Q 723. What is Non-parametric Analysis? In which type of industries is it mostly used? Highlight its advantages using some examples. 

 

Note for website visitors -

• This platform hosts two weekly questions, one on Tuesday and the other on Friday. 
• All previous questions can be found here: https://www.benchmarksixsigma.com/forum/lean-six-sigma-business-excellence-questions/. 
• To participate in the current question, please visit the forum homepage at https://www.benchmarksixsigma.com/forum/.
• The question will be open until Tuesday or Friday at 5 PM Indian Standard Time, depending on the launch day. 
• Responses will not be visible until they are reviewed, and only non-plagiarised answers with less than 5-10% plagiarism will be approved. 
• If you are unsure about plagiarism, please check your answer using a plagiarism checker tool such as https://smallseotools.com/plagiarism-checker/ before submitting. 
• All correct answers shall be published, and the top-rated answer will be displayed first. The author will receive an honourable mention in our Business Excellence dictionary at https://www.benchmarksixsigma.com/forum/business-excellence-dictionary-glossary/ along with the related term.

• Some people seem to be using AI platforms to find forum answers. This is a risky approach as AI responses are error-prone because our questions are application-oriented (they are never straightforward). Have a look at this funny example - https://www.benchmarksixsigma.com/forum/topic/39458-using-ai-to-respond-to-forum-questions/

• We also use an AI content detector at https://quillbot.com/ai-content-detector. Only answers with less than 45-50% AI-generated content will be approved.

Non-parametric analysis is a type of statistical analysis that does not assume a specific distribution for the data. This approach is particularly useful when you cannot safely assume that your data follow a normal distribution or when you have a small sample size, making it difficult to reliably estimate parameters of a distribution.

 

Industries Using Non-Parametric Analysis:

1. Pharma: In medical research, outcomes often do not follow a normal distribution, and the sample sizes can be small.
2. Finance: Financial data, such as stock returns, often do not conform to normal distribution assumptions.
3. Agriculture: Biological and agricultural data can be highly variable and not normally distributed.
4. Market Research: Consumer preference data can be skewed, making non-parametric methods useful.
5. Environmental Science: Environmental data can often be skewed and irregular.

 

Example of Non-Parametric Test:  Working in a Pharma Organization where there are lot of clinical trials that happen, this is used where a new drug is has to be tested to determine its effectiveness in lowering blood pressure in patients with hypertension. The sample size for the clinical trial is small, consisting of only 15 patients.

 

Step	Process Description	Advantage
Initial Data Collection	The blood pressure of each patient is recorded before and after the treatment.	Non-parametric methods can be used to compare the readings without assuming any underlying distribution.
Analysis of Results	The collected blood pressure readings are analyzed using non-parametric methods.	Robust for small sample sizes and allows for reliable statistical analysis without needing a large trial.
Handling Outliers	During the trial, an outlier is detected where one patient had an unusually high blood pressure post-treatment.	Non-parametric methods provide reliable results despite the outlier, as they are less sensitive to outliers.
No Assumption of Population Distribution	The distribution of blood pressure changes is found to be skewed rather than normally distributed.	Non-parametric methods do not require normal distribution, allowing analysis without transforming data.
Ease of Implementation	The researchers quickly perform the analysis using non-parametric methods with standard statistical software.	Non-parametric methods are simpler to implement and interpret, enabling prompt communication of results.

 

Non-parametric analysis is one of the statistical methods that do not make any assumptions about the underlying data distribution. Unlike traditional methods, it is not required data to be more of a specific pattern like a normal curve. It is therefore flexible, and it can be used in a lot of cases.
 

Industries Using Non-Parametric Analysis:

 

• Healthcare: Medical analysis that deals with problems where the distributions are not normal of the medical data like patient outcomes or drug efficacy is often one of the approaches.
• Social Sciences: Gathering data about people's behaviors, attitudes, and opinions is traditionally the basis for the process of information mining resulting most of the time in nonstandard structures.
• Environmental Science: environmental data which contains examples such as pollution levels and climate pattern involves non-normal distributions.
• Finance: In the case of finance, the stock market is analyzed by means of data that do not conform to a normal distribution along with investigating market trends.

Advantages of Non-Parametric Analysis with Examples: 

• Flexibility: Insensitive to Traditional Assumptions, Technically, it can analyze data that do not obey the traditional assumptions, creating the possibility of it being used in different contexts.
  • Example: How about assuming you are exploring whether the efficacy of two new drugs is truly different? When the datum on patient recovery times does not match with the Gaussian model, nonetheless, Mann-Whitney U test which is meant to be a non-parametric test can still be used efficiently between the two groups.
• Robustness To Outliers: It is more to the extent of not being as susceptible to outliers and extreme values, which sometimes may be found due to sampling error can change the results of parametric tests drastically.
  • Example: In a study on income allocation, some very rich individuals might alter traditional tests in a manner in which they become useless. Yet, a non-parametric test is relatively less disturbed by outliers and thus, conveys a clearer dataset.
• Ease of Interpretation: Non-parametric tests often lead to more precise interpretations, hence there is no need for complicated calculations and operations.
  • Example: Experiences of non-parametric tests often result in simpler models that are, sometimes, easier to handle and describe, especially in a highly sophisticated data set.

In essence, non-parametric analysis is a valuable tool that can help you make sense of data, even when it doesn't fit the traditional mold.

Non - parametric analysis is a data analysis approach or statistical method that do not assume specific distribution like normal distribution. This method is flexible as they are distribution free and are used for ordinal and categorical data.

Some of the industries where non-parametric analysis are used are:
- Healthcare & Medicine industry: Analyzing patient behaviour and side effects
- Retail and Marketing: Analyzing consumers preferences and testing the impact of advertising
- Environmental and social study: Analyzing survey responses which are ordinal data like ratings

Some of the advantages of non-parametric analysis are:
- Flexibility with the data types: Customer satisfaction surveys data like "Very Satisfied", "Neutral" & "Not Satisfied"
- Effective with small sample size: Non-parametric datasets are robust with smaller data
- Simple and easy to understand: Spearman's rank correlation between employee satisfaction and productivity ranking

Q 723. What is Non-parametric Analysis? In which type of industries is it mostly used? Highlight its advantages using some examples. 

 

 

Non parametric analysis is a type of statistical method that doesn’t rely on strict assumptions about data. This Data more flexible and work well for :

·        Ordinal data

·        Nominal data

·        Small sample sizes

·        Skewed data or outliers

 

Industries Where Non-Parametric Analysis is Used and examples

Industry	Reason of using non-parametric Analysis	Example	Test mainly used
Health care and pharmaceutical	Can experience lot of non-normal data, small sample sizes, and ordinal variables.	-Analyzing patient recovery times under different treatment. -The effectiveness of two drugs. -Patients satisfaction analysis. - Comparing adverse drug reaction among patients using 3 medications	Kruskal-Wallis H Test     Mann-Whitney U Test).   Wilcoxon Signed-Rank Test   Chi square test
Retail and consumer behavior	can handle diverse data types, such as customer preferences, purchasing habits, and survey responses.	- Customer preference by by age group - Sales performance comparison   - Discount strategy evaluation   -Loyalty program impact   -seasonal sales trend   - correlation between spend	Chi-Square Test     Kruskal-Wallis Test     Mann-Whitney U Test     Wilcoxon Signed-Rank Test   Friedman Test   Spearman’s Rank Correlation
Insurance or investment companies	deal with often non-normal, skewed, or ordinal. Non-parametric methods are ideal for analyzing claims, customer behaviors, risk assessments, and portfolio performance in these sectors.	- Comparing claim processing times - Customer satisfaction pre/post-policy change   - Investment preferences by age group or employee’s categories   -Portfolio performance by advisors - Correlation between premium and claims	Kruskal-Wallis Test   Wilcoxon Signed-Rank Test     Chi square test       Mann-Whitney U Test   Spearman’s Rank Correlation
Hotel industry	The hotel industry often deals with complex non normally distributed data, ex: customer reviews /satisfaction	-Analyzing guest satisfaction across multiple branches -Comparing room service ratings across branches - Measuring the impact of a new loyalty program - Analyzing guest preferences for room types - Evaluating staff performance pre/post training	Kruskal-Wallis Test           Wilcoxon Signed-Rank     Chi-square Test         Sign Test
Education	In Education always use in ordinal data	-Evaluating teaching methods -comparing student performance across school -Comparing academic stress level	Kruskal-Wallis Test Mann-Whitney U Test     Spearman’s Rank Correlation

 

Non-parametric analysis is a flexible and reliable method for analyzing data, especially when traditional techniques don’t work well. It’s ideal for uneven data, small samples, or ranked information. This approach is used in many industries to uncover valuable insights, even from irregular datasets.

 

 

Non-parametric analysis is a statistical method that do not o not reference specific parameters. Parameters are the values of Shape, Spread and Centering. For a normal distribution the shape is normal, the spread is s, the center is m. For every value of m and s, there is another normal distribution that is defined. A nonparametric hypothesis test looks at the sample data and calculates a test statistic based on the medians without reference to the parameters. It determines whether that test statistic is inside or outside of the chosen risk level (i.e. beyond the decision point).

 

 

 

Below are some Industries where Non-parametric Analysis is commonly Used:

 

 

 

Manufacturing: In manufacturing, non-parametric methods can be used to analyze defect rates, production times, and other quality metrics that may not follow a normal distribution.

Healthcare: In healthcare, non-parametric tests can be applied to patient satisfaction surveys, treatment outcomes, and other data that do not meet parametric assumptions.

Finance: Financial analysts may use non-parametric methods to assess risk and return distributions, especially when dealing with non-normally distributed financial data.

Retail: Retailers can use non-parametric analysis to evaluate customer feedback and sales data

 

 

Below are advantages of Non-parametric Analysis:

 

 

 

Fewer Assumptions: Non-parametric methods do not require the assumption of normality, making them applicable to a wider range of data types. For example, if a manufacturing process produces a variety of defect types that do not follow a normal distribution, non-parametric tests like the Mann-Whitney U test can be used to compare defect rates between different production lines.

Robustness to Outliers: Non-parametric methods are less sensitive to outliers, which can skew results in parametric tests. For instance, in a healthcare study analyzing patient recovery times, if a few patients had exceptionally long recovery periods, a non-parametric test like the Kruskal-Wallis test would provide a more reliable comparison of recovery times across different treatment groups.

Applicability to Ordinal Data: Non-parametric methods are ideal for analyzing ordinal data, such as survey responses. For example, in a customer satisfaction survey where responses are rated on a scale from 1 to 5, non-parametric tests can effectively analyze the differences in satisfaction levels across different demographics without assuming equal intervals between ratings.

Simplicity: Non-parametric tests are often simpler to compute and interpret, making them accessible for teams without extensive statistical training. For example, using the Wilcoxon signed-rank test to compare pre- and post-intervention scores in a quality improvement project can be straightforward and effective.

 

 

Below are some of the Non-parametric Tests:

 

 

 

Mann-Whitney U Test: Used to compare differences between two independent groups when the data is not normally distributed. For instance, comparing the defect rates of two different suppliers.

Kruskal-Wallis Test: An extension of the Mann-Whitney U test for comparing more than two groups. This could be used to analyze customer satisfaction ratings across multiple product lines.

Wilcoxon Signed-Rank Test: Used for comparing two related samples, such as measuring the impact of a process change on defect rates before and after the change.

 

One of the key things to keep in mind is that nonparametric tests tend to have less power (to detect a difference) than the parametric tests.

In Six Sigma Projects, we often need to analyze data and draw conclusion about the population from the data given. There are two types of statistical tests that can be done depending on the distribution of data. If the data is normally distributed, then we use parametric test. If the data is non-normally distributed, then we can use non-parametric tests. Non-parametric tests are also referred to as distribution free tests.

 

In non-parametric test measure the central tendency using the median values. Predominantly such tests are done on nominal/ordinal/skewed data where population knowledge is limited. Nominal data means that data cannot be arranged in any specific order and no mathematical calculations can be performed. Example: Blood groups for a human being, Gender, Religion. Ordinal data contains data that can be arranged in an order but cannot be computed. Example: school grades, ranking of products

 

Non-Parametric test can be used in Healthcare, Pharmaceutical, Manufacturing and Media industries (rating/ranking).

How are they used across the above industries:

 

1) In the Media or Film industry: Comparing the ranking of movies A, B and C across different age groups. We can compare the median ranking of different age groups to see if there is a significant difference

2) In the Pharmaceutical industry: We can use non-parametric test to compare data. Eg: Comparing the adverse effects of different type of covid vaccines

3) In the Healthcare industry: We can use non-parametric test to compare patient satisfaction levels acquired from internal surveys

4) In the Manufacturing industry: We can use non-parametric test to compare before and after results Eg: Performance of a machine after a new part has been fitted.

 

There are several kinds of non-parametric test with their functions listed below.,

 

1)      Mann- Whitney Test: to compare continuous outcome in 2 independent samples

2)      Kruskal-Wallis Test: to compare continuous outcome in > 2 independent variables

3)      Friedman Test: to compare difference between 3 or more groups

4)      Chi-Square Test: to categorical variables for Independence

5)      Mood Median Test: to test medians of two independent samples

6)      Sign Test: to compare continuous outcome in matched pairs of samples

7)      Wilcox Test: More powerful than sign test and compare the magnitude of difference

 

It was a tough decision to decide the winner for this question. All the answers are good and a must read. The answer that stands out for the examples and usage of non-parametric tests is from Asangi and hence has been declared as the best answer.