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What are the factors responsible to determine which test, parametric or non-parametric, is to be...

Question:

What are the factors responsible to determine which test, parametric or non-parametric, is to be used in quantitative research? Explain with treatments and examples.

Conditions Determining Parametric and Nonparametric Tests

For any quantitative decision making, statistical tools played a vital role. The main part of decision making is to accept or reject a statistical hypothesis. These hypothesis testing can be done by using various analysis techniques.

Answer and Explanation:

In any research procedure, data is the most important part of any analysis. There are generally two types of data, which are used in any research procedure, Continuous and Categorical:

  • Continuous Data - Data generally can have infinite values, which are numeric.
  • Categorical Data- Data is generally divided into finite groups. They are not arranged logically.

Parametric and Nonparametric Tests are conducted on Continuous Data. The factors responsible to determine which test, parametric or non-parametric are as follows:

1. Normality Test - This is the first test, to be conducted on any data. First, a Histogram is to be created. If there is Symmetry observed on both sides of the Histogram, then we may assume data to be normally distributed. This means that the mean clearly shows the center of the distribution of the pattern, in which the data is distributed. In this case, we can go for a Parametric Test. In the same way, if there is no symmetry in the distribution of data on both sides of the Histogram, then it can be assumed that the median, is displaying the center of the pattern of distribution of the data. In this case, Nonparametric Tests are used. Suppose we have records of a patient's temperature and we want to analyze the data. We first construct a Histogram, by observing both the ends of the Histogram, we will decide whether to use Parametric or Nonparametric Tests.

2. Sample Size- If there are large sample sizes, then Parametric Tests can be used. For small sample sizes, Nonparametric Tests are used.

3. Type of Tests

  • Parametric Tests
  • Non-Parametric Tests
  • T-Test
  • Wilcoxon Rank Sum Test
  • Correlation Mann - Whitney U Test
  • Logistic Regression Spearman Correlation
  • ANOVA Kruskal-Wallis test

Example - A reputed clinic of a city is wondering when to use a Parametric or Nonparametric Test. Then T-Test or Wilcoxon Rank Sum Test can be used.

If they are giving treatment for a disease and the outcome is the measure in some clinical terms - T-Test should be used if data is normally distributed and the Wilcoxon Rank Sum Test if not normally distributed.

Suppose the clinic wants to know from the test reports of patients if they are cured of a disease - Logistic Regression can be used.

If the clinic wants to predict the satisfaction level of the patients, then Linear Regression can be used for determining the dependent variable from normally distributed data.

Now if the clinic wants to know about the efficiency of the doctors according to the opinion of the people, they can categorize the data into a five or seven-point Likert Scale. They can also try to find out the difference in opinion according to gender. The opinion will vary from person to person and may be independent of each other. In this case, a Chi-Square Analysis can be used.

If the clinic wants to know about the difference in opinions about the efficiency among the group of patients according to income or age ANOVA could be used for Parametric Tests and the Kruskal-Wallis Test for not normally distributed data.

Generally, a Parametric Test is more statistically reliable than a Nonparametric Test.


Learn more about this topic:

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Parametric Equations in Applied Contexts

from Precalculus: High School

Chapter 24 / Lesson 6
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