banking firm.
Our sample population will be all males as their clothing selections are less ambiguous, as female clothing styles are much more variable with more extensive options than that of males. Furthermore, this population is old enough to have developed a work wardrobe. Additionally, this group has worked in the field long enough to understand any previously accepted standard of workplace attire, yet young enough to not have bias from the more previously accepted formal attire. Finally, we are choosing the profession of investment bankers, as this profession has traditionally been business formal but has recently started to adopt more casual policies. If we are able to see correlation within this relatively conservative profession, our results should be more widely generalized as any shift in this group towards casual attire would be a clear indication of a deviation from the norm. In order to populate our study with subjects, we will distribute a survey via LinkedIn. We will use LinkedIn to search at random for individuals that fit within our inclusion criteria. Individuals will be recruited and the study will be conducted until our sample size and groups reach their defined size. To incentivize our recruits to participate in the study, we will offer a $10 gift card.
From our population of interest, we will be selecting a sample of 200 participants, which will be split into two groups, those who work from home and those who are working on site. The groups will be split equaling in half, with 100 in each group. These proportions between groups reflect the current state of the United State workforce, where approximately 50% of the workforce is currently working remote. Thus, the groups in the study will be an accurate representation of the total population which allows for the results of our study to be generalized. With an established sample size of 200 we are striving for statistical significance in any observed differences in the proportions measured. Based on the following power test, a sample of 200 people with groups of 100, and a significance level of 0.05, our probability of rejecting the null hypothesis when it is false is 94%:
pwr.t.test(n = 100, d = 0.5, sig.level = 0.05, type = c(“two.sample”))
Based on this power test, a population of 200 subjects for the study will have statistically significant results that can be generalized to a larger population.
All of the participants will be approached via LinkedIn InMail messages. InMail messages are private messages that permit you to contact anybody on LinkedIn without a connection. An InMail can be sent straightforwardly by using the LinkedIn Recruiter candidate search feature. The first initial message would be a brief description of the study and an ask to complete a short survey with a reward of a gift card if they fit the following criteria: identify as male, 22-35 years of age, and work at a financial company as an associate. An associate or another related title can be defined as executing an assortment of bookkeeping and monetary obligations for their company. Planning spending arrangements, program accounts, and projections. Designing monetary propositions, examine operational and capital spending plans. At the bottom of the message they will provide an email and click either “Yes, interested” or “No thanks”.
After we receive their response someone will double check their eligibility based on their LinkedIn profile and send a second message to their email within 48 hours with a thank you for willing to fill out the survey and a link to the survey. Before answering the questions participants will provide demographics such as gender, age, education attainment, company name, and duration at the company. Participants will be asked 2 questions regarding our 2 research questions and presented with yes or no options.
Once the survey is completed, a research team member will send the gift card electronically to the respondent via LinkedIn message. Every two weeks, we will assess the collection number; if our goal number is not reached, we will send another 200 batches until we meet our goal of 200 completed surveys. We estimate this process will take no longer than six weeks. Data analysis will take a week, and report writing will take approximately four weeks; altogether, the research team will complete the study in eleven weeks.
Participants will complete the survey on Google Forms. Using Google Forms, we can restrict who can edit the survey, complete the survey, and view the survey results based on email. This will restrict a non-authorized participant from completing the survey and uphold our experiment integrity. One person on the research team will be responsible for creating the survey, another person on the team will be responsible for ensuring all participants filled out the survey completely. Separation of duty is best to prevent fraud and errors. Also, Google Forms allow the creator to set a respondent’s requirement to answer all questions before submission. Results will be automatically exported to a spreadsheet in Google Sheets with all of the participants’ answers.
The goal of our study is to appraise the desirability and acceptability of wearing casual clothing to work, and to determine if these factors differ between on-site and remote employees. The outcomes we will be measuring are the proportion of employees that desire to wear casual clothing and the proportion of employees that believe casual clothing is acceptable in their work environment. To gather data on these outcomes, we will be administering surveys to a group of male investment bankers between the ages of 25 to 35. One of the survey questions will ask in yes or no format whether the subject desires to wear casual clothing to work. The outcome measured in our study will be the proportion of subjects that answer ‘Yes’. Another survey question will ask in yes or no format whether the subject believes that casual clothing is acceptable in their work environment. Similarly, the outcome measured will be the proportion of subjects that answer ‘Yes’ across the study population.
The treatment variable in our study is the employee’s work environment, as we are trying to appraise if there is a statistically significant difference in the outcomes between on-site and remote workers. As this is an observational study, the treatment is not so much administered, but measured in the population surveyed. On the survey, we will be asking whether the employee currently works on-site or remotely. This will yield two study groups for analysis. The hypothesis is that the COVID-19 pandemic has changed both the desire and acceptability of wearing casual clothing to work. Studying measured outcomes across the two different levels of the independent variable, the employee’s workplace, will allow us to determine if there is a difference amongst groups.
vars = c("Age", "Race", "Company", "Years of Experience", "Workplace Continuity")
desc = c("Employee age (years)",
"Employee race",
"Employee Company – This will be used to evaluate if there are distinct companies with corporate cultures that appear to affect employee desire and perceived acceptability of wearing casual clothes to work",
"Years working in investment banking – This will be used to appraise if there is a relationship between years of experience and the desire and perceived acceptability of wearing casual clothes to work",
"This variable is an indicator describing whether the employee thinks their work location will change within the next 12 months. Possible values: “Change”, “No Change”. Example: An employee is currently remote but believes they will move on-site within the next 12 months. The recorded value would be “Change” ")
vartable <- data.table(Variable = vars, Description = desc)
datatable(vartable, rownames = F)After gathering the necessary data via LinkedIn surveys, the research group will have to analyze the information and appraise the primary research questions of the study. The study population will be randomly selected from the total group of survey recipients as to contain 100 remote workers and 100 on-site workers. The dataset containing the 200 responses from the selected population can then be divided into two sub-datasets split across the level of the independent variable. The dependent variables in this study were the employees’ desire to wear casual clothes at work and the employees’ perceived acceptability of wearing casual clothes at work. The responses to the survey questions meant to measure these variables were recorded in binary outcomes of ‘Yes’ and ‘No’. Due to this surveying methodology, a proportion test can be used to appraise the differences in each dependent variable at different work locations.
To perform a proportion test, the research group can utilize the prop.test function within R. The group would perform a proportion test for each research question. First, they would begin with appraising the level of desirability. To do this, they would first look at the group that works on-site. Amongst this group, they would record the number of people that indicated ‘Yes’ for whether they would find wearing casual clothes desirable. This would serve as the numerator in the proportion. They would then perform the same measurement amongst the group that works remote. In R, they would then run the following test:
prop.test(x=c(x_remote, x_onsite), n=c(n_remote, n_onsite))
In this calculation, x_remote is the number of people that indicated ‘Yes’ for the desire to wear casual clothing while working remotely, and x_onsite is the same for those that work on-site. For this study, n_remote and n_onsite are equal as each group contains 100 study subjects.
The outcome of this proportion test will display the proportion of ‘Yes’ within each subgroup, as well as the p-value for the statistical test. At the beginning of the study, the research group should have selected a significance value at which point they would feel comfortable rejecting the null hypothesis. A typical significance value is generally around 0.05. If the proportions across the two study subgroups are different and the p-value of the statistical test is less than the selected significance value (likely 0.05), the research group can reject the null hypothesis that the proportions are equal and assert that there is a statistically significant difference amongst the two groups. In this case, this would mean that there is a true difference in the desire to wear casual clothing between on-site and remote employees.
As there are two research questions in this study, the research team would then repeat the proportion test analysis discussed above for the values recorded in the survey for acceptability. The steps they would follow would be the same. From this second analysis, the research group would learn if there is a statistically significant difference in employees’ perception of the acceptability of wearing casual clothes in the workplace between on-site and remote workers.
Additional analyses will also be performed to understand if the other recorded variables also influence the outcome variables. As the outcomes are binary, we will perform two logistic regression analyses to understand which factors are significant predictors of the desirability and acceptability of wearing casual clothes in your workplace. From this, we might learn that other factors are also important in dictating employee’s opinions on each of these items. Further, we will use the “Workplace continuity” variable to understand how long insights gained from this study might remain true for the marketplace. If many people believe they’ll be returning from remote work in the next 6 months, this is valuable for Macy’s to understand. This will also inform a timeline for a possible repetition of this study.
Our first uncertainty is whether or not we will be able to fulfill our sample population with subjects. Based on a study by Baruch and Holtom (2008) the average response rate for an out of organization individual survey is 52.7%, with a standard deviation of 20.4. This means we will need to distribute our survey to approximately 380 individuals in order to fill our sample over the course of our study. Another limitation of the study is that we are not able to assign the treatment of remote and in person working environments as this is dependent on the subject’s current job and situation. This means there could be other variables that we are not fully able to control for. Baseline variables that we cannot control for such as work culture or pre-COVID-19 dress code policies could affect a person’s perception of workplace attire acceptability in the current climate. If a subject previously had a business formal dress code and still works in person, their perception may be very different from a subject who had a very lax and casual dress code policy and now works remote. The two ends of the spectrum could cause bias. Demographic factors such as income, race, and other socioeconomic indicators could also introduce bias into the study. A subject that grew up under the poverty level may have different preconceived notions than that of a subject that was raised in an upper-class family. Even though we can control the sample population to be that of equality in their roles, industry, gender, and age, there are always going to be some preconceived notions that the subjects carry that will cause bias. A third limitation would be the subjectivity of the responses. The study is collecting data based on the opinions of the study and while the results may support our hypothesis, we would likely receive large variation from another sample of the same size and inclusive characteristics. Additionally, if we performed the study today, versus 6 months from now, we may also receive very different results. The current climate is very fast paced and fluid, which makes getting definite and conclusion results difficult. Furthermore, a major uncertainty that we face is whether or not the COVID-19 virus will continue to impact the way Americans are working or for how long the current climate will continue. While one could theorize, perform studies, and collect articles that support the concept that remote work will continue, and in the same amounts as it is currently, there is no way to know how the virus will continue to impact the modern workforce with absolute certainty.
We simulated the results of our research study to show the potential effects of working remotely on our two research questions: desirability and acceptability of casual clothing. There are two scenarios within each research question: no effect and expected effect. No effect is what our proportion test results would look like if the proportions of our study respondents who report casual clothing in the workplace as desirable and acceptable were equal between the group working remotely and the group working onsite. Expected effect is what our proportion test results could look like if the proportions of our study respondents who report casual clothing in the workplace as desirable and acceptable were significantly higher among the group working remotely than the group working onsite, as we predict would be the case due to our research. Because we predict the remote group’s proportion to be higher than the onsite group’s proportion in both cases, we conducted the simulations using one-tailed proportion tests and measured the lower bound of the confidence intervals. We used a standard confidence level of 95%, a sample size of 200 respondents split approximately equally between remote and onsite groups as planned for our survey distribution, and a repetition of 1000 experiments to control for variation across repeated trials.
Our estimated effect sizes are a 15% higher proportion of desirability and a 20% higher proportion of acceptability in the remote group than in the onsite group. We expect the proportion of respondents who desire to wear casual clothes to be higher than the proportion who consider it acceptable across both groups, since studies show that the majority of employees would prefer for their workplace dress codes to be more relaxed or casual than they are currently as opposed to more formal. We expect that the acceptability and desirability across both groups to be at least 50% according to recent employee surveys and press releases regarding dress codes from prominent investment banks such as Goldman Sachs. We expect the difference between the proportions of the two groups to be greater for acceptability than desirability, because some employees may desire to wear casual clothing but still not feel that it is acceptable in an onsite office environment. The assumptions of proportions are as follows: -Desirability, No Effect: Remote 70%, Onsite 70% -Desirability, 15% Effect: Remote 80%, Onsite 65% -Acceptability, No Effect: Remote 60%, Onsite 60% -Acceptability, 20% Effect: Remote 70%, Onsite 50%
These tested effect sizes would be meaningful to Macy’s leadership in deciding whether or not to invest resources in developing and marketing casual clothing for men working from home. Men’s apparel accounted for approximately 20% of the company’s overall sales in 2020, down from approximately 23% in 2018 and 2019. Total annual sales for the company also declined almost 30% from 2019 to 2020, which Macy’s attributes in large part to COVID and its impact on consumer shopping patterns. If there is evidence that the desirability and/or acceptability of casual clothing is significantly more prevalent in the growing remote workforce market than in the traditional office market, it would be compelling in favor of investing in this new opportunity. If this study does not provide evidence of a significant difference between groups in either or both categories, but still demonstrates a high proportion of desirability and acceptability across groups, this could also be an indication of a growing market for casual attire and a potentially very lucrative product area for the company to further explore.
n <- 200
set.seed(329)
bp.dat <- data.table(Group = sample(x = c("Remote", "Onsite"), size = n, replace = T))
bp.dat[Group == "Remote", Desire_Casual := round(x = rbernoulli(n = .N), digits = 1)]
bp.dat[Group == "Onsite", Desire_Casual := round(x = rbernoulli(n = .N), digits = 1)]
analyze.experiment <- function(the.dat) {setDT(the.dat)
the.test <- prop.test(table(the.dat$Group,the.dat$Desire_Casual), alternative=c("greater"))
the.effect <- the.test$estimate[1] - the.test$estimate[2]
lower.bound <- the.test$conf.int[1]
p <- the.test$p.value
result <- data.table(effect = the.effect, lower_ci = lower.bound, p = p)
return(result)
}
n=200
B <- 1000
Experiment <- rep.int(x = 1:B, times = n)
Group = sample(x = c("Remote", "Onsite"), size = n * B, replace = T)
sim.dat <- data.table(Experiment, Group)
setorderv(x = sim.dat, cols = c("Experiment", "Group"), order = c(1,1))
sim.dat[Group == "Remote", Desire_Casual:= round(x= rbernoulli(n = .N, p=.7), digits = 1)]
sim.dat[Group == "Onsite", Desire_Casual:= round(x= rbernoulli(n = .N, p=.7), digits = 1)]exp.results <- sim.dat[,analyze.experiment(the.dat = .SD),keyby = "Experiment"]
d1_mean <- round(100*mean(exp.results$effect), 2)
d1_positives <- round(100*sum(exp.results$p < 0.05)/B,2)
d1_negatives <- round(100*sum(exp.results$p >= 0.05)/B,2)
d1_CI <- round(100*mean(exp.results$lower_ci), 2)n <- 200
set.seed(329)
bp.dat <- data.table(Group = sample(x = c("Remote", "Onsite"), size = n, replace = T))
bp.dat[Group == "Remote", Desire_Casual := round(x = rbernoulli(n = .N), digits = 1)]
bp.dat[Group == "Onsite", Desire_Casual := round(x = rbernoulli(n = .N), digits = 1)]
analyze.experiment <- function(the.dat) {setDT(the.dat)
the.test <- prop.test(table(the.dat$Group,the.dat$Desire_Casual), alternative=c("greater"))
the.effect <- the.test$estimate[1] - the.test$estimate[2]
lower.bound <- the.test$conf.int[1]
p <- the.test$p.value
result <- data.table(effect = the.effect, lower_ci = lower.bound, p = p)
return(result)
}
n=200
B <- 1000
Experiment <- rep.int(x = 1:B, times = n)
Group = sample(x = c("Remote", "Onsite"), size = n * B, replace = T)
sim.dat <- data.table(Experiment, Group)
setorderv(x = sim.dat, cols = c("Experiment", "Group"), order = c(1,1))
sim.dat[Group == "Remote", Desire_Casual:= round(x= rbernoulli(n = .N, p=.8), digits = 1)]
sim.dat[Group == "Onsite", Desire_Casual:= round(x= rbernoulli(n = .N, p=.65), digits = 1)]exp.results <- sim.dat[,analyze.experiment(the.dat = .SD),keyby = "Experiment"]
d2_mean <- round(100*mean(exp.results$effect), 2)
d2_positives <- round(100*sum(exp.results$p < 0.05)/B,2)
d2_negatives <- round(100*sum(exp.results$p >= 0.05)/B,2)
d2_CI <- round(100*mean(exp.results$lower_ci), 2)n <- 200
set.seed(329)
bp.dat <- data.table(Group = sample(x = c("Remote", "Onsite"), size = n, replace = T))
bp.dat[Group == "Remote", Accept_Casual := round(x = rbernoulli(n = .N), digits = 1)]
bp.dat[Group == "Onsite", Accept_Casual := round(x = rbernoulli(n = .N), digits = 1)]
analyze.experiment <- function(the.dat) {setDT(the.dat)
the.test <- prop.test(table(the.dat$Group,the.dat$Accept_Casual), alternative=c("greater"))
the.effect <- the.test$estimate[1] - the.test$estimate[2]
lower.bound <- the.test$conf.int[1]
p <- the.test$p.value
result <- data.table(effect = the.effect, lower_ci = lower.bound, p = p)
return(result)
}
n=200
B <- 1000
Experiment <- rep.int(x = 1:B, times = n)
Group = sample(x = c("Remote", "Onsite"), size = n * B, replace = T)
sim.dat <- data.table(Experiment, Group)
setorderv(x = sim.dat, cols = c("Experiment", "Group"), order = c(1,1))
sim.dat[Group == "Remote", Accept_Casual:= round(x= rbernoulli(n = .N, p=.6), digits = 1)]
sim.dat[Group == "Onsite", Accept_Casual:= round(x= rbernoulli(n = .N, p=.6), digits = 1)]exp.results <- sim.dat[,analyze.experiment(the.dat = .SD),keyby = "Experiment"]
a1_mean <- round(100*mean(exp.results$effect), 2)
a1_positives <- round(100*sum(exp.results$p < 0.05)/B,2)
a1_negatives <- round(100*sum(exp.results$p >= 0.05)/B,2)
a1_CI <- round(100*mean(exp.results$lower_ci), 2)n <- 200
set.seed(329)
bp.dat <- data.table(Group = sample(x = c("Remote", "Onsite"), size = n, replace = T))
bp.dat[Group == "Remote", Accept_Casual := round(x = rbernoulli(n = .N), digits = 1)]
bp.dat[Group == "Onsite", Accept_Casual := round(x = rbernoulli(n = .N), digits = 1)]
analyze.experiment <- function(the.dat) {setDT(the.dat)
the.test <- prop.test(table(the.dat$Group,the.dat$Accept_Casual), alternative=c("greater"))
the.effect <- the.test$estimate[1] - the.test$estimate[2]
lower.bound <- the.test$conf.int[1]
p <- the.test$p.value
result <- data.table(effect = the.effect, lower_ci = lower.bound, p = p)
return(result)
}
n=200
B <- 1000
Experiment <- rep.int(x = 1:B, times = n)
Group = sample(x = c("Remote", "Onsite"), size = n * B, replace = T)
sim.dat <- data.table(Experiment, Group)
setorderv(x = sim.dat, cols = c("Experiment", "Group"), order = c(1,1))
sim.dat[Group == "Remote", Accept_Casual:= round(x= rbernoulli(n = .N, p=.7), digits = 1)]
sim.dat[Group == "Onsite", Accept_Casual:= round(x= rbernoulli(n = .N, p=.5), digits = 1)]exp.results <- sim.dat[,analyze.experiment(the.dat = .SD),keyby = "Experiment"]
a2_mean <- round(100*mean(exp.results$effect), 2)
a2_positives <- round(100*sum(exp.results$p < 0.05)/B,2)
a2_negatives <- round(100*sum(exp.results$p >= 0.05)/B,2)
a2_CI <- round(100*mean(exp.results$lower_ci), 2)DT <- data.table(Question = c(1, 1, 2, 2),
Scenario = c("No Effect", "15% Higher Remote", "No Effect", "20% Higher Remote"),
Mean_Effect_Pct = c(d1_mean, d2_mean, a1_mean, a2_mean),
CI_Lower_Bound_95_Pct = c(d1_CI, d2_CI, a1_CI, a2_CI),
False_Pos_Pct = c(d1_positives, 0, a1_positives, 0),
True_Neg_Pct = c(d1_negatives, 0, a1_negatives, 0),
False_Neg_Pct = c(0, d2_negatives, 0, a2_negatives),
True_Pos_Pct = c(0, d2_positives, 0, a2_positives)
)
datatable(DT, rownames = F)The simulations for no effect correctly fail to reject the null in about 97% of trials and incorrectly reject the null in only about 3% of trials. The mean effect sizes are close to, but no exactly, 0, with confidence intervals spanning effects both below and above 0. The simulation for 15% higher desirability among remote workers correctly rejects the null in approximately 72% of trials and incorrectly fails to reject the null in approximately 28%. This effect size is slightly difficult, but still likely, to prove with our planned sample size. The mean effect is close to 15% with 95% confidence that the effect will be at least 3.6%, which should be compelling to Macy’s leadership because even the lower bound represents a sizable share of customers. The simulation for 20% higher acceptability among remote workers correctly rejects the null in approximately 87% of trials and incorrectly fails to reject the null in approximately 13%. This effect is larger and thus easier to prove with our planned sample size than the 15% difference in desirability. The mean effect is close to 20% with 95% confidence that the effect will be at least 7.7%, which is even more compelling to Macy’s leadership than the desirability question as it represents a larger share of potential customers and therefore a huge revenue opportunity.
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