Question

Parametric vs. Nonparametric Methods

The purpose of this assignment is to differentiate between parametric and nonparametric statistical methods. In addition, this assignment will help you understand and implement parametric or nonparametric statistical methods.

Research the following statistical topics:

• Levels of measurement
• Parametric and nonparametric methods

On the basis of your research and understanding, respond to the following:

• Find and state the definition of levels of measurement that distinguishes the five types of data used in statistical analysis.
• In your own words, compare the five types of data and explain how they differ.
• Find and state a definition of parametric and nonparametric methods that distinguishes between the two.
• In your own words, explain the difference between parametric and nonparametric methods.
• Explain which types of data require parametric statistics to be used and which types of data require nonparametric statistics to be used and why.
• Compare the advantages and disadvantages of using parametric and nonparametric statistics.
• Describe how the level of measurement helps determine which of these methods to use on the data being analyzed.

Answer 1

1)

A variable has one of four different levels of measurement: Nominal, Ordinal, Interval, or Ratio. (Interval and Ratio levels of measurement are sometimes called Continuous or Scale). It is important for the researcher to understand the different levels of measurement, as these levels of measurement, together with how the research question is phrased, dictate what statistical analysis is appropriate. In fact, the Free download below conveniently ties a variable’s levels to different statistical analyses.

The first level of measurement is nominal level of measurement. In this level of measurement, the numbers in the variable are used only to classify the data. In this level of measurement, words, letters, and alpha-numeric symbols can be used. Suppose there are data about people belonging to three different gender categories. In this case, the person belonging to the female gender could be classified as F, the person belonging to the male gender could be classified as M, and transgendered classified as T. This type of assigning classification is nominal level of measurement.

The second level of measurement is the ordinal level of measurement. This level of measurement depicts some ordered relationship among the variable’s observations. Suppose a student scores the highest grade of 100 in the class. In this case, he would be assigned the first rank. Then, another classmate scores the second highest grade of an 92; she would be assigned the second rank. A third student scores a 81 and he would be assigned the third rank, and so on. The ordinal level of measurement indicates an ordering of the measurements.

2)

1)integer 2)booleans. 3)characters. 4) floating-point numbers .5) alphanumeric strings..

3)

Parametric tests::::

assume underlying statistical distributions in the data. Therefore, several conditions of validity must be met so that the result of a parametric test is reliable. For example, Student’s t-test for two independent samples is reliable only if each sample follows a normal distribution and if sample variances are homogeneous.

Nonparametric tests:::

do not rely on any distribution. They can thus be applied even if parametric conditions of validity are not met.

Parametric tests often have nonparametric equivalents. You will find different parametric tests with their equivalents when they exist in this grid.

4)

What is the difference between a parametric and a nonparametric test? Parametric tests assume underlying statistical distributions in the data. ...Nonparametric tests do not rely on any distribution. They can thus be applied even if parametric conditions of validity are not met.

To make the generalisation about the population from the sample, statistical tests are used. A statistical test is a formal technique that relies on the probability distribution, for reaching the conclusion concerning the reasonableness of the hypothesis. These hypothetical testing related to differences are classified as parametric and nonparametric tests.The parametric test is one which has information about the population parameter.

On the other hand, the nonparametric test is one where the researcher has no idea regarding the population parameter. So, take a full read of this article, to know the significant differences between parametric and nonparametric test.

5)

it’s safe to say that most people who use statistics are more familiar with parametric analyses than nonparametric analyses. Nonparametric tests are also called distribution-free tests because they don’t assume that your data follow a specific distribution.

You may have heard that you should use nonparametric tests when your data don’t meet the assumptions of the parametric test, especially the assumption about normally distributed data. That sounds like a nice and straightforward way to choose, but there are additional considerations.

In this post, I’ll help you determine when you should use a:

• Parametric analysis to test group means.
• Nonparametric analysis to test group medians.

Parametric tests(means)	Nonparametric tests (medians)
1 - sample t test	1 - sample Sign, 1 - sample Wilcoxon
2 - sample t test	Mann - whitney test
One way ANOVA	Kruskal - Wallis, Mood's median test
Factorial DOE with one factor and one blocking variable	Friedman test

6)

Advantages parametric test.:::

Many people aren’t aware of this fact, but parametric analyses can produce reliable results even when your continuous data are nonnormally distributed. You just have to be sure that your sample size meets the requirements for each analysis in the table below. Simulation studies have identified these requirements. Read here for more information about these studies.

Advantages nonparametric test.:::

For some datasets, nonparametric analyses provide an advantage because they assess the median rather than the mean. The mean is not always the better measure of central tendency for a sample. Even though you can perform a valid parametric analysis on skewed data, that doesn’t necessarily equate to being the better method. Let me explain using the distribution of salaries.

in this situation, parametric and nonparametric test results can give you different results, and they both can be correct! For the two distributions, if you draw a large random sample from each population, the difference between the means is statistically significant. Despite this, the difference between the medians is not statistically significant. Here’s how this works.

7)

Types of Data & Measurement Scales: Nominal, Ordinal, Interval and Ratio

Nominal::::

Let’s start with the easiest one to understand. Nominal scales are used for labeling variables, without any quantitative value. “Nominal” scales could simply be called “labels.” Here are some examples, below. Notice that all of these scales are mutually exclusive (no overlap) and none of them have any numerical significance. A good way to remember all of this is that “nominal” sounds a lot like “name” and nominal scales are kind of like “names” or labels.

Ordinal::::

With ordinal scales, the order of the values is what’s important and significant, but the differences between each one is not really known. Take a look at the example below. In each case, we know that a #4 is better than a #3 or #2, but we don’t know–and cannot quantify–how much better it is. For example, is the difference between “OK” and “Unhappy” the same as the difference between “Very Happy” and “Happy?” We can’t say.

Ordinal scales are typically measures of non-numeric concepts like satisfaction, happiness, discomfort, etc.

Interval:::

Interval scales are numeric scales in which we know both the order and the exact differences between the values. The classic example of an interval scale is Celsius temperature because the difference between each value is the same. For example, the difference between 60 and 50 degrees is a measurable 10 degrees, as is the difference between 80 and 70 degrees.

Interval scales are nice because the realm of statistical analysis on these data sets opens up. For example, central tendency can be measured by mode, median, or mean; standard deviation can also be calculated.