NUR 705 Assignment 12.1 Parametric and Non-parametric Tests in JASP

Sample Answer

There are many statistical measures that can be used to describe a data set, but some of the most common are the mean, standard deviation, minimum, and maximum. Skewness and kurtosis are also important measures of central tendency and dispersion. The mean is simply the arithmetic average of a data set.

To calculate it, one simply adds up all the values in the data set and then divide by the number of values. The standard deviation is a measure of how spread out the values in a data set are. It is calculated by taking the square root of the variance. The minimum is the smallest value in a data set, while the maximum is the largest value.

Skewness and kurtosis are two measures of the shape of a distribution. Skewness measures the asymmetry of a distribution, while kurtosis measures the tailness of a distribution. Positive skew indicates that the bulk of the data is concentrated on the left side of the distribution, while negative skew indicates that the bulk of the data is concentrated on the right side of the distribution.

Kurtosis, on the other hand, can be either positive or negative. Positive kurtosis indicates that there is more data in the tails of the distribution than in a normal distribution, while negative kurtosis indicates that there is less data in tails of the distribution than in a normal distribution. The purpose of this assignment is to undertake the Descriptive Statistics on The Variable “Beginning Weight in Pounds (Ratio)”

JASP is an important statistical software that is normally applied in the analysis of descriptive statistics. JASP is an important tool in running descriptive statistics because it is -fast, -effective, – user friendly, and- intuitive allowing users to quickly and easily generate high quality results. It has a wide range of features, making it perfect for both experienced statisticians and those who are new to the field. JASP also offers excellent support and resources to accurately determine outcomes.

Descriptive Statistics on The Variable “Beginning Weight in Pounds (Ratio)”

Table 1 Descriptive Statistics

Beginning Weight in pounds (ratio)

Mean	177.300
Std. Deviation	49.835
Skewness	1.073
Std. Error of Skewness	0.427
Kurtosis	0.908
Std. Error of Kurtosis	0.833
Minimum	112.000
Maximum	302.000

From table 1, the average beginning weight in pounds is 177.300 with a standard deviation of 49.835. The maximum beginning weight is 302.00 pounds while the minimum weight beginning weight was 112.00. The table also show a skewness of 1.073 and a kurtosis of 0.908. The standard error of kurtosis is 0.833 while that of skewness is 0.427.

Graph 1 Distribution Plots

Beginning Weight in pounds (ratio)

Graph 1 shows a normal distribution of “Beginning Weight in Pounds” data. The graph reveals that mean is greater than median and median is greater than the mode. The graph does not indicate a normal distribution. When the mean, median, and mode are all equal, this indicates a normal distribution of data. This happens when there is an approximately equal number of data points that are above and below the mean.

A normal distribution of data is a statistical concept that refers to how data is distributed across different values (Lyon, 2020). This type of distribution is often seen in nature, and it can be used to model real-world phenomena. The bell-shaped curve of a normal distribution is created by taking the average of all the data points and then plotting them in order against how many standard deviations they are away from the mean.

Statistical Assumptions

The assumptions of descriptive statistics are that the data is sampled from a population and that the data is Normally distributed. The first assumption can be checked by looking at a histogram or frequency table of the data. If the data appears to be Normal, then the second assumption can be checked using a Kolmogorov-Smirnov test (Martínez-Flórez et al., 2020). However, if the data does not look Normal or there is not enough information to run a Kolmogorov-Smirnov test, then it is recommended to use nonparametric methods instead.

The Kolmogorov-Smirnov test is a powerful tool for testing whether a given sample data is from a population with a specific distribution. It is based on the idea of comparing the cumulative distribution function of the sample data to that of the population. If the two are close, then the null hypothesis is accepted (that the data is from the population), but if they are far apart, then the null hypothesis is rejected. The key advantage of this test over others is that it does not make any assumptions about the distribution of the population, making it very general and applicable to many situations. Another advantage is that it can be used even when only a small number of sample data points are available.

Assumption on the Data

The variable under consideration does not meet the assumption of normality. The graph is not symmetrical meaning that the mean, median, and mode are not equal. The graph shows positive skewness. In other words, all the values are aligned towards right.

Skewness and Kurtosis Of “Beginning Weight in Pounds.”

The data is positively skewed most of the values are lying toward the right-hand side. The mean of the data is greater than the median (a large number of data-pushed on the right-hand side) and the median is greater than the mode. The graph is also mesokurtic but positively skewed. The data does not meet normal distribution. The assumption of normality has been violated. Non-parametric tests should be used instead of parametric test in the process of data analysis.

Descriptive Statistics on “Ending Weight in pounds.”

Table 2 Descriptive Statistics

Ending Weight in pounds (ratio)

Mean	172.500
Std. Deviation	42.592
Skewness	1.073
Std. Error of Skewness	0.427
Kurtosis	1.368
Std. Error of Kurtosis	0.833
Minimum	122.000
Maximum	282.000

From table 2, the average ending weight in pounds is 172.500 with a standard deviation of 42.592. The maximum ending weight is 282.00 while the minimum is 122.00

Graph 2 Distribution Plots

Ending Weight in pounds (ratio)

From graph 2, the “Ending Weight in pounds.” Variable does not show a normal distribution. The data is positively skewed whereby the mean is greater than the median and median greater than the mode. The data is platykurtic. The data does not meet the statistical assumption of normality. Besides, the data is not normally distribution, in other word normal distribution has not been met. The statistical assumption of normality has been violated. Non-parametric tests should be applied instead of parametric tests in the analysis.

Normally Distributed Variable

Generally speaking, a variable is considered to be normally distributed when the mean, median and mode are all equal, and the graph is symmetrical. This assumes that the data has been collected randomly from a large population (Wang & Lee, 2020). However, there are many exceptions to this rule, so it is always best to use a statistical test to determine if a variable is normally distributed. Independence of the data means that the data is not biased in any way. The data is collected objectively and without any preconceptions. Independence of the data is important to ensure that research is conducted accurately and without any errors.

In terms of normal distribution, independence of the data means that the data is not dependent on any other data points. This is often referred to as “independence of errors.” This is an important concept in statistics because it helps us understand how certain statistical tests work. For example, the t-test assumes that the observations are independent of each other. This assumption is necessary for the test to be valid. If the observations were not independent, then the t-test would not produce a valid result. both variables did meet this assumption because of skewness.

References

• Lyon, A. (2020). Why are normal distributions normal?. The British Journal for the Philosophy of Science. https //www.journals.uchicago.edu/doi/abs/10.1093/bjps/axs046?journalCode=bjps
• Martínez-Flórez, G., Leiva, V., Gómez-Déniz, E., & Marchant, C. (2020). A family of skew-normal distributions for modeling proportions and rates with zeros/ones excess. Symmetry, 12(9), 1439. https //www.mdpi.com/2073-8994/12/9/1439
• Wang, C. C., & Lee, W. C. (2020). Evaluation of the normality assumption in meta-analyses. American journal of epidemiology, 189(3), 235-242. https //doi.org/10.1093/aje/kwz261