Author: johnson

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.

Know the Difference: Parametric Test and Non-Parametric Test in Statistics

Statistical tests are mind bogglers! Collection, organisation, interpretation and analysis of data and results constitutes an integral part of statistics. Statistical tests, are basically the medium through which we can approximate solutions when the processes are highly complex or unknown in their true forms.

Statistical tests are classified into

  1. parametric test, and
  2. non parametric test

Parametric test-

Parametric test (conventional statistical procedure) are suitable for normally distributed data. The majority of elementary statistical methods are parametric, and parametric tests generally have higher statistical power.

  1.  In the parametric test, the test statistic is based on distribution.
  2.  The measurement of variables of interest is done on interval or ratio level.
  3.  In general, measure of central tendency in the parametric test is mean.
  4.  Parametric test can be applied only for the variables.
  5.  This test provides you with complete information about the population.

Parametric Test for Independent Measures Between Two Groups: T-test- A t-test is used to compare between the means of two data sets, when the data is normally distributed. Here, the two groups of data must be independent from one another.

Parametric correlation test: Pearson test – A common parametric method of measuring correlation between two variables is the Pearson Product-Moment Correlation. In this test, the variables should be normally distributed.

Why should you use parametric test?

  1.  Parametric tests can perform well with skewed and non normal distributions
  2.  Parametric tests can perform well when the spread of each group is different
  3.  Parametric tests usually have more statistical power than nonparametric tests

Non parametric test

Non parametric test (distribution free test), does not assume anything about the underlying distribution. Non parametric tests are used when the data isn’t normal.

  1.  In the case of non parametric test, the test statistic is arbitrary.
  2.  The variable of interest are measured on nominal or ordinal scale.
  3.  The measure of central tendency is median in case of non parametric test.
  4.  Non parametric test doesn’t consist any information regarding the population.
  5.  This test can be applied to both variables as well as attributes.

Non Parametric Test for Independent Measures Between Two Groups: Mann-whitney test-  This test is used to compare the means between two groups of ordinal data.

Non parametric correlation test: Spearman test- This test is used when data are ordinal rather than interval. This test works the same as the Pearson Correlation test, but the data here must first be ranked.

Reasons to use non parametric test

  1. Your area of study is better represented by the median
  2. Your sample size is too small to run a parametric test
  3. Your have ordinal/ ranked data or outliers that cannot be removed

Lastly, to use parametric test or nonparametric test often depends on whether the mean or median more accurately represents the center of the data set’s distribution. If the mean represents the center of the distribution of your data, and the sample size is large enough, use  parametric test and if the median represents the center of the distribution of your data, use non parametric test.