Collecting And Analyzing Data Using Statistical Tools And Techniques

Data Collection and Statistical Analysis

Statistical data analysis plays an important role in the process of decision making in many sectors. It is important to use proper statistical tools and techniques for data analysis. Here, we have to analyse the data for the different variables regarding the employees. We have to draw the conclusions for the variables such as gender, age, education, monthly salary, monthly expense, etc. We have to use descriptive statistics, graphical analysis, correlation and regression, hypotheses tests such as independent samples t tests and one factor ANOVA tests for checking different claims regarding the variables. Let us see this statistical analysis in detail. 

For this study of statistical data collection and analysis, we consider the following research hypotheses:

1. H0: There is no any statistically significant linear relationship exists between the two variable monthly salary and monthly expense.
2. H0: There is no any significant difference exists between the average monthly salary for the female and male employees.
3. H0: There is no any significant difference in average number of TV hours for female and male employees.
4. H0: There is no any significant difference in the average number of hours for exercise for male and female employees.
5. H0: There is no any significant difference in the average monthly salary for the employees with different educations.
6. H0: There is no any statistically significant difference in the average monthly expense for the employees with different education levels.
7. H0: There is no any statistically significant difference in the average number of TV hours for the employees with different education levels.
8. H0: There is no any statistically significant difference in the average number of exercise hours for the employees with different education levels.
9. H0: Two categorical variables gender and education levels are independent from each other.

For this research study, the data is collected by using the random sampling methods and this data is archived from the government website Bureau of Labour Statistics. Data is collected for 100 employees including male and female employees. The list of the variables used for this research study is given as below: 

Variable	Type Save Time On Research and Writing Hire a Pro to Write You a 100% Plagiarism-Free Paper. Get My Paper	Scale
ID	Qualitative	Nominal
Gender	Qualitative	Nominal
Age	Quantitative	Ratio
Education	Qualitative	Ordinal
Monthly Salary ($)	Quantitative	Ratio
Monthly Expense ($)	Quantitative	Ratio
Medi-claim Insurance	Qualitative	Nominal
Pension Plan	Qualitative	Nominal
Exercise in hour per week	Quantitative	Ratio
TV hour per week	Quantitative	Ratio

First of all, we have to discuss the descriptive statistics for the variables included in the given data set. We know that the descriptive statistics gives us an idea about the nature of data for corresponding variable.

Descriptive statistics for the variable age is summarised as below:

	N	Minimum	Maximum	Mean	Std. Deviation
Age	100	27.00	58.00	43.9200	8.78553
Valid N (listwise)	100

The average age of the all employees or participants in the given data is given as 43.92 years with the standard deviation of 8.79 years. The minimum age of the participant is observed as 27 year while the maximum age is observed as 58 years.

Now, we have to see the descriptive statistics for the variable monthly salary which is summarised as below:

	N	Minimum	Maximum	Mean	Std. Deviation
Monthly Salary ($)	100	4392.00	10569.00	7481.7300	1378.83790
Valid N (listwise)	100

The average salary for all employees is given as $7481.73 per month with the standard deviation of $1378.84. The minimum salary is observed as $4392 while the maximum salary is observed as $10569.

Descriptive statistics for the variable monthly expense is given as below: 

	N	Minimum	Maximum	Mean	Std. Deviation
Monthly Expense ($)	100	2081.00	9257.00	5643.8800	1478.30870
Valid N (listwise)	100

From above table, it is observed that the average monthly expense for employees is given as $5643.88 with the standard deviation of $1478.31. Minimum monthly expense is given as $2081, while maximum monthly expense is given as $9257.00.

Descriptive statistics for the variable exercise in hours per week are summarised in the following table:

	N	Minimum	Maximum	Mean	Std. Deviation
Exercise in hours per week	100	.00	5.00	2.3400	1.75361
Valid N (listwise)	100

Average number of hours per week for all employees is given as 2.34 hour with the standard deviation of 1.75. The minimum number of hours per week is observed as 0, while the maximum number of hours per week for exercise is given as 5.

Descriptive Statistics

Descriptive statistics for the variable TV hour per week is given as below:

	N	Minimum	Maximum	Mean	Std. Deviation
TV hour per week	100	4.00	20.00	11.3700	5.02047
Valid N (listwise)	100

From above table, it is observed that the average TV hour per week for all employees is given as 11.37 hour with the standard deviation of 5.02 hours. The minimum number of TV hour is given as 4, while maximum number of TV hour is given as 20.

Now, we have to see some frequency distributions for the variables included in the given study. The frequency distribution for the variable gender is given as below: 

	Frequency	Percent	Valid Percent	Cumulative Percent
Valid	Female	54	54.0	54.0	54.0
Male	46	46.0	46.0	100.0
Total	100	100.0	100.0

The frequency distribution of the variable education is given as below:

	Frequency	Percent	Valid Percent	Cumulative Percent
Valid	Less than graduation	34	34.0	34.0	34.0
Graduation	32	32.0	32.0	66.0
Post-graduation or more	34	34.0	34.0	100.0
Total	100	100.0	100.0

Frequency distribution for the variable whether employee have a mediclaim policy or not is given as below:

	Frequency	Percent	Valid Percent	Cumulative Percent
Valid	No	55	55.0	55.0	55.0
Yes	45	45.0	45.0	100.0
Total	100	100.0	100.0

Frequency distribution for the variable pension plan is summarised as below:

	Frequency	Percent	Valid Percent	Cumulative Percent
Valid	No	54	54.0	54.0	54.0
Yes	46	46.0	46.0	100.0
Total	100	100.0	100.0

In this section, we have to see some graphical analysis for the different variables under this study. Graphical analysis plays an important role in easy understanding of the concepts of statistical analysis. For this graphical analysis, we have to use bar charts and box plots for comparison purpose. All graphical comparisons are provided in the appendix part at the end of this report.

The study of correlation gives the relationship between the two variables. The technique of linear regression is useful for the prediction of the response variable or dependent variable. Here, we have to check whether the two variables monthly salary and monthly expense are related to each other or not. We have to check whether the relationship between two variables is statistically significant or not. First of all we have to see the scatter plot for the given two variables monthly salary and monthly expense. By using scatter plot, we have to check the relationship between the two variables. Required scatter diagram for the given two variables is given as below: 

                                                  

From above scatter plot for the given two variables, it is observed that there is a very strong positive linear relationship or association exists between the two variables such as monthly salary and monthly expense. This means, higher the monthly salary indicates higher the monthly expense.

Now, we have to use the linear regression model for the prediction of monthly expense based on the monthly salary. For this linear regression model, the independent variable or explanatory variable is given as monthly salary while dependent variable or response variable for this linear regression model is given as monthly expense. For this linear relationship we have to check the following null and alternative hypothesis.

Frequency Distribution

Null hypothesis: H₀: There is no any statistically significant linear relationship exists between the two variable monthly salary and monthly expense.

Alternative hypothesis: H_a: There is a statistically significant linear relationship exists between the two variables monthly salary and monthly expense.

Required regression analysis is given as below:

Model	Variables Entered	Variables Removed	Method
1	Monthly Salary ($)a	.	Enter

a. All requested variables entered.

b. Dependent Variable: Monthly Expense ($)

For this regression, model summary is provided below:

Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.957a	.916	.915	431.43690
a. Predictors: (Constant), Monthly Salary ($)

From this table, it was observed that the linear correlation coefficient between the two variables monthly salary and monthly expense is given as 0.957, which indicate a strong positive linear relationship or association exists between dependent variable monthly expense and independent variable monthly salary. The coefficient of determination or the value of R square for this linear regression model is given as 0.916, which means about 91.60% of the variation in the dependent variable monthly expense is explained by the independent variable monthly salary.

Now, we have to see the ANOVA table for above regression model, which is stated as below:

Model	Sum of Squares	df	Mean Square	F	Sig.
1	Regression	1.981E8	1	1.981E8	1064.334	.000a
Residual	1.824E7	98	186137.798
Total	2.164E8	99

a. Predictors: (Constant), Monthly Salary ($)

b. Dependent Variable: Monthly Expense ($)

The p-value for this ANOVA table is given as 0.00 which is less than the default level of significance or alpha value 0.05, so we reject the null hypothesis that there is no any statistically significant linear relationship exists between the two variable monthly salary and monthly expense.

This means, there is sufficient evidence to conclude that there is a statistically significant linear relationship exists between the two variables monthly salary and monthly expense. So, this regression model will be useful for further prediction of the monthly expense based on the monthly salary.

The regression coefficients for this regression model are summarised in the following table:

Model	Unstandardized Coefficients	Standardized Coefficients	t	Sig.
B	Std. Error	Beta
1	(Constant)	-2031.987	239.205		-8.495	.000
Monthly Salary ($)	1.026	.031	.957	32.624	.000

a. Dependent Variable: Monthly Expense ($)

Required Regression model or regression equation is given as below:

Monthly expense = -2031.987 + 1.026*Monthly Salary

By using this regression model, we can predict the values for monthly expenses based on the salaries. 

In this section, we have to check the significance differences in the population means by using the independent samples t tests. First of all, we have to check the significant difference in the average monthly salary for the female and male. The null and alternative hypotheses for this test are given as below:

Null hypothesis: H₀: There is no any significant difference exists between the average monthly salary for the female and male employees.

Graphical Analysis

Alternative hypothesis: H_a: There is a significant difference exists between the average monthly salary for the female and male employees.

We consider 5% level of significance for this test.

The test results are summarised as below: 

	Gender	N	Mean	Std. Deviation	Std. Error Mean
Monthly Salary ($)	Female	54	7403.8704	1476.55210	200.93329
Male	46	7573.1304	1264.52132	186.44350

	t-test for Equality of Means
t	df	Sig. (2-tailed)	Mean Difference	Std. Error Difference	95% Confidence Interval of the Difference
Lower	Upper
Monthly Salary ($)	Equal variances assumed	-0.61	98	0.543	-169.26	277.5361	-720.021	381.5012
Equal variances not assumed	-0.617	97.995	0.538	-169.26	274.1083	-713.219	374.6993

The p-value for this test is given as 0.543 which is greater than alpha value of 0.05. So, we do not reject the null hypothesis. 

There is sufficient evidence to conclude that there is no any statistically significant difference between the average monthly salary for the female and male employees.

Now, we have to check another hypothesis which is stated as below:

Null hypothesis: H₀: There is no any significant difference in the average monthly expense for the female and male employees. 

We consider 5% level of significance for this test.

The test results for this test are summarised as below:

	Gender	N	Mean	Std. Deviation	Std. Error Mean
Monthly Expense ($)	Female	54	5607.2963	1615.49455	219.84096
Male	46	5686.8261	1315.51893	193.96268

	t-test for Equality of Means
t	df	Sig. (2-tailed)	Mean Difference	Std. Error Difference	95% Confidence Interval of the Difference
Lower	Upper
Monthly Expense ($)	Equal variances assumed	-0.267	98	0.79	-79.5298	298.0137	-670.928	511.8686
Equal variances not assumed	-0.271	97.818	0.787	-79.5298	293.175	-661.34	502.2799

The p-value for this test is given as 0.79 which is greater than the given level of significance or alpha value 0.05, so we do not reject the null hypothesis that there is no any statistically significant difference in the mean monthly expense for male and female employees.

Now, we have to test whether the average number of TV hours for male and female employees are same or not. The null and alternative hypotheses are given as below:

Null hypothesis: H₀: There is no any significant difference in average number of TV hours for female and male employees.

Alternative hypothesis: H_a: There is a significant difference in the average number of TV hours for the female and male employees. 

For this test, we consider 5% level of significance.

The test results are summarised below:

	Gender	N	Mean	Std. Deviation	Std. Error Mean
TV hour per week	Female	54	12.4074	5.06009	.68859
Male	46	10.1522	4.74209	.69918

	t-test for Equality of Means
t	df	Sig. (2-tailed)	Mean Difference	Std. Error Difference	95% Confidence Interval of the Difference
Lower	Upper
TV hour per week	Equal variances assumed	2.286	98	0.024	2.25523	0.98649	0.29758	4.21288
Equal variances not assumed	2.298	97.082	0.024	2.25523	0.98133	0.30758	4.20289

The p-value for this test is given as 0.024 which is less than the given level of significance or alpha value 0.05. So, we reject the null hypothesis that there is no any significant difference in average number of TV hours for female and male employees.

There is sufficient evidence to conclude that there is a significant difference in the average number of TV hours for the female and male employees. 

Now, we have to test whether the average number of hours for exercise for male and female employees is same or not. 

Null hypothesis: H₀: There is no any significant difference in the average number of hours for exercise for male and female employees. 

Alternative hypothesis: H_a: There is a significant difference in the average number of hours for exercise for male and female employees. 

Correlation and Regression

Test results for this test are given as below: 

	Gender	N	Mean	Std. Deviation	Std. Error Mean
Exercise in hours per week	Female	54	2.5926	1.83795	.25011
Male	46	2.0435	1.61873	.23867

	t-test for Equality of Means
t	df	Sig. (2-tailed)	Mean Difference	Std. Error Difference	95% Confidence Interval of the Difference
Lower	Upper
Exercise in hours per week	Equal variances assumed	1.572	98	0.119	0.54911	0.34926	-0.14399	1.24222
Equal variances not assumed	1.588	97.88	0.115	0.54911	0.34572	-0.13696	1.23519

The p-value for this test is given as 0.119 which is greater than alpha value of 0.05. So, we do not reject the null hypothesis that there is no any significant difference in the average number of hours for exercise for male and female employees. 

In this section, we have to compare the population averages for more than two groups. first we have to test whether the monthly salary for the employees with different education is same or not. For checking this hypothesis we have to use one way analysis of variance. The null and alternative hypothesis for this test is given as below:

Null hypothesis: H₀: There is no any significant difference in the average monthly salary for the employees with different educations.

Alternative hypothesis: H_a­: There is a significant difference in the average monthly salary for the employees with different educations.

We consider 5% level of significance for this test.

Test results are summarised as below:

Monthly Salary ($)

	N	Mean	Std. Deviation	Std. Error	95% Confidence Interval for Mean	Minimum	Maximum
Lower Bound	Upper Bound
Less than graduation	34	7061.706	1359.564	233.1633	6587.332	7536.08	4392	9778
Graduation	32	7225.719	1302.629	230.2744	6756.071	7695.367	5289	9731
Post-graduation or more	34	8142.706	1251.285	214.5936	7706.112	8579.3	5904	10569
Total	100	7481.73	1378.838	137.8838	7208.139	7755.321	4392	10569

Monthly Salary ($) 

	Sum of Squares	df	Mean Square	F	Sig.
Between Groups	2.295E7	2	1.147E7	6.735	.002
Within Groups	1.653E8	97	1703797.387
Total	1.882E8	99

The p-value for this ANOVA test is given as 0.002 which is less than the given level of significance or alpha value 0.05, so we reject the null hypothesis that There is no any significant difference in the average monthly salary for the employees with different educations.

There is sufficient evidence to conclude that there is a significant difference in the average monthly salary for the employees with different educations. 

Now, we have to test whether the average monthly expense for the employees with different education levels is same or not.

Null hypothesis: H₀: There is no any statistically significant difference in the average monthly expense for the employees with different education levels.

Alternative hypothesis: H_a: There is a any statistically significant difference in the average monthly expense for the employees with different education levels.

Test results for this test are given as below:

Monthly Expense ($)

	N	Mean	Std. Deviation	Std. Error	95% Confidence Interval for Mean	Minimum	Maximum
Lower Bound	Upper Bound
Less than graduation	34	5262.235	1439.163	246.8144	4760.088	5764.383	2081	8479
Graduation	32	5279.438	1376.105	243.2633	4783.299	5775.576	3074	7995
Post-graduation or more	34	6368.529	1373.395	235.5353	5889.329	6847.73	4183	9257
Total	100	5643.88	1478.309	147.8309	5350.552	5937.209	2081	9257

Monthly Expense ($)

	Sum of Squares	df	Mean Square	F	Sig.
Between Groups	2.706E7	2	1.353E7	6.932	.002
Within Groups	1.893E8	97	1951524.912
Total	2.164E8	99

The p-value for this test is given as 0.002 which is less than the given level of significance or alpha value 0.05, so we reject the null hypothesis that there is no any significant difference in the average monthly expense for the employees with different educations.

There is sufficient evidence to conclude that there is a significant difference in the average monthly expense for the employees with different educations.

Now, we have to use this test for checking the significant difference for the average number of TV hours for the employees with different levels of education.

Hypotheses Tests

Null hypothesis: H₀: There is no any statistically significant difference in the average number of TV hours for the employees with different education levels.

Alternative hypothesis: H_a: There is a any statistically significant difference in the average number of TV hours for the employees with different education levels. 

TV hour per week

	N	Mean	Std. Deviation	Std. Error	95% Confidence Interval for Mean	Minimum	Maximum
Lower Bound	Upper Bound
Less than graduation	34	10.5	4.34323	0.74486	8.9846	12.0154	4	19
Graduation	32	12.6875	4.62418	0.81745	11.0203	14.3547	4	20
Post-graduation or more	34	11	5.83615	1.00089	8.9637	13.0363	4	20
Total	100	11.37	5.02047	0.50205	10.3738	12.3662	4	20

TV hour per week

Exercise in hours per week	Sum of Squares	df	Mean Square	F	Sig.
Between Groups	85.935	2	42.967	1.730	.183
Within Groups	2409.375	97	24.839
Total	2495.310	99

P-value for this test is given as 0.183 which is greater than alpha value 0.05, so we do not reject the null hypothesis that there is no any statistically significant difference in the average number of TV hours for the employees with different education levels.

Now, we have to use same test for checking the significant difference in the average number of hour of exercise for the employees with different education levels.

Null hypothesis: H₀: There is no any statistically significant difference in the average number of exercise hours for the employees with different education levels.

Alternative hypothesis: H_a: There is a any statistically significant difference in the average number of exercise hours for the employees with different education levels.

Test results are given as below:

Exercise in hours per week

	N	Mean	Std. Deviation	Std. Error	95% Confidence Interval for Mean	Minimum	Maximum
Lower Bound	Upper Bound
Less than graduation	34	2.2059	1.80537	0.30962	1.576	2.8358	0	5
Graduation	32	2.25	1.75977	0.31109	1.6155	2.8845	0	5
Post-graduation or more	34	2.5588	1.72664	0.29612	1.9564	3.1613	0	5
Total	100	2.34	1.75361	0.17536	1.992	2.688	0	5

Exercise in hours per week

	Sum of Squares	df	Mean Square	F	Sig.
Between Groups	2.499	2	1.249	.401	.671
Within Groups	301.941	97	3.113
Total	304.440	99

P-value for this test is given as 0.671 which is greater than alpha value 0.05, so we do not reject the null hypothesis that there is no any statistically significant difference in the average number of exercise hours for the employees with different education levels. 

In this section we want to check whether the two categorical variables gender and education are independent from each other or not. For checking this claim we have to use chi square test for independence of two categorical variables. The null and alternative hypothesis for this test is given as below:

Null hypothesis: H₀: Two categorical variables gender and education levels are independent from each other.

Alternative hypothesis: H_a: Two categorical variables gender and education levels are not independent from each other.

We use 0.05 alpha level of significance for this test.

Test results are summarised below:

Count

	Education	Total
Less than graduation	Graduation	Post-graduation or more
Gender	Female	18	17	19	54
Male	16	15	15	46
Total	34	32	34	100

	Value	df	Asymp. Sig. (2-sided)
Pearson Chi-Square	.074a	2	.964
Likelihood Ratio	.074	2	.964
Linear-by-Linear Association	.059	1	.809
N of Valid Cases	100

 a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 14.72.

The p-value for this test is given as 0.964 which is greater than the alpha value 0.05, so we do not reject the null hypothesis that two categorical variables gender and education levels are independent from each other. 

From the given statistical data analysis, we get some significant results for the different tests used in this study. We used the simple descriptive statistics for getting the primary idea about the nature of variables involved in this research study. The correlation coefficient between the two variables monthly salary and monthly expense is given as 0.957, which indicate a strong positive linear relationship. We conclude that there is a statistically significant linear relationship exists between the two variables monthly salary and monthly expense. No any statistically significant difference is observed between the average monthly salary and expense for the female and male employees. A significant difference is observed in the average number of TV hours for the female and male employees. No any significant difference is observed in the average number of hours for exercise for male and female employees. A significant difference is observed in the average monthly salary and expense for the employees with different educations. Also, there is no any statistically significant difference in the average number of TV hours for the employees with different education levels. There is sufficient evidence to conclude that two categorical variables gender and education levels are independent from each other.

Conclusions

Conclusions for the given statistical data analyses are summarised as below:

1. The average age of the all employees or participants in the given data is given as 43.92 years with the standard deviation of 8.79 years. The average salary for all employees is given as $7481.73 per month with the standard deviation of $1378.84. it is observed that the average monthly expense for employees is given as $5643.88 with the standard deviation of $1478.31. All results are based on the sample of 100 observations.
2. It was observed that the linear correlation coefficient between the two variables monthly salary and monthly expense is given as 0.957, which indicate a strong positive linear relationship or association exists between dependent variable monthly expense and independent variable monthly salary. The coefficient of determination or the value of R square for this linear regression model is given as 0.916, which means about 91.60% of the variation in the dependent variable monthly expense is explained by the independent variable monthly salary.
3. There is sufficient evidence to conclude that there is a statistically significant linear relationship exists between the two variables monthly salary and monthly expense.
4. There is sufficient evidence to conclude that there is no any statistically significant difference between the average monthly salary for the female and male employees.
5. There is sufficient evidence to conclude that there is no any statistically significant difference in the mean monthly expense for male and female employees.
6. There is sufficient evidence to conclude that there is a significant difference in the average number of TV hours for the female and male employees.
7. There is sufficient evidence to conclude that there is no any significant difference in the average number of hours for exercise for male and female employees.
8. There is sufficient evidence to conclude that there is a significant difference in the average monthly salary for the employees with different educations.
9. There is sufficient evidence to conclude that there is a significant difference in the average monthly expense for the employees with different educations.
10. There is sufficient evidence to conclude that there is no any statistically significant difference in the average number of TV hours for the employees with different education levels.
11. There is sufficient evidence to conclude that there is no any statistically significant difference in the average number of exercise hours for the employees with different education levels.
12. There is sufficient evidence to conclude that two categorical variables gender and education levels are independent from each other. 

References

Antony, J. (2003). Design of Experiments for Engineers and Scientists. Butterworth Limited.

Babbie, E. R. (2009). The Practice of Social Research. Wadsworth.

Beran, R. (2000). React scatterplot smoothers: Superefficiency through basis economy. Journal of the American Statistical Association.

Bickel, P. J. and Doksum, K. A. (2000). Mathematical Statistics: Basic Ideas and Selected Topics, Vol I. Prentice Hall.

Casella, G. and Berger, R. L. (2002). Statistical Inference. Duxbury Press.

Cox, D. R. and Hinkley, D. V. (2000). Theoretical Statistics. Chapman and Hall Ltd.

Degroot, M. and Schervish, M. (2002). Probability and Statistics. Addison – Wesley.

Dobson, A. J. (2001). An introduction to generalized linear models. Chapman and Hall Ltd.

Evans, M. (2004). Probability and Statistics: The Science of Uncertainty. Freeman and Company.

Hastle, T., Tibshirani, R. and Friedman, J. H. (2001). The elements of statistical learning: data mining, inference, and prediction: with 200 full-color illustrations. Springer – Verlag Inc.

Hogg, R., Craig, A., and McKean, J. (2004).  An Introduction to Mathematical Statistics. Prentice Hall.

Liese, F. and Miescke, K. (2008). Statistical Decision Theory: Estimation, Testing, and Selection. Springer.

Pearl, J. (2000). Casuality: models, reasoning, and inference. Cambridge University Press.

Ross, S. (2014). Introduction to Probability and Statistics for Engineers and Scientists. London: Academic Press.

Website for Data collection: https://www.bls.gov/