In: Statistics and Probability
Note - Allowed to solve only 4 subquestions in one post. solved 5 questions with explanation. THe remaining the correct solution is given
A wine company wanted to examine how Big-5 Personality Traits (openness to experience, agreeableness, conscientiousness, neuroticism, and extraversion) are related to salespersons’ performance. The company measured salespersons’ personality traits using 5-point Likert scales (e.g., 1-5) with higher values representing higher levels of the personality traits. The company used the number of bottles of wine sold in the last three months as a performance measure.
Multiple regression
In this case we use,number of bottles are the dependent varibles
and the big 5 personality score as the independent variables.
The regression will provide a coefficient for each of the traits
which will help us understand the relationship of each trait to the
sales performance.
The National Youth in Transition Database (NYTD) is a federally-mandated evaluation of the use of independent living services by foster youth in Wisconsin. University of Wisconsin conducted a baseline survey of youth in foster care at age 17 as well as a follow-up survey with these youth at age 21. In both surveys, participants were asked to indicate to what extent they valued diversity and inclusion (1 = not important at all, 5 = very important). A researcher identified the participants who attended colleges as a sample and examined whether their values on diversity and inclusion changed after attending colleges.
Two paired sample mean comparison
Here the sample person is interview twice, at the age 0f 17 and at 21. Hence can find the differnce in the ratings and check if the hypothesis if there is difference in the ratings.
The College of Business conducted a survey to investigate faculty members’ perceptions of diversity and inclusion. The participants were asked to indicated to what extent they were satisfied with the current diversity climate (1 = very dissatisfied, 5 = very satisfied). After collecting the data, the Dean wanted to know whether the diversity climate perceptions differed across five departments (Finance, Accounting, Marketing, Operations Management, and Management and Human Resources) and two types of faculty members (research faculty and teaching faculty).
Two-way ANOVA
We use a two way anova because there are two factor we want to
check if there is difference in the mean score.
Factor 1 : Department
Factor 2 :Type of faculty member.
A consulting company used 115 engagement managers as a
sample to examine whether participating in a leadership training
program (0=non-participant 1= participant) was related to the
promotion results (0= not promoted 1=promoted).
Independence Chi-square test
In case we want to check if there is relationship between if promotion is relate to training based on count data. We create a contingency table as given below and then use chi square test to check the hypothesis.
According to the October 2010 issue of Harvard Business Review, Best Buy has proven by holding other factors constant the value of a 0.1% increase in employee engagement at a particular store is $100K. This led Best Buy to hold employee engagement surveys on a quarterly basis as compared to annually. What method do you think Best Buy has used to help draw the conclusion?
Regression
The store ran a regression with the dependent variables as sales
and fators effecting as independent variables.
Using the regression coefficient, they are able to come to the
intrepret that 0.01% increae in employee engagement increases sales
by $100K
As required by the Dodd-Frank financial reform act,
publicly traded U.S. companies have started to disclose how the pay
of their CEOs compares to the compensation of their median
employees (the so-called "pay ratio"). A researcher collected the
CEO-employee pay ratio data of 1,000 companies and wanted to
examine whether the pay ratio was different across industries
(e.g., finance, manufacturing, service, high-tech,
etc.)
One-way ANOVA
We need to check if the mean pay ration is different across
different industries.
A recent study examined whether using self-reflective
job titles (e.g., Goddess of Greetings for an administrative
assistant) can help reduce emotional exhaustion. The researchers
conducted a field experiment to examine this research question.
They first randomly assigned participants into a treatment group
and a control group. The researchers gave a 30-minute intervention
to teach participants in the treatment group how to create
self-reflective job titles but not those in the control group. A
month later, the researchers measured the emotional exhaustion of
participants (on a Likert scale ranging from 1 to 7) in both groups
and examined whether there was any mean difference in emotional
exhaustion between the two groups.
Two independent sample mean comparison
Nielsen is considered an exemplar company using data
analytics to make people management decision making. To predict
future attrition, Nielsen built a model with 20 employee variables
like age, gender, tenure and manager rating (in scores) and used
those variables to predict employees’ turnover intention (on a
Likert scale 1 = very likely to quit, 5 = very likely to
stay).
Multiple regression
A company used a job evaluation system to rate the values of 50 benchmarking job positions (in points). The company also collected the median market salary for each of the job positions. Eventually, the company wanted to establish a linear equation to predict how much should be paid to a job based on its value.
Simple regression
A research team measured a sample of employees’ preference
for work-life balance (on a Likert scale ranging from 1 = not
preferable at all to 5 = very preferable) and examined whether
there was a generation difference in work-life balance preference
(e.g., Gen Z, Millennials, Gen X, and Baby Boomers).
Two-way ANOVA