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Posted: December 15th, 2023

Homework 5: Work and Life Balance
Background
For this assignment, we will be working to understand the impact of different working models on the perceived satisfaction of employees with regard to their work/life balance. Corporate goals often incentivize working longer hours and in more demanding roles. However, alternative models exist. Some businesses and countries are experimenting with shorter working weeks or changes to their corporate cultures.
To further examine the issue, a team of researchers partnered with a number of companies to examine the impact of their corporate culture and the length of the working week on the overall satisfaction of employees with regard to their work/life balance. The research team had previously classified the working culture of these companies as either relaxed or demanding based upon validated research tools.
The researchers conducted an experiment with working weeks of different lengths. Prior to the experiment, all of these companies operated with conventional 5-day working weeks and standard hours. Each company was randomized to implement either a 3-day working week, a 4-day working week, or to maintain its conventional 5-day working week. The overall number of expected working hours was held in proportion to the working week (e.g. 8 hours per day for the number of days worked). However, the compensation of the participating employees remained fixed at their prior levels. Training was provided to the managers and the employees to set reasonable expectations for what should be accomplished in the shortened working weeks. The companies were monitored to ensure compliance with the schedule and the expectations. The study was conducted over a period of 6 weeks.
At the end of this period, consenting employees were given a survey that assessed their satisfaction with their balance of work and life. The answers were combined into an overall measure of satisfaction ranging from 0 to 100.
In this assignment, we will be working with the information provided to analyze the satisfaction scores and consider other possible implications of changes in the typical working conditions of companies.
Data
The data are available in the file work and life balance.csv Download work and life balance.csv.
For each consenting employee, information on their years of experience and whether they are a manager was collected. Data about each employee’s company was recorded, including its identifier, industry, and the assessment of its working culture. The company’s randomly assigned workweek was included, and each employee’s overall satisfaction score was recorded.
Instructions
Based upon the information above and the data provided, please answer the following questions. When numeric answers are requested, a few sentences of explanation should also be provided. Please show your code for any calculations performed.
Preliminary Code
This section of the report is reserved for any work you plan to do ahead of answering the questions – such as loading or exploring the data.
Question 1
Changing the length of the working week would be:
a)Not actionable because the company is unable to implement the change.
b)Not actionable because the company faces an uncertain and competitive market.
c)Actionable because the company is able to implement the change.
d)Actionable because the employees are requesting it.
Question 2
Changing the working culture of the company is
a)Not actionable because of longstanding workplace traditions.
b)Not actionable because culture cannot be mandated by management.
c)Actionable because it only requires simple changes.
d)Actionable but requires commitment to new practices.
Question 3
How should we phrase the research question related to the length of the working week?
a)Does a shorter working week lead to improved satisfaction?
b)Relative to a standard 5-day working week, would reductions to a) 4 days per week or b) 3 days per week increase the average satisfaction score for work/life balance, all while holding the employee’s income fixed?
c)Since before the advent of a standard weekend, workers have long advocated for reduced working hours. Would shifting to a shorter working week be satisfactory?
d)Relative to a standard 5-day working week, would reductions to a) 4 days per week or b) 3 days per week increase the average income, all while holding the employee’s work/life balance fixed?
Question 4
How should we phrase the research question related to the working culture?
a)Would shifting to a relaxed working culture reduce the length of the average working week?
b)Relative to a relaxed working culture, would changing to a demanding working culture increase the average satisfaction score for work/life balance?
c)Relative to a demanding working culture, would changing to a relaxed working culture take away all of the stress of work?
d)Relative to a demanding working culture, would changing to a relaxed working culture increase the average satisfaction score for work/life balance?
Question 5
With regard to evaluating the effect of changes to the working week, the study is
a)Well designed because of the randomization of companies to different lengths of working weeks.
b)Well designed because we are able to collect data.
c)Not well designed because no company will ever let its employees work 3 days a week.
d)Not well designed because of unmeasured confounding factors.
Question 6
With regard to evaluating the effect of changes to the working culture, the study is
a)Well designed because of the randomization of companies to different workplace cultures.
b)Well designed because we are able to collect data.
c)Designed to measure the effect through an observational study, which is the best we can do in these circumstances.
d)Not well designed because the study is observational.
Question 7
What kind of statistical method could be employed to analyze the data and evaluate the research questions?
a)Linear Regression or 1-Way ANOVA
b)Linear Regression or 2-Way ANOVA
c)Logistic Regression or 1-Way ANOVA
d)Logistic Regression or 2-Way ANOVA
Question 8
If we use a regression model to analyze the data and evaluate the research questions, what kind of effects will we be able to obtain? Select all that apply.
a)Estimated changes in the mean outcomes associated with changes in the independent variables.
b)The correlation between the independent and dependent variables.
c)The total and percentage of the explained variation attributed to the variable.
d)The estimated effect of each categorical level of the independent variable relative to a base case.
Question 9
If we use an ANOVA model to analyze the data and evaluate the research questions, what kind of effects will we be able to obtain? Select all that apply.
a)Estimated changes in the mean outcomes associated with changes in the independent variables.
b)The correlation between the independent and dependent variables.
c)The total and percentage of the explained variation attributed to the variable.
d)The estimated effect of each categorical level of the independent variable relative to a base case.
Question 10
The model of satisfaction:
a)Should only include the independent variables because the study involves a randomized comparison.
b)Should adjust for potentially confounding factors because the study involves an evaluation based on observational data.
c)Should be separated into different analyses since the working week has 3 levels and the culture has 2.
d)Must be paired with Tukey’s HSD test to be valid.
Question 11
Fit a multivariable regression model of satisfaction. Show a summary of its results. Include all of the variables except for the company. In particular, company-specific effects would not generalize as well to broader industries. Then build an appropriate ANOVA model with the same specifications and show its summary. Keep in mind that the ANOVA model should place the independent variables last. For our study, make the working week the final variable and include the culture next to last. Show your code and output in the box below.
Question 12
With regard to effect of the working week, the models show that:
a)Reductions in the length of the working week have no effect on the average satisfaction.
b)Reductions in the length of the working week have a positive effect on the average satisfaction.
c)Reductions in the length of the working week have a negative effect on the average satisfaction.
d)The effect is moderately predictive based on the model’s R Squared.
Question 13
With regard to effect of the working culture, the models show that:
a)Changes in the working culture lead to an increase in the average satisfaction.
b)The average satisfaction was higher for companies with a demanding working culture than for companies with a relaxed working culture.
c)The average satisfaction was higher for companies with a relaxed working culture than for companies with a demanding working culture.
d)There is no way to draw a conclusion because the study was observational.
Question 14
If a company with a 5-day working week and a demanding culture shifted to a 4-day working week and a relaxed culture, what would be the estimate of the associated increase in the average satisfaction score? Round your answer to 4 decimal places.
Question 15
What if we wanted to compare all of the average satisfaction scores in the three groups of working weeks? For this analysis, you may ignore the other variables. Use Tukey’s HSD to calculate
a) the difference in mean values,
b) the 95% confidence interval, and
c) the adjusted p-value.
Place these results in a table, with each row corresponding to one of the pairwise comparisons.
Round all numeric results to 3 decimal places. Show your code and output in the box below.
Question 16
Now conduct separate t-tests of whether a shorter working schedule increases satisfaction for each pair of schedules. Which of these results would remain significant with a Bonferroni correction for multiple comparisons? Show the p-values for the t-tests, the corrected threshold for a 0.05 significance level, and whether the differences remain significant after the adjustment. Round all numeric results to 3 decimal places. Show your code and output in the box below.
Question 17
Thinking about the evaluation of the length of the working week, the 6-week time frame is:
a)Not long because the employees would not be able to plan for the days off.
b)Not long because the managers would not be able to adjust to the shorter working week.
c)Long enough for employees and managers to reflect on how their work/life balance has changed in a way that would show up in the assessment their satisfaction with theirf work/life balance.
d)Too long, because we could just ask everyone to take the work/life balance assessment while imagining a shorter working week.
Question 18
Now the researchers would like to build upon the work of the first study they conducted. Anecdotally, those working the shorter weeks during the experiment frequently mentioned the benefit of getting more rest. This is what we want to investigate. The new study will be conducted entirely separately from the old one.
Based on the feedback of the previous experiment, a 3-day working week would not be very practical for the companies, while 4 days seemed more reasonable. The researchers will conduct a randomized comparison. One group of companies will stick with a standard 5-day working week, while another group of companies will use a 4-day working week without modification of their salaries. The companies will be randomly assigned to a group. The nightly amount of sleep will be tracked for each consenting participant. The study will continue over a 6-week period. Then, for each subject, the sleeping records will be aggregated into a single figure (e.g. 7.83 hours per night). The study will compare the average nightly hours of sleep per person for the two groups.
To implement this study, what are the primary operational challenges? Select all that apply:
a)Should we be concerned about how the participants spend their free time, such as evening plans for the extra day off?
b)To track sleeping times, should we have the participants keep a written record or wear a technological device?
c)How can we ensure training and compliance with the 4-day working week?
d)Should we ensure that the companies stick to their typical workplace culture? We would not want a demanding workplace to turn into a relaxed one while implementing a 4-day working week.
e)The companies with a 4-day working week might have employees who are not participating in the study. We should also track their sleeping times to get a larger sample size.
f)We don’t know if some of the employees working 4-day weeks will get an additional job to be worked outside of then. If we find out about it, should we adjust their sleeping times or switch them to the treatment group?
Question 19
The researchers are hoping to sample approximately 200 employees for the new study, evenly divided into two groups of 100. They have selected a minimally meaningful effect size of 30 minutes of additional sleep per night. The study will use a significance level of 0.05. For now, assume that the standard deviation of sleeping times is 1 hour. What would be the power of your proposed statistical test in this scenario? Produce a numeric answer that is rounded to 4 decimal places.
Question 20
For the new study, it may be difficult to convince companies to consider a 4-day working week and to convince employees to provide you with their records of sleep. How would these results change if you could only get 30 employees in the group with the 4-day working week? Assume that the other inputs from the previous question will be used. What would be the power of your proposed statistical test in this scenario? Produce a numeric answer that is rounded to 4 decimal places.
Question 21
Assuming that we hold the other inputs fixed from the previous 2 questions, what sample size would be needed in the 4-day working week group to achieve a power of 0.9? Make sure to round your answer up to a whole number.
Question 22
What are the trade-offs between power and sample size in statistical testing?
a)Increased power provides a greater chance of detecting statistically significant effects when the null hypothesis is true. However, it comes at the cost of greater resources in running the study on a larger sample size.
b)Increased power provides a greater chance of detecting statistically significant effects when the null hypothesis is false. However, it comes at the cost of greater resources in running the study on a larger sample size.
c)Increased power does not come with any trade-offs if we run a randomized controlled trial, since we’ll be able to determine a causal effect at any sample size.
d)Increased sample sizes are not related to the power, but they will help us get a small p-value.
Question 23
In our earlier analyses, we had assumed that the standard deviation of sleeping times was 1 hour. If this assumption is incorrect, what impact will it have on the statistical power?
a)The statistical power is not related to the standard deviation.
b)If the true standard deviation is larger than 1 hour, the power of the statistical test will increase.
c)If the true standard deviation is larger than 1 hour, the power of the statistical test will decrease.
d)We can’t know what effect the standard deviation will have because it can only be estimated from data.
Question 24
Suppose we had been able to add a third group to the planned study so that we could test the 3-day, 4-day, and 5-day working weeks. We would like to study the differences in mean nightly sleeping time across these groups using a one-way ANOVA model. The experiment would have 100 employees in each group while planning for a power of 0.8 using a significance level of 0.05. Under these circumstances, what is the minimal effect size that could be detected? Convert the calculated effect size into minutes under an assumption that the standard deviation is 1 hour. Produce a numeric answer that is rounded to 2 decimal places.
Question 25
Thinking holistically about all of the work performed in the previous questions, what have we demonstrated? Select all that apply.
a)Shorter working weeks are associated with greater average satisfaction with work/life balance.
b)Relaxed working cultures are associated with greater average satisfaction with work/life balance.
c)Shorter working weeks are associated with increases in the average nightly sleeping time.
d)Relaxed working cultures are associated with increases in the average nightly sleeping time.

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