Category: Power Analysis

How do you Determine Appropriate Sample Size for your Study?

Calculating the precise sample size is an important aspect of a research (especially in the medical field). It defines validity and applicability of the key findings of the study. Different studies follow different approach to calculate the sample size. 

Defining sample size 

Sample size is the number of observations drawn from a particular population. Sample size is represented as ‘n’ and is a positive integer. 

For example, if you want to determine how a population of specific age group respond to social policy, then you can test the social policy on a small group of people of the target population and determine the response. The sample size here would be the group of people who were interviewed. 

The selection of sample size depends on the statistical and non-statistical considerations. Non-statistical considerations include availability of sampling frame, resource, ethic and budget. Whereas the statistical considerations include precision of expected prevalence and estimate of prevalence. 

Aspects to be considered while determining the sample size are:

  • Population size – Since the proportion or percentage of overall population represented by the sample is to be determined, the total population size under study must be identified. The exact population size can be unknown and approximated between two numbers.   
  • Margin of error – Samples may not be perfect. Therefore, a small amount of error must be allowed. Margin of error, also known as confidence interval, identifies how greater or lesser than the population mean the sample mean can fall. The standard margin error is considered to be +/- 5%. 
  • Degree of variability – This refers to distribution of attributes in the population. Degree of variability varies depending on the attributes and target population. If the population is more heterogeneous, large sample size is required to achieve a greater level of precision. The moe homogenous is the population, the smaller the sample size. 50% of proportion represents the greater variability level. 
  • Confidence level – The confidence level, also known as risk level, states that when a population is sampled repeatedly, then the average value of attribute acquired  by the samples is equal to the true population value. 
  • Standard deviation – It represents the amount of expected variances. The value of standard deviation generally used is 0.5. This value ensures that the sample is large enough. 

Sample size can be determined using various approaches. These include applying formulas, using census, employing published tables and using sample size of a similar study. Let’s have a detailed look at each method. 

  • Applying formulas 

This is one of the most commonly used methods in the determination of sample size. Generally, the formula for sample size is given by, 

Sample size = (Z-score)2 * StdDev*(1-StdDev) / (margin of error)2 

However, it is important to note that there is no universal formula to calculate the sample size. For example, the formula used to calculate sample size for cross sectional studies is given by, 

Sample size = (Z1-ɑ/2 )2 p (1-p)/ d2 ( qualitative variable) and sample size = (Z1-ɑ/2 )2 SD2/ d2 (quantitative variable). 

For case studies, sample size =  (r+1/r) [(p*) (1-p*) (Zᵦ + Z ɑ/2 )]/ (p1-p2)2 

  • Using census 

Census can be used for small population. This method eliminates the sampling error and offers data on all participants in the population. The major feature this method the cost associated with developing the questionnaire remains fixed, irrespective of number of samples. Here, virtually, the whole population must be sampled to obtain the desired precision level. 

  • Using published tables

Another method is using published tables that provide sample size for a given criteria. However, when using published tables, it must be presumed that the attributes under investigation are distributed normally. If this assumption if not met, then the entire population must be surveyed. 

  • Using sample size of a similar research 

The fourth method is to use sample size from studies that are similar to you. However, prior to using the sample size, review the approaches used in that study to avoid the risk of repeating the same errors in your study. Review the literature in your field of study and identify the sample size used. 

Immense care should be taken while determining the sample size. This is because if the calculated sample size is lower, then the confidence level will be lower and margin of error will be higher, making the data less reliable. Also, trying to achieve confidence level beyond 95% can be unrealistic.

Wilcoxon Rank-Sum test : A Non Parametric Alternative to two Sample T-Test

Statistics, a scientific approach to analyzing 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, the Chi-square test is to be used.

Similarly, for the comparison of means of two independent groups, the 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 utilized 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 utilized 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<span”> – 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 utilized. 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.

6 Tips to Save Yourself From Committing Blunders in Data Analysis Stage of Research

In a research process, data analysis is considered as a crucial aspect as it helps in structuring the findings and provides meaningful insights to the critical decisions. In this step, cleaned data is put into analysis tools for identifying patterns, formulating results so as to make meaningful inferences and conclusions.  

Conducting data analysis is not every scholar’s cup of tea. One should know the types of data analysis, which approach one must use, how to perform it and which statistical tool one should use for each type. If done in an inaccurate manner, data analysis can ruin your study in one-shot. Below are a few tips that have the potential to help you with data analysis process and save your study.

  • Define your research question – Design the question such that they are measurable, concise, clear and can qualify potential solution.
  • Set measurement priorities – This step can be broken into (a) what to measure (b) how to measure it. (a) Here you will have to determine what type of data you will require to answer your research questions. Once the data surrounding the main question has been obtained, you have to ask yourself a few secondary questions. All the data obtained and the secondary questions can then be converted into useful information. It is vital to choose the apt data, the reason is that the data collected will determine how it gets analyzed in the later stage. (b) Your research dictates the research methodologies you use to measure the variables. For example, if you have collected quantitative data, you will be measuring variables and verifying existing theories/ hypothesis/ questioning them. Data is often used to create new hypotheses, that is based on the results of the data collected.
  • Gathering of data – The next phase gathering of data. Before gathering the data, check if there is any data available relevant to your research questions. Decide which method you will be using to gather data; Questionnaire method, survey method etc. It is always advisable to collect data in a simple and organised form. Once you have collected the data, screen the information for its accuracy.
  • Data scrubbing – Data scrubbing, also known as data cleansing, is the process where incorrect data is removed. Some of the data you have gathered may be duplicated, may be incomplete, or redundant. Through this you can eliminate all such “dirty data”.
  • Data analysis – Now that the data is collected, the next step is to analyse it. You can use various methods and tools for this purpose. Approaches:Descriptive statistics, inferential statistics, exploratory data analysis and many more. Tools: SPSS, STATA, SAS etc.
  • Data interpretation – Once the data has been analyzed, it can easily be interpreted. Does it help you with any of your objections? Are the results limiting or inconclusive? etc.  If all your research questions are dealt with the data gathered accurately, then your research can be considered as complete.

The data analysis process is very intensive. Different researchers prefer different approaches. Some may prefer to use the software as the main way of analyzing the data, while others may use the software only to organize and manage the information.

 

5 Essential Terms to Know Before Carrying Out Data Analysis

Understanding the results or findings of a research is a vital part of knowing whether a research study provides a compelling case for changing practice. To understand research result, it is important to understand how studies are designed and how data are analysed.

Before carrying out your data analysis it is important to know following essential terms:

1) Population:

A population is the set of all possible cases of interest.
In determining the population of interest, we usually specify the point in time that defines the population and also specify the geographic region over which the population spread, if relevant.

Eg: Am I interested in my currently enrolled science students, or those who also completed the course last year?

2) Sample:

A sample is a set of cases that does not include every member of the population.
Or

A subset of the population is called as a sample.

Eg: It may be too costly or time-consuming to include every student in the study instead choose only those students in a class whose name begins with ‘A’ and thus be only working with a sample.

3) Variable:

A variable is a quality or condition that can differ from one case to another.

The opposite notion to a variable is a constant, which is simply a condition or quality that does not vary among cases. Most research is devoted to understanding variables – whether a variable takes on certain traits for some cases and different traits for other cases.

4) Research Questions:

A research question states the aim of a research project in terms of cases of interest and the variable upon which these are thought to differ.
One needs a clear research question in mind before undertaking statistical analysis to avoid the situation where huge amounts of data are gathered unnecessarily and do not lead to any meaningful results.

Eg: What is the age distribution of the student in my science class?

5) Conceptual Definition:

The conceptual definition of a variable uses literal terms to specify the qualities of a variable.
A conceptual definition is much like a dictionary definition: it provides a working definition of the variable so that we have a general sense of what it ‘means’.

Eg: A researcher might define ‘health’ conceptually as ‘an individual’s state of well- being’.

It is clear, though, that if the researcher now instructs any other researchers to go out and measure people’s ‘state of well-being’, they would leave scratching their heads.

Study Tips That Every PhD Scholar Should Know Of!

PhD isn’t as simple as a walk in the park. All scholars have their fair share of struggles and to get some productivity and constructive outcome from their journey. If you are an avid reader and are fortunate enough to have an inspiring and encouraging mentor then you would have some good advice to simplify your journey. Hope some of these tips can help you in your journey:

Begin writing as soon as you can start: Writing often is the only way to learn how to write well. A consistent progress in your document would help you to deal with the obstacles as and when they get created. My suggestion to begin writing as early as possible in the course of your PhD is to improvise on your writing skills and become a seasoned writer by the time you are ready to deal with a full-fledged research paper. In addition, you collect content and re use at the subsequent stage of your course. Not only would it save your time when you sit to write your papers but it would also augment the quality of your document.

Read more than you can: For anyone who has told you that you need to read only research and topic related to your study, I wouldn’t support it. Reading a lot of papers gives you a very clear overview of your field of study and understand the important research done in your area but also gives you the understanding to avoid duplication of existing work and reinvention of the wheel but at the same time research is not the only challenge for a PhD scholar. There are challenges and hiccups related to non-academic issues such as time management, creativity, motivation and so on. Reading material that aids your dealing with such issues is a very good idea. It would help you to grow as a student and give you practical tips for development of essential soft skills required for the journey and the career ahead.

Look at the small signs of progress: It would become easier to lose motivation to continue working if you looked at only the bigger achievements as they would be only few and countable in the entire duration of the course. However, the small little accomplishments do pave the path for the bigger milestones an giving yourself a pat on the back for them now and then is a good idea to keep going ahead and moving forward.

Be generous with yourself, you and every PhD scholar deserves it.