Data Analysis: Descriptive Statistics and Assumption Testing

Data Analysis: Descriptive Statistics and Assumption Testing

Correlation: Descriptive Statistics and Assumption Testing

Frequency distribution table

bin	Frequency
2	1
4	6
6	31
8	42
10	19
12	4
More	0

 

Histogram

Descriptive statistics table

Mean annual sick days per employee	Descriptive statistics
Mean	7.126214
Standard Error	0.186484
Median	7
Mode	7
Standard Deviation	1.892605
Sample Variance	3.581953
Kurtosis	0.124923
Skewness	0.14225
Range	10
Minimum	2
Maximum	12
Sum	734
Count	103

Measurement scale

The minimum and maximum of Mean annual sick days per employee was 2 and 12.

Measure of central tendency

The analysis shows that mean, median, mode and standard deviation of Mean annual sick days per employee was 7.126214, 7, 7 and 1.89 respectively.

Evaluation

The Descriptive Statistics shows that the Kurtosis and skewness of Mean annual sick days per employee is 0.124923 and 0.14225. The assumptions for parametric statistical testing were met here.

Simple Regression: Descriptive Statistics and Assumption Testing

Frequency distribution table

bin	Frequency
30	2
60	9
90	13
120	23
150	29
180	18
210	49
240	31
270	17
300	24
330	4
360	4
More	0

 

Histogram

Descriptive statistics table

lost time hours	Descriptive Statistics
Mean	188.0045
Standard Error	4.803089
Median	190
Mode	190
Standard Deviation	71.72542
Sample Variance	5144.536
Kurtosis	-0.50122
Skewness	-0.08198
Range	350
Minimum	10
Maximum	360
Sum	41925
Count	223

 

Measurement scale

The minimum and maximum of lost time hours was 10 and 360.

Measure of central tendency

The analysis shows that mean, median, mode and standard deviation of lost time hours was 188.0045, 190, 190 and 71.72542 respectively.

Evaluation

The Descriptive Statistics shows that the Kurtosis and skewness of lost time hours is -0.50122 and -0.08198. The assumptions for parametric statistical testing were met here.

Multiple Regression: Descriptive Statistics and Assumption Testing

Frequency distribution table

Bin	Frequency
100	0
110	36
120	324
130	768
140	373
150	2
More	0

 

Histogram

Descriptive statistics table

Decibel	Descriptive Statistics
Mean	124.8359
Standard Error	0.177945
Median	125.721
Mode	127.315
Standard Deviation	6.898657
Sample Variance	47.59146
Kurtosis	-0.31419
Skewness	-0.41895
Range	37.607
Minimum	103.38
Maximum	140.987
Sum	187628.4
Count	1503

 

Measurement scale

The minimum and maximum of Decibel was 103.38 and 140.9871.

Measure of central tendency

The analysis shows that mean, median, mode and standard deviation of Decibel was 124.8359, 125.721, 127.315 and 6.898657 respectively.

Evaluation

The Descriptive Statistics shows that the Kurtosis and skewness of Decibel is -0.31419 and -0.41895. The assumptions for parametric statistical testing were met here.

Independent Samples t Test: Descriptive Statistics and Assumption Testing

Frequency distribution table

Bin(Group A Prior Training Scores)	Frequency
50	4
55	5
60	3
65	11
70	9
75	10
80	11
85	3
90	5
95	1
More	0

 

Bin (Group B Revised Training Scores)	Frequency
75	2
80	12
85	21
90	19
95	6
100	2
More	0

 

Histogram

Descriptive statistics table

Group A Prior Training Scores	Descriptive Statistics	Group B Revised Training Scores	Descriptive Statistics
Mean	69.79032258	Mean	84.77419355
Standard Error	1.402788093	Standard Error	0.659478888
Median	70	Median	85
Mode	80	Mode	85
Standard Deviation	11.04556449	Standard Deviation	5.192741955
Sample Variance	122.004495	Sample Variance	26.96456901
Kurtosis	-0.77667598	Kurtosis	-0.352537913
Skewness	-0.086798138	Skewness	0.144084526
Range	41	Range	22
Minimum	50	Minimum	75
Maximum	91	Maximum	97
Sum	4327	Sum	5256
Count	62	Count	62

 

Measurement scale

The minimum and maximum of Group A Prior Training Scores was 50 and 91. The minimum and maximum of Group B Revised Training Scores was 75 and 97.

Measure of central tendency

The analysis shows that mean, median, mode and standard deviation of Group A Prior Training Scores was 69.79, 70, 80 and 11.04556 respectively. Similarly, mean, median, mode and standard deviation of Group B Revised Training Scores was 84.77, 85, 85 and 5.19 respectively.

Evaluation

The Descriptive Statistics shows that the Kurtosis and skewness of Group A Prior Training Scores is -0.77667598 and -0.086798138. It also shows that the Kurtosis and skewness of Group B Revised Training Scores is -0.352537913and 0.144084526. The assumptions for parametric statistical testing were met here.

Dependent Samples (Paired-Samples) t Test: Descriptive Statistics and Assumption Testing

Frequency distribution table.

Bin (Pre-Exposure μg/dL)	Frequency
6	1
12	3
18	4
24	5
30	5
36	11
42	9
48	7
54	3
60	1
More	0

 

Bin (Post-Exposure μg/dL)	Frequency
6	1
12	3
18	4
24	5
30	5
36	7
42	12
48	8
54	3
60	1
More	0

 

Histogram

 

Descriptive statistics table

Pre-Exposure μg/dL	Descriptive Statistics	Post-Exposure μg/dL	Descriptive Statistics
Mean	32.85714	Mean	33.28571
Standard Error	1.752307	Standard Error	1.781423
Median	35	Median	36
Mode	36	Mode	38
Standard Deviation	12.26615	Standard Deviation	12.46996
Sample Variance	150.4583	Sample Variance	155.5
Kurtosis	-0.57604	Kurtosis	-0.65421
Skewness	-0.42511	Skewness	-0.48363
Range	50	Range	50
Minimum	6	Minimum	6
Maximum	56	Maximum	56
Sum	1610	Sum	1631
Count	49	Count	49

 

Measurement scale

The minimum and maximum of both Pre-Exposure μg/dL and Post-Exposure μg/dL was 6 and 56.

 

Measure of central tendency

The analysis shows that mean, median, mode and standard deviation of Pre-Exposure μg/dL was 32.85714, 35, 36 and 12.26615 respectively. Similarly, mean, median, mode and standard deviation of Post-Exposure μg/dL was 33.28571, 36, 38 and 12.46996 respectively.

Evaluation

The Descriptive Statistics shows that the Kurtosis and skewness of Pre-Exposure μg/dL is -0.57604 and -0.42511. It also shows that the Kurtosis and skewness of Post-Exposure μg/dL is -0.65421 and -0.48363. The assumptions for parametric statistical testing were met here.

ANOVA: Descriptive Statistics and Assumption Testing

Frequency distribution table.

Bin (A = Air)	Frequency
2	0
4	2
6	3
8	3
10	5
12	5
14	2
More	0

 

Bin (B = Soil)	Frequency
6	1
8	7
10	8
12	3
14	1
More	0

 

Bin (C = Water)	Frequency
2	0
4	2
6	9
8	4
10	2
12	3
More	0

 

Bin (D = Training)	Frequency
2	0
4	4
6	13
8	3
More	0

 

Histogram.

Descriptive statistics table.

A = Air	Descriptive Statistics	B = Soil	Descriptive Statistics	C = Water	Descriptive Statistics	D = Training	Descriptive Statistics
Mean	8.9	Mean	9.1	Mean	7	Mean	5.4
Standard Error	0.684028	Standard Error	0.390007	Standard Error	0.575829	Standard Error	0.265568
Median	9	Median	9	Median	6	Median	5
Mode	11	Mode	8	Mode	6	Mode	5
Standard Deviation	3.059068	Standard Deviation	1.744163	Standard Deviation	2.575185	Standard Deviation	1.187656
Sample Variance	9.357895	Sample Variance	3.042105	Sample Variance	6.631579	Sample Variance	1.410526
Kurtosis	-0.6283	Kurtosis	0.11923	Kurtosis	-0.23752	Kurtosis	0.253747
Skewness	-0.36085	Skewness	0.492002	Skewness	0.760206	Skewness	0.159183
Range	11	Range	7	Range	9	Range	5
Minimum	3	Minimum	6	Minimum	3	Minimum	3
Maximum	14	Maximum	13	Maximum	12	Maximum	8
Sum	178	Sum	182	Sum	140	Sum	108
Count	20	Count	20	Count	20	Count	20

 

Measurement scale

The minimum and maximum of air was 3 and 14. Similarly, the minimum and maximum of soil was 6 and 13. The minimum and maximum of water was 3 and 12. Similarly, the minimum and maximum of training was 3 and 8.

 

Measure of central tendency

The analysis shows that mean, median, mode and standard deviation of air was 8.9, 9, 11 and 3.059068 respectively. Similarly, mean, median, mode and standard deviation of soil was 9.1, 9, 8 and 1.744163 respectively. The mean, median, mode and standard deviation of water was 7, 6, 6 and 2.575185 respectively. Similarly, mean, median, mode and standard deviation of training was 5.4, 5, 5 and 1.187656 respectively.

Evaluation

The Descriptive Statistics shows that the Kurtosis and skewness of Air is -0.6283 and -0.36085. It also shows that the Kurtosis and skewness of soil is 0.11923 and -0.492002. Similarly, the Kurtosis and skewness of water is -0.23752 and 0.760206. Moreover, the Kurtosis and skewness of training is 0.253747 and 0.159183. The assumptions for parametric statistical testing were met here.

 

 

References

Linoff, G. S. (2010). Data Analysis Using SQL and Excel. John Wiley & Sons.

Whigham, D. (2007). Business Data Analysis Using Excel. OUP Oxford.

Nirel, R., Adar, S. D., Dayan, U., Vakulenko-Lagun, B., Golovner, M., Levy, I., . . . Peretz, A. (2018). Fine and Coarse Particulate Matter Exposures and Associations with Acute Cardiac Events among Participants in a Telemedicine Service: A Case-Crossover Study. Environmental Health Perspectives, 126(9), 097003. doi:10.1289/ehp2596