Work and Life Balance
For this project, I 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. In the first phase of the study, the researchers conducted an assessment of each company’s culture by interviewing a number of employees about the responsibilities, challenges, and stress-related to their work. The corporate culture was then rated as either relaxed or demanding by the researchers based upon a review of this information across all of the participating employees in the company.
The second stage of the study included 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). The 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 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.
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.
The data are available in the file 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.
What are the primary research questions of the study?Â
One primary research question of this study is to understand the different corporate cultures of companies and how it directly impacts employee satisfaction in terms of their work-life balance. Another primary research question is if the length of a working week is a major factor in employee satisfaction (3 day work week etc vs a typical 5 day work week difference)
This ultimately helps the company figure out what can help their corporate culture and improve their employee performance. It can help companies establish or improve upon their culture and/or gather data to establish a working week length that maximizes employee performance, efficiency, and satisfaction in relation to work-life balance.
For each research question you mentioned above, describe how well the study is designed to evaluate the question.
For my first research question (understanding different corporate cultures of companies and how does it directly impact employee satisfaction in terms of work-life balance): This study was conducted using an interview process which is very beneficial because the responses will be more detailed and reflective in comparison to random questionnaires or surveys. The con of this method is that the authenticity of the interviewees will be called into question because there is a lack of anonymity therefore many may feel the desire to withhold their true opinions. (which may lead to inaccurate results)
For my second research question (if the length of a working week is a major factor in employee satisfaction): The researchers randomly allocate the different lengths of working weeks within the company (3-day working week, 4-day working week, and 5-day working week) to their employees. The employee satisfaction score is then collected after a 6-week time frame, which is enough in my opinion for the employees to assimilate into their schedule. However, income plays a huge factor in this as well which may greatly affect results and lead to lower satisfaction scores for those working less.
What kind of statistical method could be employed to analyze the data and evaluate the research questions?
We should employ a two-way ANOVA method to analyze the data and evaluate the research questions. There are two independent variables which include the two levels (relaxing and demanding), and workweek length has three levels (3 days, 4 days, and 5 days a week). We can test the combinations of these variables.
Fit your intended model and show a summary of its results. While you may include other variables, we will specifically exclude the company from the analysis because these effects would not generalize as well to the broader industries.
ANOVA <- aov(satisfaction~culture + workweek, data = data)
summary(ANOVA)## Df Sum Sq Mean Sq F value Pr(>F)
## culture 1 193 193 5.035 0.0253 *
## workweek 2 12933 6467 168.429 <2e-16 ***
## Residuals 496 19043 38
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Corporate culture and workweek length will be our variables and will ultimately impact the satisfaction results of the employees in terms of work life balance.
Explain the results of your model. Describe how the estimates relate to your research questions and any other notable findings.
According to our results, we can see that both culture and workweeks are statistically significant since the p-values of both are less than 0.05. Culture has a p-value of 0.0253 (<0.05) and the workweek has a p-value of 2e-16 (<0.05), therefore the length of the workweek has an overall significant association to employee satisfaction.
Would variable interactions also play a role? If your research question includes multiple independent variables, then include pairwise interactions with them. If you think there is only one independent variable in the study, then create an interaction between that variable and other measured factors that you might consider relevant. Show the numeric results and comment on the interactions.
ANOVA_INTERACTION <- aov(satisfaction~culture * workweek, data=data)
summary(ANOVA_INTERACTION)## Df Sum Sq Mean Sq F value Pr(>F)
## culture 1 193 193 5.051 0.025 *
## workweek 2 12933 6467 168.961 <2e-16 ***
## culture:workweek 2 136 68 1.783 0.169
## Residuals 494 18907 38
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1The results show that the culture and work week interactions are not statistically significant. (Because the p-value is 0.1693 which is greater than 0.05).
Are there other variables that would be helpful to measure? Is this even necessary? Explain your answer and reasoning.
Yes, other variables that would be helpful to measure are the employee experience and position levels (whether they’re managers or not). Adding this will definitively change the results of the interactions, so adding this may be necessary. Industry position for example would not be necessary but position level may be.
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. Show the results of a statistical test to simultaneously evaluate the difference in satisfaction for all of the pairs of possible working weeks. Comment on the results.
anova1 <- aov(satisfaction ~ workweek, data = data)
TukeyHSD(anova1, conf.level = 0.95)## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = satisfaction ~ workweek, data = data)
##
## $workweek
## diff lwr upr p adj
## 4 Days-3 Days -9.185567 -11.160426 -7.210708 0.0000000
## 5 Days-3 Days -11.880235 -13.831328 -9.929142 0.0000000
## 5 Days-4 Days -2.694668 -4.277937 -1.111399 0.0002144For the three groups of working weeks, the difference between the employee satisfaction score of the 3 day work week in comparison to the 4 day work week is -9.185567.
The difference between the employee satisfaction score of the 3 day work week in comparison of the 5 day work week is -11.880235.
The difference between the employee satisfaction score of the 4 day work week in comparison to the 5 day work week is -2.694668.
This leads to the results that less working days a week ultimately leads to higher satisfaction levels among employees. There is evidence showing that these groups are statistically significant because the p-values are all less than 0.05.
Now conduct separate tests of whether a shorter working schedule increases satisfaction for each pair of schedules. Which of these results would remain significant with a Bonferroni correction for multiple comparisons? Show the p-values for the t-tests, the corrected threshold for a 0.05 significance level, and whether the differences remain significant after the adjustment.
table9 <- pairwise.t.test(data$satisfaction, data$workweek, p.adjust.method = 'bonf',)
table9##
## Pairwise comparisons using t tests with pooled SD
##
## data: data$satisfaction and data$workweek
##
## 3 Days 4 Days
## 4 Days < 2e-16 -
## 5 Days < 2e-16 0.00022
##
## P value adjustment method: bonferroniFor the 3 day work week in comparison to the 4 day work week, the p-value is 2.2e-16 which is less than 0.0167 threshold. For the 3 day work week in comparison to the 5 day work week, the p-value is again smaller than the 0.0167 threshold and the same can be said for the 4 day work week in comparison to the 5 day work week. This leads to a continuous significant difference.
Do you think the 6-week time frame is an appropriate length to investigate the effect of changes in the working schedule on the satisfaction of work/life balance? Explain why or why not.
I believe that the 6-week time frame given is an appropriate length to investigate the effect of changes in the working schedule on the satisfaction of work/life balance. This is because employees are given plenty of time to assimilate into their new given schedule and adapt to their work length. Personally, it would be enough time for me to do it however, every person is different. I’m very quick to adjust but maybe a 2-4 week extension may be needed for most people.
Now the researchers would like to build upon the work of the first experiment they conducted. In the comments on the surveys, a sizable number of the employees in the first study noted that they did not get enough sleep with a 5-day working week. Anecdotally, those working the shorter weeks during the experiment frequently mentioned the benefit of getting enough rest.
With this in mind, the researchers would like your help in planning their next experiment. They would once again like to randomize companies to shorter working weeks. 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 actionable. Comparing the amount of sleep of employees with 4-day schedules to the amount of sleep of those with 5-day schedules, how would you conduct the experiment to answer this question? State a research question, comment on the operational designs, and describe the type of data you would gather.
The main research question is to examine the impact of the 4 day work week and the 5 day work week on an employees sleep quality and schedule. I divided the employees into two different groups, one in the 4 day work week and another in the 5 day work week with an equal salary. A survey would then be conducted to ask how they’re feeling and how their sleep has been, on a scale of 1-5, one being terrible and 5 being amazing.
What kind of statistical test would be appropriate for your research question? Provide sufficient details on all of the choices you would make.
A two-sample t-test would be appropriate for this research question. We are able to test the mean value of the two groups and see if they have a statistically significant difference.
The H0:average sleeping time of an employee with 4 day work week schedule is equal to an employee with a 5-day working schedule Ha: average sleeping time of an employee with a 4 day work week schedule is not equal to an employee working 5 days a week
What kind of improvement in nightly sleeping times would you consider meaningful for the average employee? Explain your reasoning.
I believe that a 30 minute improvement in nightly sleep time would ultimately be considered meaningful for the average employee. An average adult requires 7-9 hours of sleep a night so a 30 hour improvement would be meaningful.
The researchers are hoping to sample approximately 200 employees for the study, roughly divided into two groups of 100. What would be the power of your proposed statistical test in this scenario? Use your suggested effect size from the previous question in units of hours and a significance level of 0.05. For now, assume that the standard error of mean sleeping times is 1 hour. Produce a numeric answer and then comment on the results.
Answer
pwr.t2n.test(n1 = 100, n2 = 100, d = 0.5 / 1, sig.level = 0.05, alternative = 'greater')## t test power calculation
##
## n1 = 100
## n2 = 100
## d = 0.5
## sig.level = 0.05
## power = 0.9698479
## alternative = greaterAccording to the code, the statistical power is 0.9698479.
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 4-day working week? Assume that the other inputs from the previous question will be used. Calculate the power and comment on the results, along with the differences from the previous question.
pwr.t2n.test(n1 = 30, n2 = 100, d = 0.5, sig.level = 0.05, alternative = 'greater')## t test power calculation
##
## n1 = 30
## n2 = 100
## d = 0.5
## sig.level = 0.05
## power = 0.7716654
## alternative = greaterAccording to the results, the statistical power is 0.7716654.
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.
pwr.t2n.test(n1 = 100, d = 0.5, sig.level = 0.05, power = 0.9, alternative = 'greater')##
## t test power calculation
##
## n1 = 100
## n2 = 52.82509
## d = 0.5
## sig.level = 0.05
## power = 0.9
## alternative = greaterAccording to our results, the sample size will be 53.
The sample size for the 4 day work week employees will be a sample size of 53.
Describe the trade-offs between power and sample size in this setting. Including considerations of the statistical issues along with the practical aspects of running the experiment.
As the sample size increases, the standard error decreases. A more significant power shows a smaller chance of inaccuracy of results. We should not use a huge sample size as it will waste too much time and resources.
In our earlier analyses, we had assumed that the standard error of mean sleeping times was 1 hour. What if this assumption is incorrect? For now, you may consider an experiment with 100 sampled employees in each treatment group and a significance level of 0.05. Describe how the power changes if our assumption is wrong in each direction.
tpower_sa <- pwr.t2n.test(n1 = 100, n2 = 100, d = c(0.5/0.5, 0.5/1, 0.5/1.5), sig.level = 0.05, alternative = 'greater')
tpower_sa##
## t test power calculation
##
## n1 = 100
## n2 = 100
## d = 1.0000000, 0.5000000, 0.3333333
## sig.level = 0.05
## power = 1.0000000, 0.9698479, 0.7593159
## alternative = greaterThe statistical power will increase when the standard error of average sleep time decreases.
The original experiment studied 3 different levels of working weeks (3, 4, and 5 days per week) and 2 levels of corporate culture (relaxed and demanding). Suppose we could randomize 100 employees into each combination of a working week and corporate culture. We would like to study the differences in mean nightly sleeping time across these groups using a two-way ANOVA model while planning for a power of 0.8 using a significance level of 0.05. Under these circumstances, what kind of effect size could be detected? Convert the calculated effect size into minutes under the assumption that the standard error is 1 hour.
pwr.anova.test(k = 6, n = 100, sig.level = 0.05, power = 0.8)##
## Balanced one-way analysis of variance power calculation
##
## k = 6
## n = 100
## f = 0.1469049
## sig.level = 0.05
## power = 0.8
##
## NOTE: n is number in each groupEffect_size <- 0.1469 * 60; Effect_size## [1] 8.814The effect size is about 8.8 minutes
Taking into account your analyses and statistical planning, what kind of recommendations would you make to the companies in order to help them to improve the satisfaction of their employees with regard to work/life balance?
We’re able to understand that the increase in working weekdays will significantly affect employee satisfaction scores. My recommendation would be to greatly improve the overall satisfaction score of the employees and testing the workweek times to also increase satisfaction and corporate culture. (Flexibility in work times)