Unit VII Research Paper Research Methods

Jovanmaires

UnitIVScholarlyActivityResearchMethodsJovanMaires.docx

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Sun Coast Data

Jovan J Maires

Columbia Southern University

Unit IV Scholarly Activity

Dr. Renee Norris-Jones

15 September 2022

Data Analysis: Descriptive Statistics and Assumption Testing

This article is going to utilize descriptive statistics techniques to describe the Sun Coast Remediation data. The purpose of this description is to determine whether the assumptions are achieved to apply the parametric statistical processes.

Correlation: Descriptive Statistics and Assumption Testing

Frequency Distribution Table

PM size	Frequency
0 _ 1	8
2 _ 4	24
5 _7	37
8 _ 10	34

PM size

Frequency

0-1

2-4

5-7

8-10

Sick

Days

Frequency

0-2

4-7

8-9

10-12

Histogram

Frequency

PM Size Sick days

The histograms for correlation and the annual sick days

Descriptive Statistics Table

Microns		Sick days
Mean	5.6572815 5	Mean	7.12621 4
Standard Error	0.2556001 4	Standard Error	0.18648 4
Median	6	Median	7
Mode	8	Mode	7
Standard Deviation	2.5940581 4	Standard Deviation	1.89260 5
Sample Variance	6.7291376 4	Sample Variance	3.58195 3
Kurtosis	-0.8521619	Kurtosis	0.12492 3
Skewness	-	Skewness	0.14225
	0.3732571 3
Range	9.8	Range	10
Minimum	0.2	Minimum	2
Maximum	10	Maximum	12
Sum	582.7	Sum	734
Count	103	Count	103
Largest (1)	10	Largest (1)	12
Smallest (1)	0.2	Smallest(1)	2
Confidence Level (95.0%)	0.5069816 7	Confidence Level (95.0%)	0.36989

Measurement Scale

The numerous metrics used in analyzing the variables investigators use in data processing are referred to as measurement scales. They are crucial in research and statistics because the level of data measurement determines the data analysis technique to be used.

In this particular instance, the measurement scale is Ordinal.

The ordinal scale is a measurement that reports data ordering and ranking without determining the degree of variation between them. Ordinal symbolizes the notion of "order." Ordinal data is also referred to as qualitative data or categorical data. It can be categorized, identified, and listed.

Measure of Central Tendency

A statistic that reflects the specific significance of an overall dataset is known as a central tendency. Examples of central tendency include mode, median, arithmetic mean, and geometric mean, among others.

The mean is a measure of central tendency that takes the average of all values in a data set. The median is better than the mean for data from skewed distributions because it is not influenced by extremely large values (Mondal et al, 2022).

A test of normality for continuous data is an important step in determining measures of central tendency and statistical methods for data analysis. When our data has a normal distribution, parametric tests are applied to make comparisons among the groups; otherwise, nonparametric methodologies are employed.

Skewness and Kurtosis

The skewness for the distribution is near zero which implies that the values are skewed to the right. The kurtosis is less than three implying that it is a broadening of the peak and thickening of the tails.

Evaluation

Considering the descriptive statistic above it is clear that the data is normally distributed indicating that the assumptions for parametric statistical testing have been met.

Simple Regression: Descriptive Statistics and Assumption Testing

Frequency Distribution Table

Expenditure

Frequency

20-500

108

501-1000

1001-

1500

1501-

2000

2001-

2500

Time

Frequency

0-50

51-100

101-200

201-300

301-400

Histogram

Frequency

Training Expenditure

120

100

500 1000 1500 2000 2275 More

Expenditure

100

200

300

400

100

120

Time

Frequency

Descriptive Statistics Table

safety training

expenditure

lost time hours

Mean	595.9843812	Mean	188.004 5
Standard Error	31.4770075	Standard Error	4.80308 9
Median	507.772	Median	190
Mode	234	Mode	190
Standard Deviation	470.0519613	Standard Deviation	71.7254 2
Sample Variance	220948.8463	Sample Variance	5144.53 6
Kurtosis	0.444080195	Kurtosis	-.50122

Skewness 0.951331922 Skewness -0.08198

Range 2251.404 Range 350 Minimum 20.456 Minimum 10

Maximum 2271.86 Maximum 360 Sum 132904.517 Sum 41925

Count 223 Count 223

Largest (1) 2271.86 Largest (1) 360

Smallest (1) 20.456 Smallest (1) 10

9.46548

Confidence Level(95.0%) 62.03197147 Confidence Level(95.0%) 4

Measurement Scale

A Nominal Scale is a measurement scale for which figures are only used as labels to distinguish or categorize an object.

Measure of Central Tendency

Since the mean is typically not in the center of a distribution, the median is frequently chosen as the preferable measure of central tendency in these skewed distributions. When the tail on the right side of the distribution is longer than the tail on the left, the distribution is said to be favorably or right skewed.

Skewness and Kurtosis

Considering the skewness and kurtosis values, the distribution the tail on the right side is long indicating that the distribution is right skewed (Braden & Matis, 2022).

Evaluation

The data analysis results in showing that the data has similar extent of variance and hence the assumption for parametric tests is attained.

Multiple Regression: Descriptive Statistics and Assumption Testing

Frequency Distribution Table

Decibel	Frequency
107 - 111	51
112 - 116	126
117 - 121	249
122 - 131	786
132 - 141	287

Histogram

106

111

116

121

131

141

200

400

600

800

1000

Sound Level

Decibles

Frequency

Descriptive Statistics Table

Decibel

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

Interval

The interval scale is a quantitative measurement scale with order, significant and equal differences between the two variables, and arbitrary zero presence. It takes measurements of variables at regular intervals along a common scale.

Measure of Central Tendency

Mean

Summary metric that aims to summarize the entirety of a set of data using a single value that corresponds to the median or center of the distribution.

The determination of normalcy is a crucial step in choosing the statistical techniques and measurements of central tendency for data analysis. Parametric tests are employed when our data have a normal distribution; otherwise, nonparametric techniqe utilized to compare the groups (Owuor et al, 2022).

Skewness and Kurtosis

The negative values of skewness and kritosis indicate that the data is skewed to the left the left tail is long relative to the right tail, also the distribution is the curve with th same mean and standard deviation.

Evaluation

The assumptions are met since the mean is the measure of central tendency implying that the distribution is not affected by extreme values.

Independent Samples t Test: Descriptive Statistics and Assumption Testing

Frequency Distribution Table

Trainin

Frequen

49-60

61-70

71-80

81-90

91-100

Trainin

Frequen

74-80

81-85

86-90

91-95

96-100

Histogram

100

Training

Frequency

Descriptive Statistics Table

Prior training		Revised training
Mean	2	Mean	9
	1.40278	0.65947
Standard Error	8	Standard Error	9
Median	70	Median	85
Mode	80	Mode	85
	11.0455	5.19274
Standard Deviation	6	Standard Deviation	2
	122.004	26.9645
Sample Variance	5	Sample Variance	7
Kurtosis	-0.77668	Kurtosis	-0.35254


Skewness	-0.0868	Skewness	0.14408 5
Range	41	Range	22
Minimum	50	Minimum	75
Maximum	91	Maximum	97
Sum	4327	Sum	5256
Count	62	Count	62
Largest(1)	91	Largest(1)	97
Smallest(1)	50	Smallest(1)	75
Confidence Level(95.0%)	2.80504 8	Confidence Level(95.0%)	1.31871

Measurement Scale

Interval, the distance between two distinct variables is significant.

Measure of Central Tendency

Mean. This measure represents the center of the distribution of the data indicating the assumption of parametric testing is achieved (Eini & Khaloozadeh, 2022).

Skewness and Kurtosis

The values of skewness and kirtosis indicate that the data is normally distributed.

Evaluation

Since the measure of central tendency is Mean. This measure represents the center of the distribution of the data indicating the assumption of parametric testing is achieved.

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

Frequency Distribution Table

Exposu

Frequen

5-15

16-25

26-35

36-45

46-56

Exposu

Frequen

5-15

16-25

26-35

36-45

46-56

Histogram

Frequency

Descriptive Statistics Table

Pre-exposed μg/dL		Post-Exposure μg/dL
	32.857142		33.2857
Mean	9	Mean	1
	1.7523065		1.78142
Standard Error	5	Standard Error	3
Median	35	Median	36
Mode	36	Mode	38
	12.266145		12.4699
Standard Deviation	8	Standard Deviation	6
	150.45833
Sample Variance	3	Sample Variance	155.5
Kurtosis	0.5760371	Kurtosis	-0.65421
	3
	-
Skewness	0.4251096	Skewness	-0.48363
	5
Range	50	Range	50
Minimum	6	Minimum	6
Maximum	56	Maximum	56
Sum	1610	Sum	1631
Count	49	Count	49
Largest(1)	56	Largest(1)	56
Smallest(1)	6	Smallest(1)	6
	3.5232484		3.58179
Confidence Level(95.0%)	5	Confidence Level(95.0%)	2

Measurement Scale

For this case, interval is applied as the measurement scale is makes it possible to assign a numerical values to any given assessment.

Measure of Central Tendency

Mean as a measure of central tendency

Skewness and Kurtosis

The data distribution is peaked and possesses thick tails on one side and also the tail of the distribution curve is longer on the right side. On the other side, the outliers of the distribution curve are toward the left and far from the mean on the right.

Evaluation

The fact that the mean more specifically reflects the center of the distribution of the data.

ANOVA: Descriptive Statistics and Assumption Testing

Frequency Distribution Table

Air

Frequency

1-3

7-9

10-12

12-15

Soil

Frequency

5-7

8-10

10-13

Water

Frequency

1-3

4-6

7-9

10-12

Training

Frequency

1-3

4-6

7-9

Histogram

Histogram Air

Air

Frequency

Histogram Soil

Soil

Frequency

Histogram Water

Water

Frequency

Histogram Training

Frequency

Descriptive Statistics Table

A = Air		B = Soil
Mean	8.9	Mean	9.1
		0.68402		0.39000
Standard Error	8	Standard Error	7
Median	9	Median	9
Mode	11	Mode	8
		3.05906		1.74416
Standard Deviation	8	Standard Deviation	3
		9.35789		3.0421
Sample Variance	5	Sample Variance	5
Kurtosis	-0.6283	Kurtosis	0.11923
				0.492
Skewness	-0.36085	Skewness	2
Range	11	Range	7
Minimum	3	Minimum	6
Maximum	14	Maximum	13
Sum	178	Sum	182
Count	20	Count	20
Largest (1)	14	Largest (1)	13
Smallest (1)	3	Smallest (1)	6
Confidence Level(95.0%)	1.43168	Confidence Level (95.0%)	0.81629 4
	8
C = Water		D = Training
Mean	7	Mean	5.4
	0.57582		0.26556
Standard Error	9	Standard Error	8
Median	6	Median	5
Mode	6	Mode	5
	2.57518		1.18765
Standard Deviation	5	Standard Deviation	6
	6.63157		1.41052
Sample Variance	9	Sample Variance	6
Kurtosis	-0.23752	Kurtosis	0.25374 7
			0.7602		0.15918
Skewness	6	Skewness	3
Range	9	Range	5
Minimum	3	Minimum	3
Maximum	12	Maximum	8
Sum	140	Sum	108
Count	20	Count	20
Largest (1)	12	Largest (1)	8
Smallest (1)	3	Smallest (1)	3
Confidence Level (95.0%)	1.20522	Confidence Level (95.0%)	0.55584
	4

Measurement Scale

Ratio, the measurement of scale is quantitative in nature. Since i has enabled the comparison of the intervals

Measure of Central Tendency

Mean, the measure of central tendency is mean since the distribution requires scores that are numerical values on ratio scale.

Skewness and Kurtosis

The skewness and kritosis for this case is within the range and hence they represent a normal distribution.

Evaluation

The assumptions for parametric testing has been achieved since the measure of central tendency is mean (Kashlak et al, 2022).

References

Braden, P., & Matis, T. (2022). Cornish–Fisher-Based Control Charts Inclusive of Skewness and Kurtosis Measures for Monitoring the Mean of a Process. Symmetry, 14(6), 1176.

Eini, E. J., & Khaloozadeh, H. (2022). Tail variance for generalized skew-elliptical distributions. Communications in Statistics-Theory and Methods, 51(2), 519-536.

Kashlak, A. B., Myroshnychenko, S., & Spektor, S. (2022). Analytic Permutation Testing for functional data ANOVA. Journal of Computational and Graphical Statistics, 1-10.

Mondal, H., Swain, S. M., & Mondal, S. (2022). How to conduct descriptive statistics online: A brief hands-on guide for biomedical researchers. Indian Journal of Vascular and Endovascular Surgery, 9(1), 70.

Owuor, O. S., Benedict, T. J., & Kevin, O. O. (2022). Outlier Detection Technique for Univariate Normal Datasets. American Journal of Theoretical and Applied Statistics, 11(1), 1-12.