Research Methods, Final Project?

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Unit IV: Data Analysis

Data Analysis: Descriptive Statistics and Assumption Testing

Correlation: Descriptive Statistics and Assumption Testing

Frequency Distribution Table

Sick days

Frequency

2

1

3

1

4

5

5

13

6

18

7

24

8

18

9

12

10

7

11

2

More

2

Histogram

Descriptive Statistics Table

Mean Annual Sick days per employee

 

 

 

Mean

7.126213592

Standard Error

0.186483898

Median

7

Mode

7

Standard Deviation

1.892604864

Sample Variance

3.58195317

Kurtosis

0.124922603

Skewness

0.142249784

Range

10

Minimum

2

Maximum

12

Sum

734

Count

103

Measurement Scale

The measurement scale used in the above data is ratio scale because the exact values between the data can be determined.

Measure of Central Tendency

The mean, median and mode of the data are identical at 7 implying that the data is perfectly identical.

Skewness and Kurtosis

The skewness of mean annual sick days per employee is 0.142 and is within the range of 0.5 and 1 implying that the data is moderately skewed. On the other hand the kurtosis of the data is 0.1249 and falls within the acceptable region because the curve is not highly picked.

Evaluation

The histogram of the above data is normally distributed and the frequency does not show outliers. The mean, median and more are closely aligned implying normalcy. The skewness and the kurtosis are within the acceptable range of -2 and + 2. The results of the descriptive statistics show that the assumption of the parametric statistics has been met.

Simple Regression: Descriptive Statistics and Assumption Testing

Frequency Distribution Table

.

Lost Time in Hours

Frequency

10

1

35

1

60

9

85

9

110

17

135

18

160

24

185

27

210

37

235

24

260

21

285

15

310

12

335

4

More

4

Histogram

Descriptive Statistics Table

Lost Time in Hours

 

 

Mean

188.0044843

Standard Error

4.803089447

Median

190

Mode

190

Standard Deviation

71.72542099

Sample Variance

5144.536016

Kurtosis

-0.501223533

Skewness

-0.081984874

Range

350

Minimum

10

Maximum

360

Sum

41925

Count

223

Measurement Scale

The lost time per member of contract is ratio data because the data can be classified and ordered.

Measure of Central Tendency

The mean, median and the mode of the data is 188.00, 190 and 190 respectively. These values are closely aligned implying the data is normally distributed.

Skewness and Kurtosis

The skewness and kurtosis of the data is within the acceptable region because the values lies between -2 and + 2.

Evaluation

From the descriptive statistics table the three measures of central tendency are close to each other indicating the normalcy of the data. On the other hand the skewness and the kurtosis of the data is within the acceptable range of -2 and + 2 which shows that the data is normally distributed. These results confirm that the assumption of the parametric statistics has been met.

Multiple Regression: Descriptive Statistics and Assumption Testing

Frequency Distribution Table

Decibel

Frequency

103.38

1

104.37

2

105.36

1

106.35

3

107.34

6

108.33

6

109.32

9

110.31

12

111.30

18

112.29

17

113.28

26

114.27

22

115.26

27

116.25

47

117.24

36

118.22

44

119.21

47

120.20

53

121.19

61

122.18

60

123.17

62

124.16

74

125.15

70

126.14

81

127.13

93

128.12

73

129.11

105

130.10

80

131.09

88

132.08

67

133.07

50

134.06

56

135.05

35

136.04

30

137.03

19

138.02

7

139.01

8

140.00

5

More

2

Histogram

Descriptive Statistics Table

Decibel

 

 

Mean

124.83594

Standard Error

0.1779447

Median

125.721

Mode

127.315

Standard Deviation

6.8986566

Sample Variance

47.591463

Kurtosis

-0.3141873

Skewness

-0.4189522

Range

37.607

Minimum

103.38

Maximum

140.987

Sum

187628.42

Count

1503

Measurement Scale

The measurement scale of decibel is ratio data because the data has meaningful distance between the data values.

Measure of Central Tendency

The mean, median and mode of the data are closely aligned implying normalcy. The results are shown in the table of descriptive statistics above.

Skewness and Kurtosis

The skewness and the kurtosis of the data is within the acceptable region of -2 and + 2. This indicates that the data is normally distributed.

Evaluation

The skewness and the kurtosis of the data show normalcy since the values lies between -2 and +2. Additionally the mean, median and the mode are closely aligned which is a sign of normal distribution. The normalcy of the data indicates that the assumption of parametric statistics has been met.

Independent Samples t Test: Descriptive Statistics and Assumption Testing

Frequency Distribution Table

Group A Prior to Training

Frequency

50

4

55.86

5

61.71

7

67.57

8

73.43

14

79.29

10

85.14

8

More

6

Group B prior to Training

Frequency

75

2

78.14

5

81.29

10

84.43

12

87.57

14

90.71

11

93.86

5

More

3

Histogram

Descriptive Statistics Table

Group A prior to Training

 

 

 

Mean

69.790323

Standard Error

1.4027881

Median

70

Mode

80

Standard Deviation

11.045564

Sample Variance

122.00449

Kurtosis

-0.776676

Skewness

-0.0867981

Range

41

Minimum

50

Maximum

91

Sum

4327

Count

62

Group B prior to Training

 

 

 

Mean

84.7741935

Standard Error

0.65947889

Median

85

Mode

85

Standard Deviation

5.19274195

Sample Variance

26.964569

Kurtosis

-0.3525379

Skewness

0.14408453

Range

22

Minimum

75

Maximum

97

Sum

5256

Count

62

Measurement Scale

The measurement scale used is ratio because the data can be classified and ordered.

Measure of Central Tendency

The mean, median and mode of group A before training are 69.79, 70 and 80. Since the range of the measure of central tendency is small it indicates that the data is normally distributed. On the other hand, mean median and mode of group B before training is 84.79, 85 and 85. This results shows that there is normality.

Skewness and Kurtosis

Skewness and kurtosis are important statistical tools of measurement that are used determine the distribution of data or the shape of the distribution curve. The skewness and kurtosis of the data for group A is -0.776676 and -0.0867981 respectively. According to George and Mallery, (2018), a normally distributed data will have skewness and kurtosis of -2 and +2. As such the data set is normally distributed because if falls within the acceptable range.

Evaluation

From the descriptive statistics table, the central measure of tendency are closely aligned indicate the normality of the data set. Additionally, the skewness and kurtosis are within the range of -2 and + 2 showing that the data is normally distributed. These results confirms the assumptions of the parametric test

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

Frequency Distribution Table

Pre-Exposureµg/DL

Frequency

6

1

13.14

3

20.29

5

27.43

6

34.57

8

41.71

13

48.86

9

More

4

Post-Exposureµg/DL

Frequency

6

1

13.14

3

20.29

5

27.43

6

34.57

8

41.71

11

48.86

11

More

4

Histogram

Descriptive Statistics Table

Pre-Exposure µg/dL

 

 

 

Mean

32.8571429

Standard Error

1.75230655

Median

35

Mode

36

Standard Deviation

12.2661458

Sample Variance

150.458333

Kurtosis

-0.5760371

Skewness

-0.4251097

Range

50

Minimum

6

Maximum

56

Sum

1610

Count

49

Post-Exposure µg/DL

 

 

 

Mean

33.28571429

Standard Error

1.781423416

Median

36

Mode

38

Standard Deviation

12.46996391

Sample Variance

155.5

Kurtosis

-0.654212507

Skewness

-0.483629097

Range

50

Minimum

6

Maximum

56

Sum

1631

Count

49

Measurement Scale

The ratio data has been used because the Return on investment per number of contracts can be classified and ordered.

Measure of Central Tendency

The mean, median and mode of the data are 33.29,36 and 38. The three values are close meaning that the data is normally distributed and there is no skewness.

Skewness and Kurtosis

The skewness and kurtosis of both pre and post exposure data are within the acceptable region because the values fall with the range of -2 and +2 for the skewness and -7 to +7 for the kurtosis.

Evaluation

The data presented in the descriptive statistics indicates normally of the data because, skewness and kurtosis fall within the acceptable range of -2 and +2. Additionally, the measure of central tendency are closely aligned which is a sign of normal data. Therefore the assumptions of the parametric statistics have been met.

ANOVA: Descriptive Statistics and Assumption Testing

Frequency Distribution Table

A=Air

Frequency

3

1

5.75

3

8.5

4

11.25

8

More

4

B=Soil

Frequency

6

1

7.75

2

9.5

10

11.25

5

More

2

C=Water

Frequency

3

1

5.25

5

7.5

8

9.75

2

More

4

D=Training

Frequency

3

1

4.25

3

5.5

7

6.75

6

More

3

Histogram

Descriptive Statistics Table

 

A=Air

B=Soil

C=Water

D=Training

 

 

 

 

 

Mean

8.9

9.1

7

5.4

Standard Error

0.6840

0.3900

0.5758

0.2656

Median

9

9

6

5

Mode

11

8

6

5

Standard Deviation

3.0591

1.7442

2.5752

1.1877

Sample Variance

9.3579

3.0421

6.6316

1.4105

Kurtosis

-0.6283

0.1192

-0.2375

0.2537

Skewness

-0.3608

0.4920

0.7602

0.1592

Range

11

7

9

5

Minimum

3

6

3

3

Maximum

14

13

12

8

Sum

178

182

140

108

Count

20

20

20

20

Measurement Scale

The measurement scale used in the above case if ratio because the data can be classified and ordered.

Measure of Central Tendency

The mean, median and mode of Air are 8.9, 9 and 11. Soil has a mean, median and mode of 9.1, 9 and 8 while water has 7, 6 and 6. On the other hand, training is 5.4, 5 and 5. These values are close to each other implying that the data is normally distributed.

Skewness and Kurtosis

The skewness and kurtosis for all the data set, for Air, soil, water and training is illustrated in the above descriptive statistic and is between -2 and +2, implying that the data is moderately distributed and the distribution curve is not peaked. This confirms that the data falls within the acceptable region.

Evaluation

The mean, median and mode of the data are closely aligned showing the normalcy of the data. Similarly the skewness and kurtosis are within the acceptable range of -2 and +2 indicating that the data is normally distributed.

References

Creswell, J. W., & Creswell, J. D. (2018). Research design: Qualitative, quantitative, and mixed methods approaches (5th ed.). SAGE.

George, D., & Mallery, P. (2018). Descriptive statistics. In IBM SPSS Statistics 25 Step by Step (pp. 126-134). Routledge.

https://api.taylorfrancis.com/content/chapters/edit/download?identifierName=doi&identifierValue=10.4324/9781351033909-14&type=chapterpdf

Histogram

Frequency 103.38 104.37 105.36 106.35 107.34 108.33 109.32 110.31 111.30 112.29 113.28 114.27 115.26 116.25 117.24 118.22 119.21 120.20 121.19 122.18 123.17 124.16 125.15 126.14 127.13 128.12 129.11 130.10 131.09 132.08 133.07 134.06 135.05 136.04 137.03 138.02 139.01 140.00 More 1 2 1 3 6 6 9 12 18 17 26 22 27 47 36 44 47 53 61 60 62 74 70 81 93 73 105 80 88 67 50 56 35 30 19 7 8 5 2

Decibel

Frequency

Histogram

Frequency 50 55.86 61.71 67.57 73.43 79.29 85.14 More 4 5 7 8 14 10 8 6

Group A prior to Training

Frequency

Histogram

Frequency 75 78.14 81.29 84.43 87.57 90.71 93.86 More 2 5 10 12 14 11 5 3

Group B prior to Training

Frequency

Histogram

Frequency 6 13.14 20.29 27.43 34.57 41.71 48.86 More 1 3 5 6 8 13 9 4

Pre-Exposure µg/dL

Frequency

Histogram

Frequency 6 13.14 20.29 27.43 34.57 41.71 48.86 More 1 3 5 6 8 11 11 4

Post-Exposure µg/dL

Frequency

Histogram

Frequency 3 5.75 8.5 11.25 More 1 3 4 8 4

A=Air

Frequency

Histogram

Frequency 6 7.75 9.5 11.25 More 1 2 10 5 2

B=Soil

Frequency

Histogram

Frequency 3 5.25 7.5 9.75 More 1 5 8 2 4

C=Water

Frequency

Histogram

Frequency 3 4.25 5.5 6.75 More 1 3 7 6 3

D=Training

Frequency

Histogram

Frequency 2 3 4 5 6 7 8 9 10 11 More 1 1 5 13 18 24 18 12 7 2 2

Mean Annual Sick days per Employee

Frequency

Histogram

Frequency 10 35 60 85 110 135 160 185 210 235 260 285 310 335 More 1 1 9 9 17 18 24 27 37 24 21 15 12 4 4

Lost Time in Hours

Frequency