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
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
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