Retail Employee Performance Analysis

The provided assignment is a statistical analysis of retail employee performance, examining variables such as dedication to work, overall tasks accomplished, and reception of rewards and recognition. The study finds that average ratings of work in all four weeks, with respect to three levels of difficulty, are equal for both types of genders. It also identifies that 'Levels of assignment quality' could be a significant predictor of reward and recognition. The analysis suggests that as employees' performance increases, so does the probability of receiving rewards and recognitions.

Running head: STATISTICS
Performance Assessing Factors in Retail Company
Name of the Student:
Name of the University:
Author’s Note:

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Executive Summary
The fictitious case study highlights the internal scenario of a retail company. The conditions
of employees depend on some personal inherent factors and behavioural aspects. It prospects
the promotion, recognition and improvement of the employee. The data description, aims-
objectives and hypotheses are stated properly. The data is analysed by linear regression,
single t-test, independent t-tests, cross-tabs, chi-square tests and one-way ANOVA is
executed for drawing conclusions and inferences. At last, interpretation about employees and
working levels are discussed. The aspects of R&R output are elaborately discussed in the
following. The analysis is incorporated with the help of SPSS-20.

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Table of Contents
Introduction:...............................................................................................................................4
Background:...........................................................................................................................4
Aims and Objectives:.............................................................................................................4
Description of Data:...............................................................................................................4
Hypotheses:................................................................................................................................4
Analysis of Data:........................................................................................................................5
A. Descriptive Statistics:..................................................................................................5
B. Regression Analysis:...................................................................................................8
1. Average monthly rating vs. IQ level, Age, Monthly completed assignment and
Average daily sleeping hours.............................................................................................8
C. Single t-test:...............................................................................................................11
1. IQ level..................................................................................................................12
2. Monthly completed assignment.............................................................................12
3. Average monthly rating.........................................................................................13
D. Independent t-test:.....................................................................................................13
1. Average monthly rating with respect to “R&R” received or not:..........................13
2. Monthly completed assignment with respect to “R&R” received or not:.............14
E. Cross tabulation:........................................................................................................15
1. Smoking habit and Overall task accomplished:.....................................................15
2. Drinking habit and Overall task accomplished:.....................................................16

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3. Gender and Overall tasks accomplished:...............................................................18
F. Chi-square test:..............................................................................................................19
1. Smoking habit and drinking habit:.........................................................................19
2. Overall level of tasks accomplished and “R&R” received:...................................21
G. One-way ANOVA:....................................................................................................24
1. Average monthly ratings with respect to Level of tasks accomplished:................24
2. Monthly completed assignment with respect to Gender:.......................................26
Conclusion:..............................................................................................................................27
References:...............................................................................................................................28

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Introduction:
Background:
The report considers the fictitious data set of a retail company. The report aims to
discover the inherent facts about the status of employees in that company. Measuring
effectiveness is a key point to ensure the reward and recognition of the employees in that
company. Many factors like as physiological, behavioural and experience put their influences
in the performance of the employees (Source: Greatplacetowork.in., 2018). Betterment of
these factors helps to result lower attrition rate, increment of customer satisfaction and
retention, enhanced productivity, greater peer recognition and referral of higher employee.
The analysis intends to find out the relevance among personal profile, individual
habits and professional performance indicators of employees. Not only that, the research
analysis also finds how these factors cause the professional achievement of the employees.
The report discusses about data analysis executed with the help of SPSS 20.
Aims and Objectives:
The analysis focuses to find and examine the effect of several determining factor and
consistent factor of the performance of employees. According to this analysis, the number of
monthly completed assignments and difficulty level of work solved and average rating of
four weeks (monthly) are the main determining factors that render the achievement of R&R
of the employees in the company. The data analysis has an objective to verify the
performance of the employees on the basis of situational and environmental factor, individual
behavioural differences and variability of personal habits.
Description of Data:
The data set involves more than two variables as asked in the requirement files. The
categorical variables are “Gender”, “Smoking habits”, “Drinking habits” and the “Difficulty
level of accomplished task” and “R&R received or not”. The numerical variables are age,
average sleeping hours, monthly completed assignments, IQ level, overall level of task
accomplished, rating of work of four consecutive weeks and average rating of the month.
Hypotheses:
1)
Null Hypothesis (H0): Monthly average rating of all employees is associated with IQ level,
age, daily average sleeping hours and monthly amounts of tasks accomplished.
Alternative Hypothesis (HA): Monthly average rating of all employees is not associated with
IQ level, age, daily average sleeping hours and monthly amounts of tasks accomplished.
2)

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Null Hypothesis (H0): Smoking habit and drinking habit among employees is associated to
each other.
Alternative Hypothesis (HA): Smoking habit and drinking habit among employees is
independent to each other.
3)
Null Hypothesis (H0): Overall tasks accomplished and R&R received among employees is
associated to each other.
Alternative Hypothesis (HA): Overall tasks accomplished and R&R received among
employees is independent to each other.
4)
Null Hypothesis (H0): Average monthly ratings with respect to levels of tasks accomplished
of the employees are not equal.
Alternative Hypothesis (HA): Average monthly ratings with respect to levels of tasks
accomplished of the employees are not equal.
5)
Null Hypothesis (H0): Number of monthly accomplished assignments with respect to Gender
of the employees is equal.
Alternative Hypothesis (HA): Number of monthly accomplished assignments with respect to
Gender of the employees is not equal.
Analysis of Data:
A. Descriptive Statistics:
Table 1: The descriptive statistics of quantitative variables
The average “Age” of the 40 employees of the company is 30 years with standard
deviation 5.5 years. The age of the employees ranges from 23 years to 42 years. On an
average, the daily sleeping hours is 7 hours having standard deviation 2 hours. A person

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sleeps at most 10.5 hours and at least 3 hours (Source: Understanding Descriptive and
Inferential Statistics., 2018).
The average amount of monthly completed assignment completed by all the employees is
36. The minimum amount of monthly completed assignment is 25 and maximum amount of
monthly completed assignment by an employee is 47.
The IQ level is measured by an ordinal scale. The minimum IQ level of an employee is
found as 78 and maximum IQ level of an employee is 287 with the IQ range 209. The mean
score of the IQ level of all the 40 employees is 153. The standard deviation of the IQ level is
42.
The mean working rating of the employees is in all the four weeks is 4.25 out of 5. It
indicates a satisfactory scenario of the company. The spread of average rating of work is 0.2.
An employee has monthly minimum average rating 3.85 and maximum average rating 4.6.
Figure 1: Frequency distribution of Gender
The graph shows that male employees are significantly greater than female employees
in the company.
Figure 2: Distribution of age of the employees

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The fitted histogram plot indicates that the distribution of age is not normally
distributed.
Figure 3: Frequency Distribution of overall difficulty level of the assignments
The overall difficulty level of tasks of the employees is mostly “Hard” followed by
“Medium”. The employees whose levels of assignments are “Easy” are least in frequency.
Figure 4: Distribution of Level of IQ

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The distribution of IQ level shows that neglecting one outlier, the median of the IQ
level is just above 150 ranging in a very high range.
Figure 5: Average monthly rating of the employees vs. number of monthly completed assignments
The comparative distribution of average monthly rating and number of monthly
completed assignment is scattered.
B. Regression Analysis:
1. Average monthly rating vs. IQ level, Age, Monthly completed assignment and
Average daily sleeping hours.
Table 2: Tables of Linear Regression Model

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The linear model finds linear association between response (dependent) and predictor
(independent) variables. The regression equation undertakes average monthly rating of work
of the employees as dependent factor. The independent variables are IQ level, age, number of
monthly completed assignments and amount of daily sleeping hours.
The value of multiple R-square is found as 0.688. The measure is also known as
“Coefficient of Variation”. Therefore, the independent variables can describe only 68.8%
variability of the dependent variable. According to the R2 value, it could be stated that the
linear relation between the dependent and independent variables is moderately strong.
The significant p-value of F-statistic of the model is 0.0(<0.05). Therefore, we accept
the null hypothesis of significant linear relation between dependent variable and independent
variables. It is 95% evident that the dependent factor is predicted by independent variables
(Source: Linear Regression Analysis in SPSS Statistics, 2018).

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The ANOVA table of linear regression model indicates that- according to the slope
(B-values) all the factors except IQ level is negativity associated with the average rating of all
the four weeks. Therefore, due to increase of IQ level, average rating of the work of the four
weeks also increases.
The linear regression model is –
Avg_monthly_rating = 4.34 – 0.007*Age – 0.027*Avg_daily_sleeping_hours –
0.004*Monthly_completed_assignment + 0.003*IQ_level.
The factors that have significant p-values of the t-statistics less than 0.05, interpret
that those factors significantly predicts the outcome variable. The p-value refers that IQ level
(0.0<0.05) significantly predicts outcome variable. Age (p-value = 0.058), average daily
sleeping hours = 0.053 and monthly completed assignments (p-value = 0.34) significantly do
not predict the response variable. Hence, the null hypothesis of linear association between
dependent and independent variables is accepted.
Figure 6: Normal Probability Plot of Linear regression Model

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The normal probability plot indicates that the fitting of the regression model is good.
Figure 7: The residual plot of standardized predicted value
C. Single t-test:
The One-sample t-test helps to determine the normality of the dataset. It also helps to
verify whether there is any significant outlier in the dataset or not (Source: One-Sample T-
Test in SPSS Statistics, 2018).

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1. IQ level
Table 3: One sample t-test of IQ level
Mean IQ level (M = 152.8, SD = 42.74) is greater than population “normal” IQ level
(average hypothetical IQ = 150). The calculated value t(39) = 0.419, p-value = 0.678. The
significant p-value is greater than 0.05. Therefore, it is 95% probable that average IQ level of
40 employees is 140 with fulfilling the assumption of normality. The 95% confidence
intervals of difference of calculated and hypothetical IQ level are (-10.7, 16.3).
2. Monthly completed assignment
Table 4: One sample t-test of Monthly Completed Assignment
Mean number of completed assignment (M = 35.55, SD = 6.28) is greater than population
“normal” number of completed assignment (average hypothetical monthly completed
assignment = 35). The calculated value t(39) = 0.554, p-value = 0.583. The significant p-
value is greater than 0.05. Therefore, it is 95% probable that average number of completed
assignment of 40 employees is 35 with fulfilling the assumption of normality. The 95%
confidence intervals of difference of calculated and hypothetical monthly completed
assignment are (-1.457, 2.56).

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3. Average monthly rating
Table 5: One sample t-test of Average Monthly Rating
Mean average monthly rating (M = 4.2462, SD = 0.19195) is greater than population
“normal” average monthly rating (average hypothetical average monthly rating = 4). The
calculated value t(39) = 8.114, p-value = 0.0. The significant p-value is less than 0.05.
Therefore, it is 95% probable that average monthly rating of 40 employees is 4 with fulfilling
the assumption of normality. The 95% confidence intervals of difference of calculated and
hypothetical average monthly rating are (0.1849, 0.3076).
D. Independent t-test:
1. Average monthly rating with respect to “R&R” received or not:
Table 6: Average Monthly Rating according to the “R&R” receipt
The people who received R&R have average ratings in all the four weeks 4.46,
whereas the people who did not receive R&R have average ratings in all the four weeks 4.18.

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The monthly average work ratings of two groups, grouped by achievement of R&R have
F-statistic = 3.307 with significant p-value = 0.077 (>0.05). Hence, by Levene’s test of
equality, we found that these two groups have equal variances (Source: Independent t-test in
SPSS Statistics, 2018). The t-test for equality of means shows significant p-value = 0.0 with t-
statistic. Hence, these two groups have unequal averages at 5% level of significance.
2. Monthly completed assignment with respect to “R&R” received or not:
Table 7: Monthly Completed Assignment according to the “R&R” receipt
The people who received R&R performed average monthly assignments in all the four
weeks 37.56, whereas the people who did not receive R&R have performed average monthly
assignments in all the four weeks 34.97.

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The monthly average work ratings of two groups, grouped by achievement of R&R have
F-statistic = 11.751 with significant p-value = 0.001 (<0.05). Hence, by Levene’s test of
equality, we found that these two groups have unequal variances. The t-test for equality of
means shows significant p-value = 0.119 (unequal variances are assumed) with t-statistic.
Hence, these two groups have equal averages at 5% level of significance.
E. Cross tabulation:
1. Smoking habit and Overall task accomplished:
Table 8: The Cross tabulation between Smoking habit and Overall level of task accomplished
(Packages et al., 2018)
The cross-tabulation table hereby shows –

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a) The frequencies of employees who smoke and perform easy task is 4
b) The frequencies of employees who smoke and perform hard task is 7
c) The frequencies of employees who smoke and perform medium task is 8
d) The frequencies of employees who do not smoke and perform easy task is 5
e) The frequencies of employees who do not smoke and perform hard task is 8
f) The frequencies of employees who do not smoke and perform hard task is 8
(Source: LibGuides: SPSS Tutorials: Crosstabs., 2018)
The p-value of Somers’d statistic of this cross-tabulation is 0.78. Here, 0.78>0.05.
Therefore, the association between the ordinal dependent variables “Smoking habit” and
“Overall level of tasks” is statistically insignificant. Hence, these two factors are found
independent (Source: Somers' d using SPSS Statistics, 2018).
Figure 8: Graph of overall level of task accomplished with respect to Smoking habit
2. Drinking habit and Overall task accomplished:
Table 9: The Cross tabulation between Drinking habit and Overall level of task accomplished

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The cross-tabulation table hereby shows –
a) The frequencies of employees who drink and perform easy task is 6
b) The frequencies of employees who drink and perform hard task is 12
c) The frequencies of employees who drink and perform medium task is 10
d) The frequencies of employees who do not drink and perform easy task is 3
e) The frequencies of employees who do not drink and perform hard task is 3
f) The frequencies of employees who do not drink and perform hard task is 6
The p-value of Somers’d statistic of this cross-tabulation is 0.648. Here, 0.648>0.05.
Therefore, the association between the ordinal dependent variables “Drinking habit” and
“Overall level of tasks” is statistically insignificant. Hence, these two factors are found
independent.
Figure 9: Graph of overall level of task accomplished with respect to drinking habit

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3. Gender and Overall tasks accomplished:
Table 10: The Cross tabulation between Gender and Overall level of task accomplished
The cross-tabulation table hereby shows –
a) The frequencies of female employees who perform easy task is 6
b) The frequencies of female employees who perform hard task is 2
c) The frequencies of female employees who perform medium task is 5
d) The frequencies of male employees who perform easy task is 3
e) The frequencies of male employees who perform hard task is 13
f) The frequencies of male employees who perform hard task is 11
The p-value of Somers’d statistic of this cross-tabulation is 0.262. Here, 0.262>0.05.
Therefore, the association between the ordinal dependent variables “Gender” and “Overall
level of tasks” is statistically insignificant. Hence, these two factors are found independent to
each other.
Figure 10: Graph of overall level of task accomplished with respect to Gender

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F. Chi-square test:
Chi-square test verifies the association or independence between two categorical variables.
1. Smoking habit and drinking habit:
Table 11: Chi-square test table of Smoking habit with respect to drinking habit
The cross-tabulation table shows that out of 40 employees, 21 employees smoke and
12 people takes alcohol. Out of 40 employees, 9 people have both smoking and drinking
habit. Note that, 3 people have drinking habit but not have smoking habit, whereas 12 people

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have smoking habit but not have drinking habit (Source: Chi-Square Test for Association
using SPSS Statistics, 2018).
According to the table of Chi-Square test, “Pearson Chi-Square” (χ1) = 3.48 and its p-
value is 0.062. This shows us that there is no statistically significant association between
“Smoking habit” and “Drinking habit” (Source: Chi-Square Goodness-of-Fit Test in SPSS
Statistics, 2018). It means both smokers and non-smokers equally prefer drinking.
The Phi and Cramer’ V both examines the strength of association. As 0.062>0.05, the
association between these two factors is very weak. The null hypothesis of significant
association is rejected with 95% probability.
Overall these two factors are independent to each other.
Figure 11: Graph of Smoking habit with respect to drinking habit

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2. Overall level of tasks accomplished and “R&R” received:
Table 12: Chi-square test table of Overall level of tasks accomplished with respect to receiving of “R&R”

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The cross-tabulation table shows that out of 40 employees, 6 employees who
accomplished hard task, 2 employees who accomplished medium task and only 1 employee
who accomplished easy task, achieved R&R. Total 22.5% employees received reward and
recognition. The percentage of achieving R&R for employees who executed hard task (40%)
is significantly greater than medium task (12.5%) and easy task (11.1%).

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According to the table of Chi-Square test, “Pearson Chi-Square” (χ2) = 4.221 and its
p-value is 0.121. This shows us that there is no statistically significant association between
“Overall level of task accomplished” and “R&R achievement”. The p-values of Phi and
Cramer’s V (p-value = 0.121) indicate that these two factors are associated rather than
independent.
The null hypothesis of significant association is rejected with 95% probability.
Figure 12: Graph of Overall level of tasks accomplished with respect to reception of R&R

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G. One-way ANOVA:
1. Average monthly ratings with respect to Level of tasks accomplished:
Table 13: Tables of One-way ANOVA Average monthly ratings according to the level of tasks
(Source: One-way ANOVA in SPSS Statistics, 2018)
The level of tasks achieved is “1” as “Easy”, “2” as “Moderate” and “3” as “Hard”.
The average rating of four weeks is high for hard assignments (4.27) followed by moderate
assignments (4.25). The least average rating of four weeks is lowest for easy assignments
(4.2). The Analysis of variance table indicates that F (2, 37) = 0.306 with significant p-value
= 0.738. The p-value is greater than 0.05.
Therefore, we can accept the null hypothesis of no statistical significance difference
among the average rating of all difficulty levels of scores.

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The post hoc test of “Tukey” is usually the preferred test for accomplishing post hoc
tests on a one-way ANOVA. It can seen from the above table that there is no statistically
significant pair-wise differences of three levels of tasks accomplished in terms of monthly
task ratings of the employees. The reason is that all the pair wise p-values (0.868, 0.716 and
0.942) are greater than 0.05 (Source: One-way ANOVA, 2018).
The Tuckey’s test of homogeneity of all the three goups under study has significant p-
value = 0.691. The significant p-value is greater than 0.05. Hence, average monthly ratings
divided in three groups are homogeneous in nature at 5% level of significance.
Figure 13: Mean plots of Average monthly ratings according to the level of tasks

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2. Monthly completed assignment with respect to Gender:
Table 14: Tables of One-way ANOVA Monthly Completed assignment according to the Gender
The gender is leveled as “1” as “Male” and “2” as “Female”. The average number of
completed assignments by males (35.41) is greater than females (35.85). The Analysis of
variance table indicates that F (1, 38) = 0.042 with significant p-value = 0.839. The p-value is
greater than 0.05.
Therefore, we can accept the null hypothesis of no statistical significance difference
between the average numbers of completed assignments for two kinds of gender.
Figure 14: Mean plots of Monthly Completed assignments according to the Gender

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Conclusion:
Decisions:
As a conclusion, it is extracted that the linear regression model is moderately fitted.
IQ level is linearly associated with average work rating of employees. The drinking and
smoking habit are independent to each other. Overall tasks accomplished and R&R reception
are not associated to each other. Average ratings of work in all the four weeks with respect to
three levels of difficulty are equal to each other. However, averages of monthly completed
assignments with respect to both types of genders have equality of means.
Dedication towards work helps an employee to prosper in the future. Enhancement of
detected significant variables increases performances of the employees. As their performance
in terms of average monthly rating and monthly accomplished assignments increases, the
probability of getting rewards and recognitions also increases.
Recommendation:
It is recommended that another variable such as “Levels of assignment quality” of the
employees could be recommended for further analysis. The variable may be appeared to be a
significant predictor of reward and recognition in the retail company.

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