Applied probability to predict the chance of employees whopass the mt program to officially become the brand manager

HANOI MINISTRY OF EDUCATION AND TRAINING National Economics University School of Advanced Educational Programs *** ASSIGNMENT REPORT International Business Administration Intake 62B Group Authors: Nguyễn Thảo Linh Nguyễn Thùy Dung Trần Lê Thu Hà Nguyễn Thị Tâm Giang Hồ Minh Huyền Đỗ Thị Ngọc Ánh Course: BUSINESS STATISTICS Report title: Application of probability in evaluating the potential of candidates for the Management Trainee program: Research the case of PwC Date of completion: October 13th, 2022 Table of Content Part 1: Article summarizing I Introduction .3 What is PwC? What is Management Trainee Program? II Summarizing the ariticle What is the issue of interest? Why you care about the technique as the organization manager? .3 Additional Source 4 Application of Probability in this article Hypotheses: Part 2: Data Analyzing .5 Gender 2) Age Academic level The awareness of candidates about the management trainee program since their high school Experiment Skills .11 III Extra part: Applied probability to predict the chance of employees who pass the MT program to officially become the brand manager 12 The sample space .12 Probability distribution 13 Describing the probability distribution 13 Bivariate Distribution 14 Bivariate Probability of Distribution 15 IV Discussion 16 V Conclusion 18 Summary 18 Limitation 19 VI Reference 20 Part 1: Article summarizing I Introduction What is PwC? Formed in 1998 when Price Waterhouse merged with Coopers and Lybrand, PwC, also known as PricewaterhouseCoopers, offers clients various professional business services, including accounting, auditing, human resources consulting, and strategy management It is among the “Big Four” professional services firms, alongside Deloitte, Ernst & Young, and KPMG What is Management Trainee Program? Management trainees, sometimes referred to as "MTs," are often hired to work and train alongside managers and executives with the intention that one day they will become a manager within the organization Current managers and other experienced, senior personnel in various departments supervise the instruction and development of these trainees, teaching them the techniques and systems necessary to keep the company running efficiently and effectively This type of position is most often found in particular industries, such as operations, finance, sales or marketing II Summarizing the ariticle What is the issue of interest? Purpose: Predicting the probability of passing or failing through the characteristics of candidates participating in the PwC management program entrance exam Why you care about the technique as the organization manager? - For the company: get an overview of common characteristics commonly found in candidates with a high probability of passing the MT program => Therefore, it helps the company to evaluate and make decisions to choose suitable candidates - For candidates who are or will be taking the MT exam: Understanding the probability of passing MT through common characteristics in a potential candidate will help them make adjustments and change themselves to increase their chances of being recruited Additional Source + Predicting customer consumption trends Source: (Mahajan, 2015): https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4456898/ + Predicting risks in finance, business, insurance Source: (G Shafer, V Vovk , 2005) https://books.google.com.vn/books? hl=vi&lr=&id=dYxsZzMmvHoC&oi=fnd&pg=PR5&dq=probability+finance& ots=CR0SJI72Mg&sig=o4mfOKuAtqlSURZedHOuz5SBeQM&redir_esc=y#v =onepage&q=probability%20finance&f=false Source: (B Lipstein - Journal of Marketing Research, 1965) https://journals.sagepub.com/doi/abs/10.1177/002224376500200305 Application of Probability in this article + Sex (Male/Female) + Age (18-21/22-25/26-29/30-33/34+) + Academic Level (High-school graduation/ Undergraduate/ Undergraduate) + Aawareness of candidates about the management trainee program since their high school (Don’t know/ Know but not research about it/ Know and research about it) + Candidates experiment (No experiment/ Related course experiment/ Part-time job experiment/ Full-time job experiment/ Extra-curricular activities) + Candidates skills (Communication, Leadership/ Problem solving/ Teamwork/ Self awareness/ Critical thinking) Hypotheses: Theory of Planned Behavior: The theory of planned behavior is a theory used to understand and predict behaviors, which posits that behaviors are immediately determined by behavioral intentions and under certain circumstances, perceived behavioral control Behavioral intentions are determined by a combination of three factors: attitudes toward the behavior, subjective norms, and perceived behavioral control Part 2: Data Analyzing Gender Pass Fail Total Female 0,25 0,25 0,5 Male 0,25 0,25 0,5 Total 0,5 0,5 This table illustrates the common Gender of the candidates who participate in the management trainee program (analyzing the actual case of PwC Company) Therefore predicting the probability of each category of age helps the company, as well as the wannabe candidates, have the overall view of the probability of each age to fail/pass the management trainee program For more details, we can easily see the Joint probability (P(x and y) - x is the gender category, y is the probability to pass/fail) through the table More specifically, the joint probability of Female and Pass (abbreviate as P(Female and Pass) is 0.25, and P(Female and Fail) is 0,25 Do the same for others, we have P(Male and Pass) is 0.25, P(Male and Fail) is 0.25 When it comes to the Marginal probability, we can also calculate the marginal probability of event Female (abbreviated as P(female)) = P(Female and Pass) + P(female and Fail) = 0.5 In addition, we can calculate P(male) = P(male and Pass) + P(female and Fail) = 0.5 Besides that, we can calculate the marginal probability of Pass (abbreviated as P(pass)) = P(Pass and Female) + P(Pass and Male) = 0.5, P(fail) = P(Fail and Male) + P(Fail and Female) = 0.5 In this gender category table, use the formula P(A/B) = P(A and B)/P(B) to take the conditional probability, then compare it with P(A) We can see that P(Pass/Female) = 0.25 / 0.5 = 0.5 and it is equal to P(Pass), P(Pass/Male) = 0.25 / 0.5 =0.5 and it also equal to P(Pass) too Therefore these are independent events Doing the same with the other events, we can conclude that event Female and event Male are independent with event Pass 2) Age Pass Fail Total 18-21 0,05 0,15 0,2 22-25 0,06 0,10 0,16 26-29 0,03 0,16 0,19 30-33 0,01 0,19 0,2 34+ 0,05 0,20 0,25 Total 0,2 0,8 This table illustrates the common age of the candidates who participate in the management trainee program (analysing the actual case of PwC Company) Therefore, predicting the probability of each category of age helps the company and the wannabe candidates have the overall view of the probability of each age to fail/pass the management trainee program For more details, we can easily see the Joint probability (P(x and y) - x is the age category, y is the probability to pass/fail) through the table More specifically, the joint probability of age 18-21 and Pass (abbreviate as P(18-21 and Pass)) is 0.05 Do the same for others, we have P(22-25 and Pass) is 0.06 Besides, we have P(26-29 and Pass) is 0.03 In addition, P(30-33 and Pass) is 0.01 and lastly we have P(34+ and Pass) is 0.05 When it comes to the Marginal probability, we can also calculate the marginal probability of age cat 18-21 (abbreviated as P(18-21)) = P(18-21 and Pass) + P(18-21 and Fail) = 0.2 Doing the same for the others, we can calculate P(2225) = 0,16; P(26-29) = 0,19; P(Pass) = 0,2; P(Fail) = 0,8 In this age category table, use the formula P(A/B) = P(A and B)/P(B) to take the conditional probability, then compare it with P(A) We can see that P(Pass/34+) = 0.05/0.25=0.2 and it equal to P(Pass) Therefore these are independent events Doing the same with the other events, we can conclude that except 34+, others are dependent with event Pass Academic level Pass Fail Total High-school graduation 0,03 0,12 0,15 Undergraduate 0,04 0,33 0,37 Postgraduate 0,13 0,35 0,48 Total 0,2 0,8 This table illustrates the academic level of the candidates who participate in the management trainee program (analyzing the actual case of PwC Company) Therefore, predicting the probability of each category of academic level helps the company and the wannabe candidates have the overall view of the probability of each academic level to fail/pass the management trainee program For more details, we can easily see the Joint probability (P(x and y) - x is the academic level category, y is the probability to pass/fail) through the table More specifically, the joint probability of High-school graduation and Pass (abbreviate as P(High graduation and Pass) is 0.03, P(Undergraduate and Pass) is 0,04 Do the same for others, we have P(Postgraduation and Pass) is 0.13 In addition, the joint probability of High-school graduation and Fail (abbreviate as P(High graduation and Fail) is 0.12, P(Undergraduate and Fail) is 0,33 and lastly P(Postgraduation and Fail) is 0.35 When it comes to the Marginal probability, we can also calculate the marginal probability of event High-school graduation (abbreviated as P(High-school graduation)) = P(High-school graduation and Pass) + P(High-school graduation and Fail) = 0.15 In addition, we can calculate P(Undergraduate) = P(Undergraduate and Pass) + P(Undergraduate and Fail) = 0.37 Also, we can calculate P(Postgraduation) = P(Postgraduation and Pass) + P(Postgraduation and Fail) = 0.48; P(pass) = P(Pass and High-school graduation) + P(Pass and Undergraduate)+P(Pass and Postgraduation) = 0.2 In addition, we can calculate P(Fail) = P(Fail and High-school graduation) + P(Fail and Undergraduate) + P(Fail and Postgraduation) = 0.8 In this academic level table, use the formula P(A/B) = P(A and B)/P(B) to take the conditional probability, then compare it with P(A) We can see that P(Pass/High-school graduation) = 0.03/0.15=0.2 and it equal to P(Pass) Therefore these are independent events Doing the same with the other events, we can conclude that except event High-school graduation, others are dependent with event Pass The awareness of candidates about the management trainee program since their high school Pass Fail Total Don’t know 0,03 0,31 0,34 Know but not research about it 0,1 0,25 0,35 Know and research about it 0,19 0,21 0,40 Total 0,23 0,77 This table illustrates the awareness of candidates about the management trainee program since their high school (analyzing the actual case of PwC Company) Therefore predicting the probability of each category of information helps the company, as well as the wannabe candidates, have the overall view of the probability of each information to fail/pass the management trainee program For more details, we can easily see the Joint probability (P(x and y) - x is the information category, y is the probability to pass/fail) through the table More specifically, the joint probability of event Don’t know and event Pass (abbreviated as P(Don’t know and Pass) is 0.03 Do the same for others, we have P(Know but not research about it and Pass) is 0.1; P(Know and research about it and Pass) is 0.19 When it comes to the Marginal probability, we can also calculate P(Don’t know) = P(Don’t know and Pass) + P(Don’t know and Fail) = 0.34 In addition, we can calculate P(Know but not research about it)) = P(Know but not research about it and Pass) + P(Know but not research about it and Fail) = 0.35 Also, we can calculate P(Know and research about it) = P(Know and research about it and Pass) + P(Know and research about it and Fail) = 0.40 Besides, calculate the marginal probability of Pass (abbreviated as P(pass)) = P(Pass and Don’t know) + P(Pass and Know but not research about it)+P(Pass and Know and research about it) = 0.23 In addition, we can calculate P(fail) = 0.77 In this experiment at the table, use the formula P(A/B) = P(A and B)/P(B) to take the conditional probability, then compare it with P(A) We can see that P(Pass/Don’t know) = 0.03/0.34=0.08 and it is not equal to P(Pass) Therefore, these are dependent events Doing the same with the other events, we can conclude that all are dependent events Experiment Pass Fail Total No experiment 0,01 0,18 0,19 Related course experiment 0,24 0,03 0,27 Part-time job experiment 0,09 0,06 0,15 Full-time job experiment 0,19 0,04 0,23 Extra-curricular 0,07 0,07 0.14 activities Total 0,62 0,38 This table illustrates the common experiment of the candidates who participate in the management trainee program (analyzing the actual case of PwC Company) Therefore predicting the probability of each category of experiment helps the company, as well as the wannabe candidates, have the overall view of the probability of each experiment to fail/pass the management trainee program For more details, we can easily see the Joint probability (P(x and y) - x is the experiment category, y is the probability to pass/fail) through the table More specifically, the joint probability of no experiment and Pass (abbreviated as P(no experiment and Pass) is 0.01 Do the same for others, we have P(related course experiment and Pass) is 0.24 Besides, we have P(part-time job experiment and Pass) is 0.09 and P(full-time job experiment and Pass) is 0.19 Lastly, we have P(extra-curricular activities and Pass) is 0.07 When it comes to the Marginal probability, we can also calculate P(no experiment) = P(no experiment and Pass) + P(no experiment and Fail) = 0.19 In addition, we can calculate P(related course experiment)) = P(related course experiment and Pass) + P(related course experiment and Fail) = 0.27 Also, we can calculate P(part-time job experiment) = P(part-time job experiment and Pass) + P(part-time job experiment and Fail) = 0.15 Moreover, we can calculate P(full-time job experiment) = P(full-time job experiment and Pass) + P(full-time job experiment and Fail) = 0.23 Besides, calculate the marginal probability of Pass (abbreviated as P(pass)) = P(Pass and no experiment) + P(Pass and related course experiment)+P(Pass and part-time job experiment) + P(Pass and fulltime job experiment) + P(Pass and extra-curricular activities) = 0.62 In addition, we can calculate P(fail) = 0.38 In this experiment at the table, use the formula P(A/B) = P(A and B)/P(B) to take the conditional probability, then compare it with P(A) We can see that P(Pass/no experiment) = 0.01/019=0.05 and it is not equal to P(Pass) Therefore these are dependent events Doing the same with the other events, we can conclude that all are dependent events 10 Skills Pass Fail Total Communication 0,02 0.19 0,21 Leadership 0.18 0.02 0,20 Problem-solving 0.05 0.05 0,1 Teamwork 0.07 0.04 0,11 Self-awareness 0.03 0.16 0,19 0.16 0,19 0.62 Critical thinking Total 0.03 0.38 This table illustrates the common skills of the candidates who participate in the management trainee program (analysing the actual case of PwC Company) For more details, we can easily see the Joint probability (P(x and y) - x is the skill category, y is the probability to pass/fail) through the table More specifically, the joint probability of Communication and Pass (abbreviated as P(Communication and Pass) is 0.02 Do the same for others, we have P(Leadership and Pass) is 0.18 Besides, we have P(Problem-solving and Pass) is 0.05, P(Teamwork and Pass) is 0.07, and P(Self-awareness and Pass) is 0.03 Lastly, we have P(Critical thinking and Pass) is 0.03 11 When it comes to the Marginal probability, we can also calculate P(Communication) = P(Communication and Pass) + P(Communication and Fail) = 0.21 In addition, we can calculate P( Leadership) = P(Leadership and Pass) + P(Leadership and Fail) = 0.20 Also, we can calculate P( Problemsolving)) = P(Problem-solving and Pass) + P(Problem-solving and Fail) = 0.1 Moreover, we can calculate P(Teamwork)) = P(Teamwork and Pass) + P(Teamwork and Fail) = 0.11 Next, we can calculate P(Self-awareness)) = P(Self-awareness and Pass) + P(Self-awareness and Fail) = 0.19 Lastly, we can calculate P(Critical thinking)) = P(Critical thinking and Pass) + P(Critical thinking and Fail) = 0.19 Besides, calculate the marginal probability of Pass (abbreviated as P(pass)) = P(Pass and Communication) + P(Pass and Leadership)+P(Pass and Problem solving) + P(Pass and Teamwork) + P(Pass and Self awareness) + P(Pass and Critical thinking) = 0.38 In addition, we can calculate P(fail) = 0.62 In this experiment at the table, use the formula P(A/B) = P(A and B)/P(B) to take the conditional probability, then compare it with P(A) We can see that P(Pass/Communication) = 0.02/0.21=0.09 and it is not equal to P(Pass) Therefore these are dependent events Doing the same with the other events, we can conclude that all are dependent events III Extra part: Applied probability to predict the chance of employees who pass the MT program to officially become the brand manager (Given information: In PwC, for each MT recruitment period, there are only people who are officially employed as the brand management trainee After a period of working, they will have the opportunity to be selected as a brand manager So, “What is the probability of the number of people selected?”, “How it is distributed?” are what the MTs want to know Through this, our team has done a few calculations related to probability to give the clearest view) The sample space Abbreviating: 1) MTs named respectively as A, B, C, D 2) P = Pass the brand manager 3) F = Fail the brand manager 12 The sample space is listed based on the order of employees from A to D respectively Therefore, we have the sample space of the probability of these MTs to pass the brand manager: S = {PFFF, FPFF, FFPF, FFFP, PPFF, FPPF, FFPP, PFPF, PFFP, FPFP, PPPF, FPPP, PFPP, PPFP, PPPP, FFFF} (16 equally likely outcomes) Probability distribution Let X be the number of MTs who can pass the brand manager X can take the values: 0, 1, 2, 3, (X can be considered as a discrete random variable) We have the discrete probability distribution for the probability of MTs who are chosen to become a brand manager: x P(X=x) 1/16 1/4 3/8 1/4 1/16 Frequency (%) 6,25 25 37,5 25 6,25 According to this table, we can see that the overall statistic of the number of MTs that have the highest probability to pass the brand manager position as well as the statistic of the number of MTs that have the lowest probability to pass For more details, is the number of employees that have the most probability to pass, followed by and are the number of people that have the lowest probability to pass the brand manager position Lastly, and are residential Describing the probability distribution Expected value Symbol Variance Standardize Deviation or 13 Value Meaning Measure the mean Measure the of the data set distance between the variable and the expected value Measure the dispersion of the data set In this case, we have expected value equal to 2, and also the value of the variance equals to the standardize deviation, which equals to It means that: + is the mean of the data set + is the distance between the variable and the expected value as well as the dispersion of the data set In this situation, means that the spread out of the data set is not quite large and it further confirms that the normalized residuals follow a symmetric distribution Bivariate Distribution Abbreviating: + x be the number of employees who are chosen to be the brand manager + y be the number of changes of sequence, i.e the number of times we change from P → F or F → P We have the table of outcomes below: Outcomes x y PFFF 1 FPFF FFPF FFFP 1 PPFF FPPF 2 FFPP PFPF PFFP 2 14 FPFP PPPF FPPP PFPP PPFP PPPP FFFF 0 This table simply lists all the outcomes that can be happened It includes variables x and y (x is listed as the number of employees who are chosen to be the brand manager (x can be from to 4), y is the number of changes of sequence (y can be from to 3)) Bivariate Probability of Distribution y x px(x) 1/16 0 1/16 2/16 2/16 4/16 2/16 2/16 2/16 6/16 2/16 2/16 4/16 1/16 0 1/16 py(y) 2/16 6/16 6/16 2/16 Mean/Expected value Symbol µx µy Value 1.5 Variance x y 0,75 15 We can calculate the Bivariate Probability of Distribution of x and y ( x is the number of employees who are chosen to be the brand manager, y be the number of changes of sequence, i.e the number of times we change from P → F or F → P.) Looking at these table, these MTs can have an insight view about the overall probability of them to fail/pass the brand manager position And also, we can calculate the Expected value of x and y as well as the Varience of x and y to be more specific IV Discussion Regarding the potential of candidates in the office environment, up to now, there have been many studies published and we have also learned about a few articles related to this issue In 2019, Julia Astegiano in the research article "Unraveling the gender productivity gap in science: a meta-analytical review" showed that the gender event, in which the event "Female" and "Male" is independent of the event "Employee performance" Men's success rate is higher only in productivity proxies involving peer recognition (e.g evaluation committees, academic positions) Men's articles showed a tendency to have higher global impact but only if studies include self-citations In this article, Julia detected gender bias against women in research fields where women are underrepresented Globally, Julia's meta-analyses suggest that the historical underrepresentation of women in science itself and socio-psychological and cultural factors underpinning gender bias against women may modulate gender inequality in the workplace However, women and men show similar success rates when the researchers' work is directly evaluated Our study also gave similar results, showing that gender is not a factor that gets too much attention when considering the results According to the findings of Alex Jones (Professor of Leadership, AUE), it is pointed out that leadership, teamwork and critical thinking are the most important inputs when considering a candidate's skills In the 2019 research article "The role of team leadership and critical thinking", the researcher developed ten criteria for the purpose of observing group dynamics The aim of which was to record each group interaction and collaboration among group members of each team The terms group and teams were used interchangeably during this section The ten criteria included: 1-Collaborative climate; 216 Knowledge and skills; 3-Trust; 4-Effectiveness of the team; 5-Leadership; 6Critical thinking; 7-Problem solving; 8-Goal; 9-Communication, and 10Resources The rating of each was based on three level measurement criteria highest to lowest as follows: a) Excellent, b) Adequate, and c) Inadequate The analysis of the ten above criteria had shown that collaboration among teams was significantly excellent This study brings to the forefront a unique discovery showing the impact of team leadership and critical thinking while conducting negotiation role-play activities The findings highlight the importance of teamwork, leadership, critical thinking and how it helps candidates to be appreciated in the workplace In terms of age of applicants, also in 2019, research from Anglia Ruskin and Cyprus universities showed that today the age of applicants is getting younger and younger Specifically, academics from this university applied for 811 sales and service jobs in England, sending in applications from fictional British job seekers Researchers found that fifty-year-old job seekers are up to three times less likely to be selected for an interview than younger applicants with less relevant experience Compared with our study, as we have analyzed above, the calculated data show that people aged 34 and older have a marked decrease in their ability to be employed and even in the level of salary offered Dr Paraskevopoulou told the British Sociological Association’s annual conference in Glasgow that the study showed that “Despite the growing participation of older workers in the labor market, many employers are prejudiced against older workers These results originate from stereotypical beliefs that the physical strengths and job performance decline with age." Besides, the study belongs to OECD showing that over the past 14 years, employment rates for men and women with tertiary education has been consistently higher than for those without The OECD average falls to about 74% for people with upper secondary and post-secondary non-tertiary education and to just below 56% for those without an upper secondary education During the recent economic crisis, the increase in the average unemployment rate for individuals without an upper secondary education was 1.1 points higher than for those with at least an upper secondary degree Overall, the study pointed out that the difference is particularly marked between those who have included upper secondary education and those who have not 17 In the case of PwC, our data indicate that there is a noticeable gap between those with highschool graduates and postgraduates While the pass rate of highschool graduated candidates is 3%, after postgraduate, that rate has increased to 13% That said, education level plays an important role in how employers evaluate and select candidates for their organization It directly affects whether a worker can accept the job or not V Conclusion Summary The case of PwC in this survey is researched as an example of the Application of Probability The results are aggregated and calculated according to the Probability formula on the candidates of the Management Trainee program including factors: Sex, age, academic level, time to know the program MT, candidates experiences, candidates skills The research shows that the gap between people is highest in these factors: Sex, academic level and candidates experiences Therefore, people can know about what is important in a program Overall, gender, age and education level are characteristics that contain at least one variable that is independent with event "Pass" Specifically: + In gender characteristics: Both the "Male" event and the "Female" event are independent with the "Pass" event Thereby, it can be seen that gender is not an important variable when considering candidates in the recruitment process + In the "Age" feature: Event "34+" is independent of the "Pass" event Thereby when considering candidates, potential candidates will focus on the age group 18-33 Employers can also pay more attention to this age when selecting candidates + In the feature "Education level": event "highschool graduation" is independent of event "Pass" Thereby, employers should focus on candidates with college degrees or higher because they are more likely to be potential candidates + In the remaining characteristics, the factors examined in them are not independent of the "Pass" event, so the employers should consider all aspects of the candidate in these characteristics 18 Limitation Our survey on the Application of Probability in evaluating the potential of candidates for the Management Trainee program, the case of PwC is used for the research so that the volunteers still be limited Therefore, the findings will not be thorough enough to improve the accuracy of the result Further research will be conducted to get a more precise and comprehensive outcome VI Reference (JE Sheridan, JW Slocum, R Buda - Journal of Business and Psychology, 1997) https://link.springer.com/article/10.1007/BF02195900 19 (Mahajan, 2015): https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4456898/ (G Shafer, V Vovk , 2005) https://books.google.com.vn/books? hl=vi&lr=&id=dYxsZzMmvHoC&oi=fnd&pg=PR5&dq=probability+fina nce&ots=CR0SJI72Mg&sig=o4mfOKuAtqlSURZedHOuz5SBeQM&redir _esc=y#v=onepage&q=probability%20finance&f=false (B Lipstein - Journal of Marketing Research, 1965) https://journals.sagepub.com/doi/abs/10.1177/002224376500200305 (Julia Astegiano, 2019) "Unraveling the gender productivity gap in science: a meta-analytical review" (Alex Jones , 2019) "The role of team leadership and critical thinking" 20