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Most often, repeated measures ANOVA test is the first choice among the researchers for determining the difference between 3 or more variables. However, if assumptions such as normal distribution isn’t met, an alternative test known as Friedman test is used.
Friedman test, an extended version of one-way ANOVA with repeated measures, is a non-parametric test used to determine the difference between 3 or more matched or paired groups. Basic ANOVA test has the assumptions of a normal distribution with their corresponding variances, but Friedman test eliminates these assumptions of normal distribution. The method incorporates ranking for each block together afterwards analyzing the values of ranks in each column. The Friedman test is primarily a 2-way ANOVA used for the data that is Non - parametric.
In Friedman test one variable serves as a treatment/group variable and another as a blocking variable. Here, the dependent variable must be continuous (but not normally distributed) and independent variable must be categorical (time/condition)
Like any other statistical test, this test too consists of a few assumptions including:
Prior to conducting this test, a researcher must set up hypothesis such as:
Today, although several tools such as SPSS, SAS, etc. are used to perform Friedman test, the most tool among the researchers is R language.
So, how do you conduct this test in R?
In order to conduct this test in R, import the file into R and refer to the variables directly within the data set. This is followed by analysing the data using the command “Friedman.test.” Create a matrix or table, fill the data and run the test using the “Friedman test ()” command.
Upon completion of the analysis, the next step is to interpret the results. I.e. to check if the test is statistically significant or not. To accomplish this, compare the P value with the significance level.
However, before interpreting the results, it should be noted that the Friedman test ranks values in each row. As a result, the test is not affected by sources of variability that equally affect all values in a row. Typically, a significance level of 0.05 works well. We check the value at 5 % significance level.
P-value ≤ significance level : If the p-value less than significance level, then we can reject the idea that the difference between the columns are the result of random sampling, concluding that at least one column differs from another.
P-value > significance level : If the P value is greater than the significance level, then the data doesn’t provide you with significant evidence to conclude that overall medians differ. However, this isn’t similar to stating that all medians are similar.
Although the outcome of Friedman tells you if the groups are significantly different from each other, they do not tell you which groups differ from each other. This is when post hoc analysis for the Friedman’s test comes into the picture.
The primary goal here is to investigate which all pairs of groups are significantly different from each other. If you have N groups, to check all of their pairs, you will have to perform n^2 comparisons, therefore the need of correcting multiple comparisons arise.
The initial step in a post hoc analysis in R to find out which groups are responsible for the rejection of the null hypothesis. For simple ANOVA test, there exists a readily available package that can directly calculate post hoc analysis -TukeyHSD.
This is followed by understanding the outputs from the test run. In the case of simple ANOVA, a box plot would be sufficient, but in the case of repeated measure test, a boxplot approach can be misleading. Therefore you can consider using two plots: (a) one for parallel coordinates (b) other boxplots of the differences between all pairs.
Glimpse at an example for Friedman test
Consider an experiment where 6 persons (block) received 6 different diuretics (groups) that were A to F. Here the response determines the concentration of Na in human urine and the observations were recorded after each treatment.
> require(PMCMR) [library used to perform Friedman test]
> r <- matrix(c(
+ 3.88, 5.44, 8.96,8 .25, 4.91, 12.33, 28.58, 31.14, 16.92,
+ 24.19, 26.84, 10.91, 25.24, 39.52, 25.45, 16.85, 20.45,
+ 28.67, 4.44, 7.94, 4.04, 4.4, 4.23, 4.36, 29.41, 37.72,
+ 39.92, 28.23, 28.35, 12, 38.87, 35.12, 39.15, 28.06, 38.23,
Nrow = 6,
Ncol = 6,
+ dimnames = list (1:,c("a”,"b","g","h","i","j")))
> print (r)
a b g h i j 1 3.88 5.4 48.96 8 .25 4.91 12.33 28.58 31.14 16.92,
24.19 26.8 10.91 25.2 39.5 25.45 16.85 20.45
28.67 4.4 47.94 4.04 4.4 4.23 4.3629.41 37.72
39.9228.23 28.35 12 38.87 35.12 39.15 28.06 38.23
STS > friedman .test(y)
Friedman chi-squared (χ 2) = 23.333,
Degree of freedom = 5 , p-value = 0.000287
Result - using friedman test
χ 2 (5) = 23.3- chi square test
p < 0.01
A different post hoc tests can be performed by using the command posthoc.friedman.conover.test in the PMCMR package.
Data occupies the ultimate position in the research process. A research procedure involves collection, analysis and interpretation of data. In the current era, one can easily collect plenty of information from various sources. However, not all data gathered will be useful and relevant to a study. One should thoroughly inspect and decide which information would help them in conducting their study. This is when the data mining process comes into the picture.
Data mining process involves filtering and analysing the data. It uses various tools to identify patterns and relationships in the information, which is then used to make valid predictions.
This process involves several techniques such as clustering, association, classification, prediction, decision tree, sequential pattern techniques have been developed which are widely used in various fields.
To conduct data ming process without any hassle, plenty of tools are available in the market. Among them, the most popular software trusted by the research community include:
Weka - This machine learning tool, also called as Waikato Environment, is built at the University of Waikato in New Zealand. Written in the JAVA programming language, this software supports significant data mining tasks such as data processing, visualisation, regression, and many more. Additionally, Weka is best suited for data analysis as well as predictive modeling. It consists of algorithms, visualisation software that support the machine learning process and operates on the assumption that data is available in the form of a flat-file. Weka has a GUI to give easy access to all its features in addition to SQL Databases via database connectivity.
Orange - This component based software aids data mining and visualisation process. Written in Python computing language, its components are known as ‘widgets’. The widgets range from data visualisation, preprocessing to the evaluation of algorithms and predictive modeling. The widgets offer characteristics such as presenting data table & enabling to choose features, reading the data, comparing learning algorithms, etc. Data in Orange gets formatted to the desired pattern swiftly and can be easily moved by simply flipping/moving the widgets. It also allows the user to make smarter decisions by comparing & analyzing the data.
KNIME - This tool is considered as the best integration platform for data analytics. Operating on the theme of the modular data pipeline, KNIME uses the assembly of nodes to preprocess the data for analytics & visualisation process. It constitutes different data mining and machine learning components embedded together. This tool is popularly used by the researchers for performing a study in the pharmaceutical field. KNIME includes some excellent characteristics, such as quick deployment and scaling efficiency. Additionally, predictive analysis is made accessible to even naive users.
Sisense - Considered as the best suited BI tool, Sisense has the potential to manage and process small as well as a large amount of data. Designed specially for non-technical users, this software enables widgets as well as drag & drop features. Sisense produces reports that are highly visual and lets combining data from different sources to develop a common repository. Further various widgets can be selected to develop the reports in the form of line charts, pie charts, bar graphs, etc. based on the purpose of a study. Reports can be drilled down merely by clicking to investigate details and comprehensive data.
DataMelt - DataMelt, also called as DMelt is a visualisation and computation environment offering an interactive framework to perform data mining and visualisation. DMelt is written in JAVA programming language, is designed mainly for technical users and for the science community. It is a multi-platform utility and can work on any operating system that is compatible with Java Virtual Machine (JVM). DMelt consists of scientific libraries to produce 2D/3D plots and mathematical libraries to develop curve fitting, random numbers, algorithms, etc. This software can also be utilised for analysis of large data volumes or statistical analysis.
SAS data mining - SAS or Statistical Analysis System is developed by SAS Institute for the purpose of analytics & data management. This tool can mine data, modify it, and handle data from various sources and conduct statistical analysis. It allows the user to analyse big data and derives precise insight to make timely decisions. SAS offers a graphical UI for non-technical users and is well suited for text mining, data mining, & optimisation. The added advantage of this tool is that it has a highly scalable distributed memory processing architecture.
IBM SPSS modeler - Owned by IBM, this software suite is used for data mining & text analytics to develop predictive models. IBM SPSS modeler consists of a visual interface that lets the user to work with data mining algorithms without any need for programming. It offers additional features such as text analytics, entity analytics etc. and removes the unnecessary hardships faced during the data transformation process. It also allows the user to access structured as well as unstructured data and makes it easy for them to use predictive models.
Data mining tools are important to leverage the existing data. Adopt trusted & relevant tools, use them to the fullest potential, uncover hidden patterns & relationships in data and make an impact for your research.
During your PhD journey, you will face various obstacles. Preparing an impressive dissertation proposal is one of them. Even though your dissertation topic is approved by your supervisor, you now have to pass the hurdle of submitting a great dissertation proposal. The proposal needs to contain essential sections including introduction, literature review, methodology, findings, summary and so on. If you have no or little knowledge about writing a dissertation proposal, you may feel stressed and anxious.
A paraphrase, or indirect quotation, translates another person’s ideas or words in your own words. Unlike summary, it doesn’t shorten or condense the original statements and is used with short passages like a sentence or two. Paraphrasing is used when you wish to incorporate the source material into your paper, thesis, or dissertation, and you cannot string together a series of quotations. While direct quotation is used when you want to preserve the sourced words initially, therefore the words of those authors should be noteworthy to quote them directly.
Are you looking towards developing skills that help you to develop networking and develop the base for your perfect career that you foresee after you finish your education? For this, you must first learn to correspond effectively and build networks to stay connected.
These days Email is an effective form of communication. But there is always a right and wrong way to do electronic communication. These are few important but right tricks to communicate effectively: