Wilcoxon Rank-Sum test : A nonparametric alternative to two sample t-test

Statistics, a scientific approach to analysing numerical data, is employed to discover relationships among the phenomena to describe, predict and control their occurrence. 

Statistics helps the researcher to acquire precise, steadfast and dependable findings. Although there are several statistical tests such as ANOVA, independent t-test, etc. to arrive at the right result, one must choose the test according to the type of study. 

For instance, if one wants to investigate if the means of two or more groups are different from each other, then he/she must use the ANOVA test. On the other hand, if a researcher wants to test the relationship between categorical variables, Chi-square test is to be used. Similarly, for the comparison of means of two independent groups, two-sample t-test is used. However, if the t-test doesn’t satisfy the requirements for two independent samples, then Wilcoxon Rank-Sum is used as it can offer the two independent samples drawn from populations with an ordinal distribution. This test does not assume known distributions, does not deal with parameters, and hence it is considered as a non-parametric test. 

Wilcoxon Rank-Sum test also known as Mann-Whitney U test, makes two important assumptions. That is the assumption of independence and equal variance. These assumptions are sufficient for determining if the two populations are different. Additionally, if we assume that the two populations are identical (except for a difference in location), then Wilcoxon Rank-Sum can be utilised as a test of equal means or medians. 

Power calculation for Wilcoxon Rank-Sum test

Power is nothing but the probability of rejecting the null hypothesis when it is false. The power calculation for the Wilcoxon Rank-Sum or Mann-Whitney U test is similar to that of the two sample equal-variance t-test except a few modifications are made to the sample size based on the assumed data distribution. 

The sample size ni| is equal to ni|= ni/𝑊, 

where 𝑊 is known as the Wilcoxon adjustment factor, which is based on the assumed data distribution. 

In general, the valid range for the probability of accepting a false null hypothesis is 0 to 1. However, different domains have different standards for setting power. 

Sample size conditions 

While solving for sample size, the researcher must choose a condition that describes the constraints either on N1 or N2 or both.

  1. Equal (N1 = N2) – This condition is utilised when a researcher has equal sample sizes in each group. Since both sample sizes are solved at once, no additional sample size parameters are required here. 
  2. Include N1, solve for N2 –  This condition is chosen to fix N1 at some value, and then solve only for N2. However, for some values of N1, N2 value that is large enough to acquire the desired power may be absent. 
  3. Enter N2, solve for N1–  In case a researcher wants to fix N2 at some value, and then solve only for N1, this condition is used. In this case too, N1 that is large enough to get the desired power might be absent for some values of N2. 
  4. Enter R = N2/N1, solve for N1 & N2 – To choose this condition, one must set a suitable value for the ratio of N2 to N1. This is followed by the determination of required N1 & N2 to obtain the desired power using PASS approach. An equivalent representation of R is N2 = R * N1. 
  5. Include percentage in group 1, solve for N1 & N2 – Here, the researcher must set a definite value for the percentage of the total sample size in group1. Next, PASS determines the required N1 and N2 with the value of percentage entered to acquire the desired power. 
  6. N1 (sample size, group 1) – This condition is used if group allocation = “Enter N1, solve for N2.” Where N1 is the number of individuals sampled from the group 1 population and must be equal or greater than 2. Here a single or a series of values can be entered. 
  7. N2 (sample size, group 2) If group allocation = “Enter N2, solve for N1,” this condition is utilised. Here N2 is the number of individuals sampled from the group 2 population and must be greater or equal to 2. A single or a series of values can be entered in this condition. 

The Wilcoxon Rank-Sum test is less sensitive to outliers when compared to that of the two-sample t-test and valid for data from any distribution.  However, it reacts to other differences between the distributions such as differences in shape, especially if the focus is on the differences in location between the two distributions. This is considered as the major disadvantage of the Wilcoxon test. Also, when the assumptions of the two-sample t-test hold, this test is less likely to detect a location shift in comparison with the t-test.

If you ever have to be an Interviewer: you should be like…..?

A good interviewer is a person, who has to be multi-faceted. He is a “jack of all trades” because his role is very complex and challenging.

If you are researcher, there is a strong chance that you would get that opportunity to be an interviewer, once at least, because it is an integral technique of data collection. It surely requires some homework and preparation from your side before you venture into the field with the cap of an interviewer:

List down the cooperation and involvement you expect from your respondents: You have to identify your respondents, with their availability and schedule. You must know who will be the best people to interview, according to what kind of expectations you have from them, and what is your objective of the research.

Ways to motivate respondents to perform well: As an interviewer, first of all, you go to take the work seriously so that your respondent also absorbs and depict seriousness of similar intensity in their work. Remember, only when you are convinced about the importance of your research, that you can convince others.

Have clarifications ready for all concerns: You should be prompt enough to handle all questions that come up from respondents, instantly. You can be prepared for some questions and some may come to you unanticipated. Your candid, spontaneous and prompt response is sought here.

Have parameters ready to assess quality: While you are in the process of interviewing, not all respondents would be authentic and genuine, in the same degree. Some may give you casual answers and others may be more focused. Ignoring casual and non-serious responses is imperative for the quality outcome of a research. While in the process of interviewing, the interviewer must be ready, and smart enough to assess the quality of the responses, either through the body language or seriousness in responses given by the respondent.

Bring consistency for quality: Doing interviews is not a one day process, and requires consistency in effort and motivation throughout the endeavour, despite challenges of poor, uninterested respondents and other distractions that may come in the way throughout the process in terms of time, money and quality of responses.

In a conference: How to handle the questions that follow your presentation?

A conference is a serious affair and your research is serious business too. You surely prepare hard and toil a lot, to not only create the research, but also present it effectively in the conference, so that none of the unique features and specialities of your research get unnoticed. But, how much do you actually prepare for the post presentation part; the questions that follow you presentation? They could be about unanswered queries of the presentation. They could come from experts in the subject matter who are here to test your knowledge and expertise on the area you have researched. You cannot take that lightly and give a disrespectful response, lest you know with all the seriousness that you presented the paper, has gone down the drain. With all this kept in mind while preparing yourself to deal with it, know very well that all the questions that will be shot at your or your team may not be benign. Some of the questions may, of course, be genuine queries and may ask you to give more information about your research, enlightening in the process on how you could further enrich and improvise your research. At the same time, there would be some questions that may not be the ones you want to hear or even answer. These could be bringing up your flaws in the research or presentation or something important that you have missed on to. The best thing to do here is to admit to your flaws and not get too defensive. Be graceful and gracious and thank the person for his contribution and at the same time, say that you would surely take the suggestions seriously, and see the best way in which they could be incorporated.

Being polite in your response to questions shot at you is required and imperative in the situation. Keep the moral ground higher and be courteous. However, you can handle them swiftly, and move on in a jiffy rather than hanging on to the question for a long time. Do not hold your attention to that one person in the audience who intends to pull you down, focus on the other audience, as quick as you can.

If you wish and have people such as peer, friends or family who can help you practice these responses with impromptu questions, it would be a great help. So, while you are preparing for your conference presentations, think beyond as well, and prepare for the Q & A session too. The more prepared you are the better you handle, always.

Do you know the facts and rules related to the use of ITALICS?

We often see writers using italics in their writing, as and when they wish to. Sometimes writers use italics to highlight some content they wish to like a quotation or a proverb. In fact, most of the times, at their free will, we see writers using italics to highlight, beautify or showcase their content. There are some facts in English language that are related to the use of italics. If you haven’t heard of them before, don’t forget to do so now and note then down for all your further writing attempts.

  1. Italics can be used when you are incorporating few words from a foreign language in your content.
  2. Italics has to be used to write algebraic expressions. For instance, when you are writing the value of “x” in any formula, so “x” has to be in italics.
  3. Like I said before, italics is used by writers for the purpose of emphasis on a specific word, however it should not be done in the case of formal, especially academic writing.
  4. In some places, if you feel the dire need to emphasise on a specific word and you feel the content would be incomplete without it. It is a good idea to mention in brackets, just next to the word that the purpose of italics is to emphasise on the word.
  5. Most of the styling guidelines such as APA & Chicago Manual of Style have their own specifications about the use of italics and according to the guidelines, most of the Latin words are not italicised.

As a researcher you must be careful of not overusing italics as it may create a negative impact about your research rather than solving the purpose you had in your mind. In a state of complete ignorance, often writers try to beautify their document by using italics liberally but it goes against the norms of formal academic writing often supervisors feel put off with over use of italics. The writing shouldn’t be just simple and easy in terms of content but also simple and as much as possible uncomplicated in terms of font and formatting. When you do that, you send a message to your reader that your content is strong enough to not need the support of complexity in language or display. It is sufficient in its strength to engage you as a reader.

The Love Hate Relationship Between You and Your Supervisor

What are dream supervisors made up of? Well, a dream supervisor has the following qualities

  • Wisdom
  • Positivity
  • Communication skills
  • Analytical clarity
  • Patience
  • In-depth knowledge
  • Creativity
  • Empathy, to name a few.

I am sure by the end of the list, you have understood pretty well that dream supervisors do not exist and are merely utopian. Even if you come across a person who has all the above traits and is willing to be your supervisors, remember to acknowledge that they are humans and not saints and most of the time they are so pressurised with their own jobs and perhaps even frustrated that they can’t shower all their goodness on their scholars. Whatever be your supervisor like, but he would surely want to see you succeed and not be a failure. It is an expectation with a selfish expectation attached to it as with your success is associated their reputation and subsequent promotions in the future. For a while during your PhD course, if you stop performing it starts to reflect in the position of your supervisor in the department. No way can you take this relationship for granted, even for a short while during your complete PhD journey.

With all the connection that you and you supervisor have and where you success is interdependent, surprisingly your supervisor may not exactly tell you what to do or what is expected from you. This can frustrate you or make you feel disconnected with your supervisor but don’t do that. As a scholar, you need to be pragmatic and take initiatives to meet and interact with your supervisor as you would need that advice from time to time. You need not wait or look for an initiative from your supervisor rather ask queries and seek advice from time to time. Rarely would you find supervisors who themselves get in touch and provide inputs without the scholar asking for it.

Remember that the ball is in your court always and at the same time, whether you like it or not but your success is dependent on the single most significant individual. You have to be focused on understanding the role and advice of your supervisor for a smooth as well as successful PhD experience.

Try to schedule quality time for discussion with your supervisor. They are busy people and may give you erratic responses depending on their work pressure and state of mind. Give them attention if you want them to give you attention. That’s the only way that you can ensure they focus on you and your PhD remains on their priority list.