U VIII

Descriptive Statistics

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Data Analysis: Descriptive Statistics and Assumption Testing

Descriptive statistics tool will quantitatively summarize or describe data in a sensible way. Sun Coast Remediation data description will involve use of univariate analysis that allow examination of a single variable at a time. Three major characteristics of observing a single variable are central tendency, distribution, and dispersion (Ali & Bhaskar, 2016). In terms of measures of central tendency, the median, mode or mean are used to describe data. In terms of distribution, the frequency of individual or ranges of value for variables is summarized. Data assumptions commonly used in statistical research include assumptions of normality where the distribution of the test assumes a normal distribution with a standard deviation of 1 and mean of zero. Kurtosis and Skewness can be used to test for normal distribution with Kurtosis values and Skewness value should be zero or near zero (Norman & Streiner, 2008). Independence of the data is also tested and the typical assumption is that data are independent.

Correlation: Descriptive Statistics and Assumption Testing

Frequency distribution table. Insert table here. Cut and paste from Excel.

Histogram. Insert histogram here. Cut and paste from Excel.

Descriptive statistics table.

Measurement scale.

The measurement scale used here is ratio scale since it has quantity and equality of units. It is worth noting that the scale has an absolute zero meaning no number exists below the zero (Pagano, 2012). The measure of microns and mean annual sick days per employee of different job sites have quantity, equal units and no number exists below zero. In short, negative mean or microns are impossible.

Measure of central tendency.

For the microns, the mean is 5.62, mode is 8 and median 6. This means that on average employees are exposed to 5.62 microns in their given job sites. They imply that the center of the data set lies between these measured of central tendency. For the mean annual sick days per employee, the median and mode have the same value 7 while the mean is 7.13. This implies that the center of the data set lies at 7 days sick days per employee each annually.

Evaluation.

There are measures of central tendency essential for descriptive statistics. The Skewness and kurtosis coefficient value ranges between -2 and +2 for correlation an indication that the data is normally distributed (Karataş, n.d). The Skewness and kurtosis value for microns is near zero. However, the values are negative indicating that they are skewed left. Similarly, the Skewness and kurtosis of the annual sick days per employee is near zero though skewed to the right. This implies that it is a normal distribution thus meeting the assumptions for parametric statistical testing.

Simple Regression: Descriptive Statistics and Assumption Testing

Frequency distribution table. Insert table here. Cut and paste from Excel.

Histogram. Insert histogram here. Cut and paste from Excel.

Descriptive statistics table.

Measurement scale.

The contract number can be said to follow nominal scale. The contract are assigned numbers for identification purposes. The measurement scale used for expenditure and time is the ratio scale with properties of equal intervals, magnitude as well as absolute zero (Hanna & Dempster, 2012). It is impossible to spend less than zero amount on safety training or to record negative value of time.

Measure of central tendency.

On average, there are 358 contracts with a mode of 205 and median of 145. On average, the Sun Coast Company will incur 596 dollars on safety training with a mode of 234 and median of 507.8. On average, the lost time in hours due to safety training is 188 hours with a median and mode of 190.

Evaluation.

The presence of central tendency measures is essential in describing descriptive statistics. The Sun Coast Remediation should weigh on the average cost of training as well as the lost hours due to the training. The skewness and kurtosis coefficient of safety training expenditure and lost hours is near zero indicating normal distribution a key characteristic of parametric statistical testing (Norman & Streiner, 2008).

Multiple Regression: Descriptive Statistics and Assumption Testing

Frequency distribution table. Insert table here. Cut and paste from Excel.

Histogram. Insert histogram here. Cut and paste from Excel.

Descriptive statistics table.

Measurement scale.

Frequency can be said to have interval scale with properties of equal intervals, magnitude and identity. The chord length follows a ratio scale with the magnitude, equal intervals and absolute zero properties (Hanna & Dempster, 2012). There cannot be a negative length value though there can be no length. In terms of angles in degrees, it follows a ratio scale with a true zero. Additionally, the values can be divided or multiplied.

Measure of central tendency.

The chord length has at least mean and median. In terms of chord length, the skewness and kurtosis coefficient are near zero and they are both negative values. The negative kurtosis means light tailed distribution while negative skewness indicates the data is skewed left.

Evaluation.

The presence of central tendency measures is essential in describing descriptive statistics. The Sun Coast Remediation should weigh on the average chord length of 0.12 of the different contracts. The skewness and kurtosis coefficient of the chord length indicate normal distribution a key characteristic of parametric statistical testing (Norman & Streiner, 2008).

Independent Samples t Test: Descriptive Statistics and Assumption Testing

Frequency distribution table. Insert table here. Cut and paste from Excel.

Histogram. Insert histogram here. Cut and paste from Excel.

Descriptive statistics table.

Measurement scale.

The training scores can be said to follow ratio scale as they have properties of absolute zero, magnitude as well as equal intervals. Not unless there was no training taking place, the training score cannot be less than zero or record a negative score.

Measure of central tendency.

The training scores both prior training for Group A and revised training for Group B have mean, mode and median. Revised training for Group B has the same mode and median.

Evaluation.

The presence of central tendency measures is essential in describing descriptive statistics. The Sun Coast Remediation should weigh on the average scores of the prior training for Group A and the revised training for Group B in order to determine whether it is necessary to conduct the revised training or just the training. The skewness and kurtosis coefficient of the training scores indicate normal distribution a key characteristic of parametric statistical testing (Norman & Streiner, 2008). However, Group A training is skewed left while Group B training is skewed right.

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

Frequency distribution table. Insert table here. Cut and paste from Excel.

Histogram. Insert histogram here. Cut and paste from Excel.

Descriptive statistics table.

Measurement scale.

The pre-exposure and post-exposure can be said to follow ratio scale as they have properties of absolute zero, magnitude as well as equal intervals. They both record the same microgram per liter exposure of employees before exposure and after exposure.

Measure of central tendency.

The pre-exposure and post-exposure have the same mean, mode and median because there is no change in level of exposure among employees before and after exposure.

Evaluation.

The presence of central tendency measures is essential in describing descriptive statistics. The Sun Coast Remediation should weigh on the average scores of the exposure level before and after employees are exposed in their work environments. The skewness and kurtosis coefficient of the exposure levels indicate normal distribution a key characteristic of parametric statistical testing (Norman & Streiner, 2008). Additionally, the data is skewed left with a light tailed distribution.

ANOVA: Descriptive Statistics and Assumption Testing

Frequency distribution table. Insert table here. Cut and paste from Excel.

Histogram. Insert histogram here. Cut and paste from Excel.

Descriptive statistics table.

Measurement scale.

The project return on investment in air, training, water and soil can be said to follow ratio scale as they have properties of absolute zero, magnitude as well as equal intervals. They record positive values of percentage on each variable.

Measure of central tendency.

The variables have mean, mode and median. The mean, for instance, illustrates the average percentage of project return on investment of each variable.

Evaluation.

The presence of central tendency measures is essential in describing descriptive statistics. The Sun Coast Remediation should weigh on the average percentage of project return on each variable in order to determine the variables that will reap the most returns to invest in them. The skewness and kurtosis coefficient of the project return on investment indicate normal distribution a key characteristic of parametric statistical testing (Norman & Streiner, 2008).

References Ali, Z., & Bhaskar, S. S. (2016). Basic statistical tools in research and data analysis. Indian Journal of Anaesthesia, 60(10): 790. Hanna, H., & Dempster, B. (2012). Psychology Statistics For Dummies. John Wiley & Sons. Karataş, M. (n.d). Strategic Researches II: From Local to Global: Working Life And Social Policy. Ijopec Publication. Norman, G. R., & Streiner, D. L. (2008). Biostatistics: The Bare Essentials. PMPH USA. Pagano, R. R. (2012). Understanding Statistics in the Behavioral Sciences. Cengage Learning.