Employee Attrition: Human Resource concern
Charanjeet Singh Ahluwalia
1. Introduction
Attrition in business can mean the reduction in staff and employees in a company through normal means, such as retirement and resignation, the loss of customers or clients to old age or growing out of the company’s target demographic.Changes in management style, company structure, or other aspects of the company might cause employees to leave the company voluntarily, resulting in a higher attrition rate. Another possible cause of attrition is when a company eliminates a job completely. There are different turnover rates across industries, with hospitality and retail having higher rates compared to other industries. But a high turnover rate can be costly. When you think about your investment in recruiting and training employees and only having them stay on for a short period of time, you are not getting back a return on your investment.Customer attrition generally has a negative effect on the company’s profits and growth. This paper addresses the following issues concerning the attrition of an employee with respect to several paramters. In this paper, we investigate how the general parameters like Education, Department, Monthly Income, OverTime and others impact the attrition of an employee.
2. Literature Review
The specific objective of this literature is to predict if an employee is going to resign or not. The ultimate goal is reduction in attrition using the analysis collected. A proper idea or knowledge about the reasons concerning the attrition of employees helps the human resource team eliminate the skepticism. It majorly helps in cutting down the costs, that a company incurs when its employees resign. It’s rightly said that “It takes a lot of resources to build the Human Resource”. The output variable “Attriton” is a dichotomous variable with values “Yes/No”. The analysis uncovers the factors that lead to employee attrition and explore important questions such as ‘show me a breakdown of distance from home by job role and attrition’ or ‘compare average monthly income by education and attrition’. Methodology: 1. We shall be looking at all variables through some plots and infer about it in our exploratory analysis.2. Through our analysis we intend to build a model which can predict if an employee is about to quit. We will see the implelementaion of logistic regression model which is part of a larger class of algorithms known as Generalized Linear Model (glm).
3. Data Description
For this study, we collected data from IBM Watson Analytics website (https://www.ibm.com/communities/analytics/watson-analytics-blog/hr-employee-attrition/). This is a fictional data set created by IBM data scientists. The original datset is in csv form. It consists of 1470 rows/data points and 35 columns/attributes which tend to impact employee attrition. Some attributes such as EmployeeNumber, EmployeeCount, Over18 and StandardHours,being same for each employee are not related to our study.Therefore among the remaining relevant attributes, there are 16 categorical variables in the dataset viz. (Attrition,BusinessTravel,Department,Education,EducationField,EnvironmentSatisfaction,Gender,JobInvolvement,JobLevel,JobRole,JobSatisfaction,‘’ MaritalStatus,OverTime,PerformanceRating,RelationshipSatisfaction,WorkLifeBalance); and 11 numeric variables namely (Age,DistanceFromHome,MonthlyIncome,NumCompaniesWorked,PercentSalaryHike,TotalWorkingYears,TrainingTimesLastYear,YearsAtCompany,‘’ YearsInCurrentRole,YearsSinceLastPromotion, YearsWithCurrManager). Some categorical variables are coded with numeric values. Such variables are called dummy variables. For example
Education 1 ‘Below College’ 2 ‘College’ 3 ‘Bachelor’ 4 ‘Master’ 5 ‘Doctor’
EnvironmentSatisfaction 1 ‘Low’ 2 ‘Medium’ 3 ‘High’ 4 ‘Very High’
JobInvolvement 1 ‘Low’ 2 ‘Medium’ 3 ‘High’ 4 ‘Very High’
JobSatisfaction 1 ‘Low’ 2 ‘Medium’ 3 ‘High’ 4 ‘Very High’
PerformanceRating 1 ‘Low’ 2 ‘Good’ 3 ‘Excellent’ 4 ‘Outstanding’
RelationshipSatisfaction 1 ‘Low’ 2 ‘Medium’ 3 ‘High’ 4 ‘Very High’
WorkLifeBalance 1 ‘Bad’ 2 ‘Good’ 3 ‘Better’ 4 ‘Best’
#Reading the dataset
setwd("C:/Users/CJ With HP/Desktop/IIM Lucknow/Datasets")
att.df <- read.csv(paste("WA_Fn-UseC_-HR-Employee-Attrition.csv",sep = ""))
names(att.df)[1]<-"Age"
attach(att.df)
#Description of the attributes
str(att.df)## 'data.frame': 1470 obs. of 35 variables:
## $ Age : int 41 49 37 33 27 32 59 30 38 36 ...
## $ Attrition : Factor w/ 2 levels "No","Yes": 2 1 2 1 1 1 1 1 1 1 ...
## $ BusinessTravel : Factor w/ 3 levels "Non-Travel","Travel_Frequently",..: 3 2 3 2 3 2 3 3 2 3 ...
## $ DailyRate : int 1102 279 1373 1392 591 1005 1324 1358 216 1299 ...
## $ Department : Factor w/ 3 levels "Human Resources",..: 3 2 2 2 2 2 2 2 2 2 ...
## $ DistanceFromHome : int 1 8 2 3 2 2 3 24 23 27 ...
## $ Education : int 2 1 2 4 1 2 3 1 3 3 ...
## $ EducationField : Factor w/ 6 levels "Human Resources",..: 2 2 5 2 4 2 4 2 2 4 ...
## $ EmployeeCount : int 1 1 1 1 1 1 1 1 1 1 ...
## $ EmployeeNumber : int 1 2 4 5 7 8 10 11 12 13 ...
## $ EnvironmentSatisfaction : int 2 3 4 4 1 4 3 4 4 3 ...
## $ Gender : Factor w/ 2 levels "Female","Male": 1 2 2 1 2 2 1 2 2 2 ...
## $ HourlyRate : int 94 61 92 56 40 79 81 67 44 94 ...
## $ JobInvolvement : int 3 2 2 3 3 3 4 3 2 3 ...
## $ JobLevel : int 2 2 1 1 1 1 1 1 3 2 ...
## $ JobRole : Factor w/ 9 levels "Healthcare Representative",..: 8 7 3 7 3 3 3 3 5 1 ...
## $ JobSatisfaction : int 4 2 3 3 2 4 1 3 3 3 ...
## $ MaritalStatus : Factor w/ 3 levels "Divorced","Married",..: 3 2 3 2 2 3 2 1 3 2 ...
## $ MonthlyIncome : int 5993 5130 2090 2909 3468 3068 2670 2693 9526 5237 ...
## $ MonthlyRate : int 19479 24907 2396 23159 16632 11864 9964 13335 8787 16577 ...
## $ NumCompaniesWorked : int 8 1 6 1 9 0 4 1 0 6 ...
## $ Over18 : Factor w/ 1 level "Y": 1 1 1 1 1 1 1 1 1 1 ...
## $ OverTime : Factor w/ 2 levels "No","Yes": 2 1 2 2 1 1 2 1 1 1 ...
## $ PercentSalaryHike : int 11 23 15 11 12 13 20 22 21 13 ...
## $ PerformanceRating : int 3 4 3 3 3 3 4 4 4 3 ...
## $ RelationshipSatisfaction: int 1 4 2 3 4 3 1 2 2 2 ...
## $ StandardHours : int 80 80 80 80 80 80 80 80 80 80 ...
## $ StockOptionLevel : int 0 1 0 0 1 0 3 1 0 2 ...
## $ TotalWorkingYears : int 8 10 7 8 6 8 12 1 10 17 ...
## $ TrainingTimesLastYear : int 0 3 3 3 3 2 3 2 2 3 ...
## $ WorkLifeBalance : int 1 3 3 3 3 2 2 3 3 2 ...
## $ YearsAtCompany : int 6 10 0 8 2 7 1 1 9 7 ...
## $ YearsInCurrentRole : int 4 7 0 7 2 7 0 0 7 7 ...
## $ YearsSinceLastPromotion : int 0 1 0 3 2 3 0 0 1 7 ...
## $ YearsWithCurrManager : int 5 7 0 0 2 6 0 0 8 7 ...The attributes are self explanatory.
Hypothesis: The independent variable strongly impact the attrition of an employee, and they can be collectively grouped together to decide upon attrition.
4. Model Analysis
Logistic regression is a method for fitting a regression curve, y = f(x), when y is a categorical variable. The typical use of this model is predicting y given a set of predictors x. The predictors can be continuous, categorical or a mix of both.
The categorical variable y, in general, can assume different values. In the simplest case scenario y is binary meaning that it can assume either the value 1 or 0. A classical example used in machine learning is email classification: given a set of attributes for each email such as number of words, links and pictures, the algorithm should decide whether the email is spam (1) or not (0). In this post we call the model “binomial logistic regression”, since the variable to predict is binary, however, logistic regression can also be used to predict a dependent variable which can assume more than 2 values. In this second case we call the model “multinomial logistic regression”. A typical example for instance, would be classifying films between “Entertaining”, “borderline” or “boring”.
Logistic regression implementation in R
R makes it very easy to fit a logistic regression model. The function to be called is glm() and the fitting process is not so different from the one used in linear regression.
In order to test Hypothesis, we proposed the following model:
#We split the data into two chunks: training and testing set. The training set will be used to fit our model.
train <- att.df[1:799,]
test<-att.df[800:1400,]
model <- glm(Attrition ~ Age+BusinessTravel+Department+DistanceFromHome+
Education+EducationField+EnvironmentSatisfaction+Gender+JobInvolvement+
JobLevel+JobRole+JobSatisfaction+MaritalStatus+MonthlyIncome+NumCompaniesWorked+
OverTime+PercentSalaryHike+PerformanceRating+RelationshipSatisfaction+
TotalWorkingYears+TrainingTimesLastYear+WorkLifeBalance+
YearsAtCompany+YearsInCurrentRole+YearsSinceLastPromotion+
YearsWithCurrManager,family=binomial(link='logit'),data=train)
summary(model)##
## Call:
## glm(formula = Attrition ~ Age + BusinessTravel + Department +
## DistanceFromHome + Education + EducationField + EnvironmentSatisfaction +
## Gender + JobInvolvement + JobLevel + JobRole + JobSatisfaction +
## MaritalStatus + MonthlyIncome + NumCompaniesWorked + OverTime +
## PercentSalaryHike + PerformanceRating + RelationshipSatisfaction +
## TotalWorkingYears + TrainingTimesLastYear + WorkLifeBalance +
## YearsAtCompany + YearsInCurrentRole + YearsSinceLastPromotion +
## YearsWithCurrManager, family = binomial(link = "logit"),
## data = train)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.0043 -0.4501 -0.2306 -0.0739 3.1932
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.150e+01 5.322e+02 -0.022 0.982766
## Age -6.303e-02 1.870e-02 -3.371 0.000749
## BusinessTravelTravel_Frequently 1.974e+00 5.809e-01 3.397 0.000680
## BusinessTravelTravel_Rarely 1.242e+00 5.368e-01 2.315 0.020630
## DepartmentResearch & Development 1.343e+01 5.322e+02 0.025 0.979876
## DepartmentSales 1.241e+01 5.322e+02 0.023 0.981394
## DistanceFromHome 5.480e-02 1.518e-02 3.610 0.000307
## Education -1.416e-02 1.225e-01 -0.116 0.907997
## EducationFieldLife Sciences 6.837e-02 1.322e+00 0.052 0.958766
## EducationFieldMarketing 7.414e-01 1.385e+00 0.535 0.592426
## EducationFieldMedical 7.745e-02 1.318e+00 0.059 0.953129
## EducationFieldOther 4.266e-01 1.416e+00 0.301 0.763285
## EducationFieldTechnical Degree 1.253e+00 1.343e+00 0.933 0.351036
## EnvironmentSatisfaction -5.098e-01 1.224e-01 -4.164 3.12e-05
## GenderMale 4.900e-01 2.633e-01 1.861 0.062752
## JobInvolvement -6.840e-01 1.773e-01 -3.858 0.000114
## JobLevel -1.189e-01 4.370e-01 -0.272 0.785478
## JobRoleHuman Resources 1.552e+01 5.322e+02 0.029 0.976744
## JobRoleLaboratory Technician 2.067e+00 7.027e-01 2.942 0.003260
## JobRoleManager 1.022e+00 1.085e+00 0.942 0.346325
## JobRoleManufacturing Director 1.970e-01 8.023e-01 0.246 0.806014
## JobRoleResearch Director -7.318e-02 1.163e+00 -0.063 0.949819
## JobRoleResearch Scientist 1.190e+00 7.076e-01 1.682 0.092531
## JobRoleSales Executive 2.355e+00 1.492e+00 1.579 0.114428
## JobRoleSales Representative 3.407e+00 1.560e+00 2.184 0.028947
## JobSatisfaction -4.023e-01 1.119e-01 -3.596 0.000323
## MaritalStatusMarried 6.020e-01 3.579e-01 1.682 0.092589
## MaritalStatusSingle 1.823e+00 3.700e-01 4.928 8.30e-07
## MonthlyIncome 3.624e-05 1.134e-04 0.320 0.749292
## NumCompaniesWorked 2.039e-01 5.323e-02 3.830 0.000128
## OverTimeYes 2.251e+00 2.805e-01 8.026 1.01e-15
## PercentSalaryHike 2.623e-02 5.463e-02 0.480 0.631104
## PerformanceRating -2.494e-01 5.370e-01 -0.464 0.642297
## RelationshipSatisfaction -3.057e-01 1.157e-01 -2.643 0.008220
## TotalWorkingYears -1.451e-02 3.963e-02 -0.366 0.714155
## TrainingTimesLastYear -1.129e-01 9.801e-02 -1.152 0.249230
## WorkLifeBalance -5.250e-01 1.827e-01 -2.874 0.004059
## YearsAtCompany 9.193e-02 5.055e-02 1.819 0.068960
## YearsInCurrentRole -1.616e-01 6.191e-02 -2.611 0.009039
## YearsSinceLastPromotion 1.841e-01 5.753e-02 3.200 0.001376
## YearsWithCurrManager -1.465e-01 6.478e-02 -2.261 0.023754
##
## (Intercept)
## Age ***
## BusinessTravelTravel_Frequently ***
## BusinessTravelTravel_Rarely *
## DepartmentResearch & Development
## DepartmentSales
## DistanceFromHome ***
## Education
## EducationFieldLife Sciences
## EducationFieldMarketing
## EducationFieldMedical
## EducationFieldOther
## EducationFieldTechnical Degree
## EnvironmentSatisfaction ***
## GenderMale .
## JobInvolvement ***
## JobLevel
## JobRoleHuman Resources
## JobRoleLaboratory Technician **
## JobRoleManager
## JobRoleManufacturing Director
## JobRoleResearch Director
## JobRoleResearch Scientist .
## JobRoleSales Executive
## JobRoleSales Representative *
## JobSatisfaction ***
## MaritalStatusMarried .
## MaritalStatusSingle ***
## MonthlyIncome
## NumCompaniesWorked ***
## OverTimeYes ***
## PercentSalaryHike
## PerformanceRating
## RelationshipSatisfaction **
## TotalWorkingYears
## TrainingTimesLastYear
## WorkLifeBalance **
## YearsAtCompany .
## YearsInCurrentRole **
## YearsSinceLastPromotion **
## YearsWithCurrManager *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 725.87 on 798 degrees of freedom
## Residual deviance: 448.26 on 758 degrees of freedom
## AIC: 530.26
##
## Number of Fisher Scoring iterations: 14Now we can run the anova() function on the model to analyze the table of deviance
anova(model, test="Chisq")## Analysis of Deviance Table
##
## Model: binomial, link: logit
##
## Response: Attrition
##
## Terms added sequentially (first to last)
##
##
## Df Deviance Resid. Df Resid. Dev Pr(>Chi)
## NULL 798 725.87
## Age 1 31.065 797 694.80 2.496e-08 ***
## BusinessTravel 2 8.372 795 686.43 0.015210 *
## Department 2 2.298 793 684.13 0.316889
## DistanceFromHome 1 6.101 792 678.03 0.013510 *
## Education 1 0.023 791 678.01 0.878955
## EducationField 5 7.552 786 670.46 0.182731
## EnvironmentSatisfaction 1 10.023 785 660.43 0.001546 **
## Gender 1 1.472 784 658.96 0.224988
## JobInvolvement 1 20.252 783 638.71 6.789e-06 ***
## JobLevel 1 16.670 782 622.04 4.448e-05 ***
## JobRole 8 15.308 774 606.73 0.053435 .
## JobSatisfaction 1 9.577 773 597.16 0.001970 **
## MaritalStatus 2 19.656 771 577.50 5.392e-05 ***
## MonthlyIncome 1 0.287 770 577.21 0.591974
## NumCompaniesWorked 1 15.189 769 562.02 9.725e-05 ***
## OverTime 1 74.021 768 488.00 < 2.2e-16 ***
## PercentSalaryHike 1 0.104 767 487.90 0.746720
## PerformanceRating 1 0.254 766 487.64 0.614543
## RelationshipSatisfaction 1 4.847 765 482.80 0.027696 *
## TotalWorkingYears 1 0.436 764 482.36 0.508824
## TrainingTimesLastYear 1 1.705 763 480.66 0.191613
## WorkLifeBalance 1 8.887 762 471.77 0.002873 **
## YearsAtCompany 1 0.001 761 471.77 0.975419
## YearsInCurrentRole 1 8.053 760 463.71 0.004543 **
## YearsSinceLastPromotion 1 10.375 759 453.34 0.001277 **
## YearsWithCurrManager 1 5.075 758 448.26 0.024273 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 15. Disussion
Interpreting the results of our logistic regression model
Now we can analyze the fitting and interpret what the model is telling us. First of all, we can see that (Age, BusinessTravel, DistanceFromHome, EnvironmentSatisfaction, JobInvolvement, JobRole, JobSatisfaction,MaritalStatus, NumCompaniesWorked, OverTime, RelationshipSatisfaction, WorkLifeBalance, YearsInCurrentRole, YearsSinceLastPromotion, YearsWithCurrManager) are statistically significant.
As for the statistically significant variables, Overtime and Marital Staus has the lowest p-value suggesting a strong association.In the logit model the response variable is log odds: ln(odds) = ln(p/(1-p)) = a/x1 + b/x2 + . + z*xn.
The difference between the null deviance and the residual deviance shows how our model is doing against the null model (a model with only the intercept). The wider this gap, the better. Analyzing the anova table we can see the drop in deviance when adding each variable one at a time. A large p-value here indicates that the model without the variable explains more or less the same amount of variation. Ultimately what you would like to see is a significant drop in deviance and the AIC.
6. Conclusion
This paper was motivated by the need for research that could reduce the attrition rate in an industry, therby incrementing the productivity. The unique contribution of this paper is that we investigated the attributes which majorly contribute in the attrition. We found that parameters such as Overtime, Marital Status, Previous Work Experience, Environmental Satisfaction are some of the parameters, which show strong association with attrition, positively or negatively.
7. References
An introduction to logistic regression analysis and reporting CYJ Peng, KL Lee, GM Ingersoll - . journal of educational research, 2002 - Taylor & Francis . & Kravitz, 1994; Tolman & Weisz, 1995)
Goodness-of-fit test for a logistic regression model fitted using survey sample data KJ Archer, S Lemeshow - Stata Journal, 2006
Comparison of landslide susceptibility mapping methodologies for Koyulhisar, Turkey: conditional probability, logistic regression, artificial neural networks, and .I Yilmaz - Environmental Earth Sciences, 2010 - Springer
Calculation of polychotomous logistic regression parameters using individualized regressions
7. Appendix : Online Resources
https://www.analyticsvidhya.com/blog/2015/11/beginners-guide-on-logistic-regression-in-r/
https://rpubs.com/bpr1989/HRAnalysis
http://rpubs.com/SameerMathur/HTNF
http://recruitloop.com/blog/7-ways-reduce-employee-attrition/
https://www.kaggle.com/pavansubhasht/ibm-hr-analytics-attrition-dataset/data
8. R Code supporting the study
1. Creating a descriptive analysis for each variable
str(att.df)## 'data.frame': 1470 obs. of 35 variables:
## $ Age : int 41 49 37 33 27 32 59 30 38 36 ...
## $ Attrition : Factor w/ 2 levels "No","Yes": 2 1 2 1 1 1 1 1 1 1 ...
## $ BusinessTravel : Factor w/ 3 levels "Non-Travel","Travel_Frequently",..: 3 2 3 2 3 2 3 3 2 3 ...
## $ DailyRate : int 1102 279 1373 1392 591 1005 1324 1358 216 1299 ...
## $ Department : Factor w/ 3 levels "Human Resources",..: 3 2 2 2 2 2 2 2 2 2 ...
## $ DistanceFromHome : int 1 8 2 3 2 2 3 24 23 27 ...
## $ Education : int 2 1 2 4 1 2 3 1 3 3 ...
## $ EducationField : Factor w/ 6 levels "Human Resources",..: 2 2 5 2 4 2 4 2 2 4 ...
## $ EmployeeCount : int 1 1 1 1 1 1 1 1 1 1 ...
## $ EmployeeNumber : int 1 2 4 5 7 8 10 11 12 13 ...
## $ EnvironmentSatisfaction : int 2 3 4 4 1 4 3 4 4 3 ...
## $ Gender : Factor w/ 2 levels "Female","Male": 1 2 2 1 2 2 1 2 2 2 ...
## $ HourlyRate : int 94 61 92 56 40 79 81 67 44 94 ...
## $ JobInvolvement : int 3 2 2 3 3 3 4 3 2 3 ...
## $ JobLevel : int 2 2 1 1 1 1 1 1 3 2 ...
## $ JobRole : Factor w/ 9 levels "Healthcare Representative",..: 8 7 3 7 3 3 3 3 5 1 ...
## $ JobSatisfaction : int 4 2 3 3 2 4 1 3 3 3 ...
## $ MaritalStatus : Factor w/ 3 levels "Divorced","Married",..: 3 2 3 2 2 3 2 1 3 2 ...
## $ MonthlyIncome : int 5993 5130 2090 2909 3468 3068 2670 2693 9526 5237 ...
## $ MonthlyRate : int 19479 24907 2396 23159 16632 11864 9964 13335 8787 16577 ...
## $ NumCompaniesWorked : int 8 1 6 1 9 0 4 1 0 6 ...
## $ Over18 : Factor w/ 1 level "Y": 1 1 1 1 1 1 1 1 1 1 ...
## $ OverTime : Factor w/ 2 levels "No","Yes": 2 1 2 2 1 1 2 1 1 1 ...
## $ PercentSalaryHike : int 11 23 15 11 12 13 20 22 21 13 ...
## $ PerformanceRating : int 3 4 3 3 3 3 4 4 4 3 ...
## $ RelationshipSatisfaction: int 1 4 2 3 4 3 1 2 2 2 ...
## $ StandardHours : int 80 80 80 80 80 80 80 80 80 80 ...
## $ StockOptionLevel : int 0 1 0 0 1 0 3 1 0 2 ...
## $ TotalWorkingYears : int 8 10 7 8 6 8 12 1 10 17 ...
## $ TrainingTimesLastYear : int 0 3 3 3 3 2 3 2 2 3 ...
## $ WorkLifeBalance : int 1 3 3 3 3 2 2 3 3 2 ...
## $ YearsAtCompany : int 6 10 0 8 2 7 1 1 9 7 ...
## $ YearsInCurrentRole : int 4 7 0 7 2 7 0 0 7 7 ...
## $ YearsSinceLastPromotion : int 0 1 0 3 2 3 0 0 1 7 ...
## $ YearsWithCurrManager : int 5 7 0 0 2 6 0 0 8 7 ...library(psych)
describe(att.df)## vars n mean sd median trimmed
## Age 1 1470 36.92 9.14 36.0 36.47
## Attrition* 2 1470 1.16 0.37 1.0 1.08
## BusinessTravel* 3 1470 2.61 0.67 3.0 2.76
## DailyRate 4 1470 802.49 403.51 802.0 803.83
## Department* 5 1470 2.26 0.53 2.0 2.25
## DistanceFromHome 6 1470 9.19 8.11 7.0 8.08
## Education 7 1470 2.91 1.02 3.0 2.98
## EducationField* 8 1470 3.25 1.33 3.0 3.10
## EmployeeCount 9 1470 1.00 0.00 1.0 1.00
## EmployeeNumber 10 1470 1024.87 602.02 1020.5 1023.40
## EnvironmentSatisfaction 11 1470 2.72 1.09 3.0 2.78
## Gender* 12 1470 1.60 0.49 2.0 1.62
## HourlyRate 13 1470 65.89 20.33 66.0 66.02
## JobInvolvement 14 1470 2.73 0.71 3.0 2.74
## JobLevel 15 1470 2.06 1.11 2.0 1.90
## JobRole* 16 1470 5.46 2.46 6.0 5.61
## JobSatisfaction 17 1470 2.73 1.10 3.0 2.79
## MaritalStatus* 18 1470 2.10 0.73 2.0 2.12
## MonthlyIncome 19 1470 6502.93 4707.96 4919.0 5667.24
## MonthlyRate 20 1470 14313.10 7117.79 14235.5 14286.48
## NumCompaniesWorked 21 1470 2.69 2.50 2.0 2.36
## Over18* 22 1470 1.00 0.00 1.0 1.00
## OverTime* 23 1470 1.28 0.45 1.0 1.23
## PercentSalaryHike 24 1470 15.21 3.66 14.0 14.80
## PerformanceRating 25 1470 3.15 0.36 3.0 3.07
## RelationshipSatisfaction 26 1470 2.71 1.08 3.0 2.77
## StandardHours 27 1470 80.00 0.00 80.0 80.00
## StockOptionLevel 28 1470 0.79 0.85 1.0 0.67
## TotalWorkingYears 29 1470 11.28 7.78 10.0 10.37
## TrainingTimesLastYear 30 1470 2.80 1.29 3.0 2.72
## WorkLifeBalance 31 1470 2.76 0.71 3.0 2.77
## YearsAtCompany 32 1470 7.01 6.13 5.0 5.99
## YearsInCurrentRole 33 1470 4.23 3.62 3.0 3.85
## YearsSinceLastPromotion 34 1470 2.19 3.22 1.0 1.48
## YearsWithCurrManager 35 1470 4.12 3.57 3.0 3.77
## mad min max range skew kurtosis se
## Age 8.90 18 60 42 0.41 -0.41 0.24
## Attrition* 0.00 1 2 1 1.84 1.39 0.01
## BusinessTravel* 0.00 1 3 2 -1.44 0.69 0.02
## DailyRate 510.01 102 1499 1397 0.00 -1.21 10.52
## Department* 0.00 1 3 2 0.17 -0.40 0.01
## DistanceFromHome 7.41 1 29 28 0.96 -0.23 0.21
## Education 1.48 1 5 4 -0.29 -0.56 0.03
## EducationField* 1.48 1 6 5 0.55 -0.69 0.03
## EmployeeCount 0.00 1 1 0 NaN NaN 0.00
## EmployeeNumber 790.97 1 2068 2067 0.02 -1.23 15.70
## EnvironmentSatisfaction 1.48 1 4 3 -0.32 -1.20 0.03
## Gender* 0.00 1 2 1 -0.41 -1.83 0.01
## HourlyRate 26.69 30 100 70 -0.03 -1.20 0.53
## JobInvolvement 0.00 1 4 3 -0.50 0.26 0.02
## JobLevel 1.48 1 5 4 1.02 0.39 0.03
## JobRole* 2.97 1 9 8 -0.36 -1.20 0.06
## JobSatisfaction 1.48 1 4 3 -0.33 -1.22 0.03
## MaritalStatus* 1.48 1 3 2 -0.15 -1.12 0.02
## MonthlyIncome 3260.24 1009 19999 18990 1.37 0.99 122.79
## MonthlyRate 9201.76 2094 26999 24905 0.02 -1.22 185.65
## NumCompaniesWorked 1.48 0 9 9 1.02 0.00 0.07
## Over18* 0.00 1 1 0 NaN NaN 0.00
## OverTime* 0.00 1 2 1 0.96 -1.07 0.01
## PercentSalaryHike 2.97 11 25 14 0.82 -0.31 0.10
## PerformanceRating 0.00 3 4 1 1.92 1.68 0.01
## RelationshipSatisfaction 1.48 1 4 3 -0.30 -1.19 0.03
## StandardHours 0.00 80 80 0 NaN NaN 0.00
## StockOptionLevel 1.48 0 3 3 0.97 0.35 0.02
## TotalWorkingYears 5.93 0 40 40 1.11 0.91 0.20
## TrainingTimesLastYear 1.48 0 6 6 0.55 0.48 0.03
## WorkLifeBalance 0.00 1 4 3 -0.55 0.41 0.02
## YearsAtCompany 4.45 0 40 40 1.76 3.91 0.16
## YearsInCurrentRole 4.45 0 18 18 0.92 0.47 0.09
## YearsSinceLastPromotion 1.48 0 15 15 1.98 3.59 0.08
## YearsWithCurrManager 4.45 0 17 17 0.83 0.16 0.092. Creating a one way contingency table for all the categorical variables in the dataset
table(Attrition)## Attrition
## No Yes
## 1233 237table(BusinessTravel)## BusinessTravel
## Non-Travel Travel_Frequently Travel_Rarely
## 150 277 1043table(Department)## Department
## Human Resources Research & Development Sales
## 63 961 446table(EducationField)## EducationField
## Human Resources Life Sciences Marketing Medical
## 27 606 159 464
## Other Technical Degree
## 82 132table(Education)## Education
## 1 2 3 4 5
## 170 282 572 398 48table(EnvironmentSatisfaction)## EnvironmentSatisfaction
## 1 2 3 4
## 284 287 453 446table(Gender)## Gender
## Female Male
## 588 882table(JobInvolvement)## JobInvolvement
## 1 2 3 4
## 83 375 868 144table(JobRole)## JobRole
## Healthcare Representative Human Resources
## 131 52
## Laboratory Technician Manager
## 259 102
## Manufacturing Director Research Director
## 145 80
## Research Scientist Sales Executive
## 292 326
## Sales Representative
## 83table(JobLevel)## JobLevel
## 1 2 3 4 5
## 543 534 218 106 69table(JobSatisfaction)## JobSatisfaction
## 1 2 3 4
## 289 280 442 459table(MaritalStatus)## MaritalStatus
## Divorced Married Single
## 327 673 470table(OverTime)## OverTime
## No Yes
## 1054 4163. Creating a two way contingency table for all the categorical variables in the dataset
mytable<- xtabs(~PerformanceRating+Attrition,data=att.df)
round(prop.table(mytable,1)*100,2)## Attrition
## PerformanceRating No Yes
## 3 83.92 16.08
## 4 83.63 16.37mytable<- xtabs(~OverTime+Attrition,data=att.df)
round(prop.table(mytable,1)*100,2)## Attrition
## OverTime No Yes
## No 89.56 10.44
## Yes 69.47 30.53mytable<- xtabs(~WorkLifeBalance+Attrition,data=att.df)
round(prop.table(mytable,1)*100,2)## Attrition
## WorkLifeBalance No Yes
## 1 68.75 31.25
## 2 83.14 16.86
## 3 85.78 14.22
## 4 82.35 17.65mytable<- xtabs(~JobRole+Attrition,data=att.df)
round(prop.table(mytable,1)*100,2)## Attrition
## JobRole No Yes
## Healthcare Representative 93.13 6.87
## Human Resources 76.92 23.08
## Laboratory Technician 76.06 23.94
## Manager 95.10 4.90
## Manufacturing Director 93.10 6.90
## Research Director 97.50 2.50
## Research Scientist 83.90 16.10
## Sales Executive 82.52 17.48
## Sales Representative 60.24 39.76mytable<- xtabs(~NumCompaniesWorked+Attrition,data=att.df)
round(prop.table(mytable,1)*100,2)## Attrition
## NumCompaniesWorked No Yes
## 0 88.32 11.68
## 1 81.19 18.81
## 2 89.04 10.96
## 3 89.94 10.06
## 4 87.77 12.23
## 5 74.60 25.40
## 6 77.14 22.86
## 7 77.03 22.97
## 8 87.76 12.24
## 9 76.92 23.08mytable<- xtabs(~MaritalStatus+Attrition,data=att.df)
round(prop.table(mytable,1)*100,2) ## Attrition
## MaritalStatus No Yes
## Divorced 89.91 10.09
## Married 87.52 12.48
## Single 74.47 25.53mytable<- xtabs(~Gender+Attrition,data=att.df)
round(prop.table(mytable,1)*100,2)## Attrition
## Gender No Yes
## Female 85.20 14.80
## Male 82.99 17.01mytable<- xtabs(~EnvironmentSatisfaction+Attrition,data=att.df)
round(prop.table(mytable,1)*100,2)## Attrition
## EnvironmentSatisfaction No Yes
## 1 74.65 25.35
## 2 85.02 14.98
## 3 86.31 13.69
## 4 86.55 13.45mytable<- xtabs(~BusinessTravel+Attrition,data=att.df)
round(prop.table(mytable,1)*100,2)## Attrition
## BusinessTravel No Yes
## Non-Travel 92.00 8.00
## Travel_Frequently 75.09 24.91
## Travel_Rarely 85.04 14.96mytable<- xtabs(~EducationField+Attrition,data=att.df)
round(prop.table(mytable,1)*100,2)## Attrition
## EducationField No Yes
## Human Resources 74.07 25.93
## Life Sciences 85.31 14.69
## Marketing 77.99 22.01
## Medical 86.42 13.58
## Other 86.59 13.41
## Technical Degree 75.76 24.24mytable<- xtabs(~JobSatisfaction+Attrition,data=att.df)
round(prop.table(mytable,1)*100,2)## Attrition
## JobSatisfaction No Yes
## 1 77.16 22.84
## 2 83.57 16.43
## 3 83.48 16.52
## 4 88.67 11.33mytable<- xtabs(~Education+Attrition,data=att.df)
round(prop.table(mytable,1)*100,2)## Attrition
## Education No Yes
## 1 81.76 18.24
## 2 84.40 15.60
## 3 82.69 17.31
## 4 85.43 14.57
## 5 89.58 10.424. Boxplots
boxplot(Age~Attrition,main="Boxplot",xlab="Age",ylab = "Attrition(Yes/No)",horizontal=TRUE,col=c("pink","lightblue"))
boxplot(DistanceFromHome~Attrition,main="Boxplot",xlab="DistanceFromHome",ylab = "Attrition(Yes/No)",horizontal=TRUE,col=c("pink","lightblue"))
boxplot(MonthlyIncome~Attrition,main="Boxplot",xlab="MonthlyIncome",ylab = "Attrition(Yes/No)",horizontal=TRUE,col=c("pink","lightblue"))
boxplot(YearsWithCurrManager~Attrition,main="Boxplot",xlab="YearsWithCurManager",ylab = "Attrition(Yes/No)",horizontal=TRUE,col=c("pink","lightblue"))
boxplot(MonthlyRate~Attrition,main="Boxplot",xlab="MonthlyRate",ylab = "Attrition(Yes/No)",horizontal=TRUE,col=c("pink","lightblue"))
boxplot(DailyRate~Attrition,main="Boxplot",xlab="DailyRate",ylab = "Attrition(Yes/No)",horizontal=TRUE,col=c("pink","lightblue"))
boxplot(HourlyRate~Attrition,main="Boxplot",xlab="HourlyRate",ylab = "Attrition(Yes/No)",horizontal=TRUE,col=c("pink","lightblue"))
5.Histograms
hist(Age,xlab="age",ylab="count",breaks=20,main="Age variability in the company",col="lightblue",freq=FALSE)
hist(MonthlyIncome,xlab="MonthlyIncome",ylab="count",breaks=20,main="MonthlyIncome",col="lightblue",ylim=c(0,400))
hist(YearsAtCompany,xlab="YearsAtCompany",ylab="count",breaks=20,main="YearsAtcompany",col="lightblue",ylim=c(0,400))
hist(YearsWithCurrManager,xlab="YearswithCurManager",ylab="count",breaks=20,main="YearsWithCurManager",col="lightblue",ylim=c(0,400))
hist(PercentSalaryHike,xlab="PercentSalaryHike",ylab="count",breaks=20,main="PercentSalaryHike",col="lightblue")
library(lattice)
histogram(~Attrition|JobRole) 
histogram(~Attrition|Department,layout=c(4,1),col=c("lightblue","pink")) 
histogram(~PercentSalaryHike|Attrition) 
histogram(~Education|Attrition) 
6. CorrelationMatrix
round(cor(att.df[,c(1,4,6,7,11,13,14,15,17,19,20,21,24,25,26,29:35)]),2)## Age DailyRate DistanceFromHome Education
## Age 1.00 0.01 0.00 0.21
## DailyRate 0.01 1.00 0.00 -0.02
## DistanceFromHome 0.00 0.00 1.00 0.02
## Education 0.21 -0.02 0.02 1.00
## EnvironmentSatisfaction 0.01 0.02 -0.02 -0.03
## HourlyRate 0.02 0.02 0.03 0.02
## JobInvolvement 0.03 0.05 0.01 0.04
## JobLevel 0.51 0.00 0.01 0.10
## JobSatisfaction 0.00 0.03 0.00 -0.01
## MonthlyIncome 0.50 0.01 -0.02 0.09
## MonthlyRate 0.03 -0.03 0.03 -0.03
## NumCompaniesWorked 0.30 0.04 -0.03 0.13
## PercentSalaryHike 0.00 0.02 0.04 -0.01
## PerformanceRating 0.00 0.00 0.03 -0.02
## RelationshipSatisfaction 0.05 0.01 0.01 -0.01
## TotalWorkingYears 0.68 0.01 0.00 0.15
## TrainingTimesLastYear -0.02 0.00 -0.04 -0.03
## WorkLifeBalance -0.02 -0.04 -0.03 0.01
## YearsAtCompany 0.31 -0.03 0.01 0.07
## YearsInCurrentRole 0.21 0.01 0.02 0.06
## YearsSinceLastPromotion 0.22 -0.03 0.01 0.05
## YearsWithCurrManager 0.20 -0.03 0.01 0.07
## EnvironmentSatisfaction HourlyRate JobInvolvement
## Age 0.01 0.02 0.03
## DailyRate 0.02 0.02 0.05
## DistanceFromHome -0.02 0.03 0.01
## Education -0.03 0.02 0.04
## EnvironmentSatisfaction 1.00 -0.05 -0.01
## HourlyRate -0.05 1.00 0.04
## JobInvolvement -0.01 0.04 1.00
## JobLevel 0.00 -0.03 -0.01
## JobSatisfaction -0.01 -0.07 -0.02
## MonthlyIncome -0.01 -0.02 -0.02
## MonthlyRate 0.04 -0.02 -0.02
## NumCompaniesWorked 0.01 0.02 0.02
## PercentSalaryHike -0.03 -0.01 -0.02
## PerformanceRating -0.03 0.00 -0.03
## RelationshipSatisfaction 0.01 0.00 0.03
## TotalWorkingYears 0.00 0.00 -0.01
## TrainingTimesLastYear -0.02 -0.01 -0.02
## WorkLifeBalance 0.03 0.00 -0.01
## YearsAtCompany 0.00 -0.02 -0.02
## YearsInCurrentRole 0.02 -0.02 0.01
## YearsSinceLastPromotion 0.02 -0.03 -0.02
## YearsWithCurrManager 0.00 -0.02 0.03
## JobLevel JobSatisfaction MonthlyIncome
## Age 0.51 0.00 0.50
## DailyRate 0.00 0.03 0.01
## DistanceFromHome 0.01 0.00 -0.02
## Education 0.10 -0.01 0.09
## EnvironmentSatisfaction 0.00 -0.01 -0.01
## HourlyRate -0.03 -0.07 -0.02
## JobInvolvement -0.01 -0.02 -0.02
## JobLevel 1.00 0.00 0.95
## JobSatisfaction 0.00 1.00 -0.01
## MonthlyIncome 0.95 -0.01 1.00
## MonthlyRate 0.04 0.00 0.03
## NumCompaniesWorked 0.14 -0.06 0.15
## PercentSalaryHike -0.03 0.02 -0.03
## PerformanceRating -0.02 0.00 -0.02
## RelationshipSatisfaction 0.02 -0.01 0.03
## TotalWorkingYears 0.78 -0.02 0.77
## TrainingTimesLastYear -0.02 -0.01 -0.02
## WorkLifeBalance 0.04 -0.02 0.03
## YearsAtCompany 0.53 0.00 0.51
## YearsInCurrentRole 0.39 0.00 0.36
## YearsSinceLastPromotion 0.35 -0.02 0.34
## YearsWithCurrManager 0.38 -0.03 0.34
## MonthlyRate NumCompaniesWorked PercentSalaryHike
## Age 0.03 0.30 0.00
## DailyRate -0.03 0.04 0.02
## DistanceFromHome 0.03 -0.03 0.04
## Education -0.03 0.13 -0.01
## EnvironmentSatisfaction 0.04 0.01 -0.03
## HourlyRate -0.02 0.02 -0.01
## JobInvolvement -0.02 0.02 -0.02
## JobLevel 0.04 0.14 -0.03
## JobSatisfaction 0.00 -0.06 0.02
## MonthlyIncome 0.03 0.15 -0.03
## MonthlyRate 1.00 0.02 -0.01
## NumCompaniesWorked 0.02 1.00 -0.01
## PercentSalaryHike -0.01 -0.01 1.00
## PerformanceRating -0.01 -0.01 0.77
## RelationshipSatisfaction 0.00 0.05 -0.04
## TotalWorkingYears 0.03 0.24 -0.02
## TrainingTimesLastYear 0.00 -0.07 -0.01
## WorkLifeBalance 0.01 -0.01 0.00
## YearsAtCompany -0.02 -0.12 -0.04
## YearsInCurrentRole -0.01 -0.09 0.00
## YearsSinceLastPromotion 0.00 -0.04 -0.02
## YearsWithCurrManager -0.04 -0.11 -0.01
## PerformanceRating RelationshipSatisfaction
## Age 0.00 0.05
## DailyRate 0.00 0.01
## DistanceFromHome 0.03 0.01
## Education -0.02 -0.01
## EnvironmentSatisfaction -0.03 0.01
## HourlyRate 0.00 0.00
## JobInvolvement -0.03 0.03
## JobLevel -0.02 0.02
## JobSatisfaction 0.00 -0.01
## MonthlyIncome -0.02 0.03
## MonthlyRate -0.01 0.00
## NumCompaniesWorked -0.01 0.05
## PercentSalaryHike 0.77 -0.04
## PerformanceRating 1.00 -0.03
## RelationshipSatisfaction -0.03 1.00
## TotalWorkingYears 0.01 0.02
## TrainingTimesLastYear -0.02 0.00
## WorkLifeBalance 0.00 0.02
## YearsAtCompany 0.00 0.02
## YearsInCurrentRole 0.03 -0.02
## YearsSinceLastPromotion 0.02 0.03
## YearsWithCurrManager 0.02 0.00
## TotalWorkingYears TrainingTimesLastYear
## Age 0.68 -0.02
## DailyRate 0.01 0.00
## DistanceFromHome 0.00 -0.04
## Education 0.15 -0.03
## EnvironmentSatisfaction 0.00 -0.02
## HourlyRate 0.00 -0.01
## JobInvolvement -0.01 -0.02
## JobLevel 0.78 -0.02
## JobSatisfaction -0.02 -0.01
## MonthlyIncome 0.77 -0.02
## MonthlyRate 0.03 0.00
## NumCompaniesWorked 0.24 -0.07
## PercentSalaryHike -0.02 -0.01
## PerformanceRating 0.01 -0.02
## RelationshipSatisfaction 0.02 0.00
## TotalWorkingYears 1.00 -0.04
## TrainingTimesLastYear -0.04 1.00
## WorkLifeBalance 0.00 0.03
## YearsAtCompany 0.63 0.00
## YearsInCurrentRole 0.46 -0.01
## YearsSinceLastPromotion 0.40 0.00
## YearsWithCurrManager 0.46 0.00
## WorkLifeBalance YearsAtCompany YearsInCurrentRole
## Age -0.02 0.31 0.21
## DailyRate -0.04 -0.03 0.01
## DistanceFromHome -0.03 0.01 0.02
## Education 0.01 0.07 0.06
## EnvironmentSatisfaction 0.03 0.00 0.02
## HourlyRate 0.00 -0.02 -0.02
## JobInvolvement -0.01 -0.02 0.01
## JobLevel 0.04 0.53 0.39
## JobSatisfaction -0.02 0.00 0.00
## MonthlyIncome 0.03 0.51 0.36
## MonthlyRate 0.01 -0.02 -0.01
## NumCompaniesWorked -0.01 -0.12 -0.09
## PercentSalaryHike 0.00 -0.04 0.00
## PerformanceRating 0.00 0.00 0.03
## RelationshipSatisfaction 0.02 0.02 -0.02
## TotalWorkingYears 0.00 0.63 0.46
## TrainingTimesLastYear 0.03 0.00 -0.01
## WorkLifeBalance 1.00 0.01 0.05
## YearsAtCompany 0.01 1.00 0.76
## YearsInCurrentRole 0.05 0.76 1.00
## YearsSinceLastPromotion 0.01 0.62 0.55
## YearsWithCurrManager 0.00 0.77 0.71
## YearsSinceLastPromotion YearsWithCurrManager
## Age 0.22 0.20
## DailyRate -0.03 -0.03
## DistanceFromHome 0.01 0.01
## Education 0.05 0.07
## EnvironmentSatisfaction 0.02 0.00
## HourlyRate -0.03 -0.02
## JobInvolvement -0.02 0.03
## JobLevel 0.35 0.38
## JobSatisfaction -0.02 -0.03
## MonthlyIncome 0.34 0.34
## MonthlyRate 0.00 -0.04
## NumCompaniesWorked -0.04 -0.11
## PercentSalaryHike -0.02 -0.01
## PerformanceRating 0.02 0.02
## RelationshipSatisfaction 0.03 0.00
## TotalWorkingYears 0.40 0.46
## TrainingTimesLastYear 0.00 0.00
## WorkLifeBalance 0.01 0.00
## YearsAtCompany 0.62 0.77
## YearsInCurrentRole 0.55 0.71
## YearsSinceLastPromotion 1.00 0.51
## YearsWithCurrManager 0.51 1.007. Creating a corrgram
library(corrplot)## corrplot 0.84 loadedcorrplot(corr=cor(att.df[,c(1,4,6,7,11,13,14,15,17,19,20,21,24,25,26,29:35)],use="complete.obs"),method="ellipse")
8. Checking hypothesis using t-test
H1. To check whether there is a significant difference in the means of the monthly income of the employees who leave and those who don’t
log.trans.Income = log(MonthlyIncome)
t.test(log.trans.Income~Attrition,var.equal=TRUE)##
## Two Sample t-test
##
## data: log.trans.Income by Attrition
## t = 7.7481, df = 1468, p-value = 1.73e-14
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 0.2673770 0.4486555
## sample estimates:
## mean in group No mean in group Yes
## 8.610236 8.252220H2. To check whether there is a significant difference in the means of the monthly rate of the employees who leave and those who don’t
log.trans.Rate = log(MonthlyRate)
t.test(log.trans.Rate~Attrition,var.equal=TRUE)##
## Two Sample t-test
##
## data: log.trans.Rate by Attrition
## t = -0.47592, df = 1468, p-value = 0.6342
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.10954526 0.06676779
## sample estimates:
## mean in group No mean in group Yes
## 9.398882 9.420271H3. To check whether there is a significant difference in the means of the daily rate of the employees who leave and those who don’t
log.trans.DailyRate = log(DailyRate)
t.test(log.trans.DailyRate~Attrition,var.equal=TRUE)##
## Two Sample t-test
##
## data: log.trans.DailyRate by Attrition
## t = 1.9013, df = 1468, p-value = 0.05746
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.002824123 0.180830501
## sample estimates:
## mean in group No mean in group Yes
## 6.525604 6.4366019. Chi-square test
mytable<- xtabs(~BusinessTravel+Attrition,data=att.df)
round(prop.table(mytable,1)*100,2)## Attrition
## BusinessTravel No Yes
## Non-Travel 92.00 8.00
## Travel_Frequently 75.09 24.91
## Travel_Rarely 85.04 14.96chisq.test(mytable)##
## Pearson's Chi-squared test
##
## data: mytable
## X-squared = 24.182, df = 2, p-value = 5.609e-06mytable<- xtabs(~JobSatisfaction+Attrition,data=att.df)
round(prop.table(mytable,1)*100,2)## Attrition
## JobSatisfaction No Yes
## 1 77.16 22.84
## 2 83.57 16.43
## 3 83.48 16.52
## 4 88.67 11.33chisq.test(mytable) ##
## Pearson's Chi-squared test
##
## data: mytable
## X-squared = 17.505, df = 3, p-value = 0.0005563library(vcd)## Loading required package: grid##
## Attaching package: 'vcd'## The following object is masked from 'att.df':
##
## JobSatisfactionfisher.test(mytable)##
## Fisher's Exact Test for Count Data
##
## data: mytable
## p-value = 0.0005767
## alternative hypothesis: two.sidedassocstats(mytable)## X^2 df P(> X^2)
## Likelihood Ratio 17.356 3 0.00059691
## Pearson 17.505 3 0.00055630
##
## Phi-Coefficient : NA
## Contingency Coeff.: 0.108
## Cramer's V : 0.109