 Hello all, in this video I am going to deal about basics of sample size calculation. Our ultimate aim is to select a sample size from the population. We cannot do our study in all of our population because it involves more cost, time and personal. It is neither feasible nor ethical also. So we are taking a few sample from the study population and we are doing our research. While doing so we should ensure the representativeness of the sample to the population so that the results from the sample will be generalizable to the population. We have five major steps in sample size calculation. First is we need to identify the major study variable and its type whether it is a number or a percentage. After identifying the major study variable and its type the step two is doing a thorough review of literature and identifying the expected frequency from a similar study. Step three is understanding the parameters used for sample size calculation followed by calculating the sample size which can be done by formula or online calculators, apps and software. Formulas are going to be the more complicated method to calculate the sample size which I am going to demonstrate and online calculators are the most easiest which also will be demonstrated in the end. Step five is the adjustments. There are three adjustments here. Adjustments for population size, design effect and response rate. So now we are going to deal with each steps in detail. Step one is identifying the major study variable and its type. For example if the study variable is exam result then we need to decide whether we are going to measure the average or mean marks of the study population or we are going to measure the mere pass or fail status from the study population. If your study interest is on anemia we need to fix whether we are going to measure the hemoglobin level of the population or we are going to check the status of anemia present or not. After fixing the study variable and its type we need to do a thorough review of literature, identify prevalence from the similar study. If we are not able to get a similar study then we are supposed to do a pilot study or we need to go with the maximum prevalence for proportion as 50% which will yield the maximum sample size. In the third step we need to understand the parameters involved in calculation of sample size. For sample size calculation we need to be clear about the types of errors. We have two types of errors that is type one or alpha error and type two or beta error. The null hypothesis which says that there is no significant difference may be true or false. Our study result may accept it or reject it. If we correctly accept a true null hypothesis then that is the right decision. If we correctly reject a false null hypothesis then that is also a right decision. If we falsely reject a true null hypothesis then that is called as type one error or alpha error and if we falsely accept a false null hypothesis then it is called as type two error or beta error. The 100 minus beta will yield you the power of the study. The probability of committing an alpha error is called as p-value. After fixing the level of these errors which is most commonly going to be 0.05 or 0.20 we need to look at this z-table corresponding to the alpha and beta error values which we fixed before calculating the sample size. We have the liberty to allow this alpha error and beta error before calculating the sample size. As we are stingent in allowing this alpha error and beta error then your z-value is going to increase and increase your sample size because z-value is directly proportional to the sample size. The step four is going to calculate the sample size. There are various ways to calculate sample size that is you can calculate directly by applying the formula or online calculators, absence software. In this presentation I am going to show you calculating the sample size through formulas and online calculators. When proportion is the parameter of our study then the formula is going to be n is equal to z-square p-q by d-square where z is the standard normal dv8 or the z-value p is the proportion or prevalence of the interest from the similar study which we got through the review of literature and q is 100 minus p, q is 100 minus p, d is clinically expected variation or precision. This can be either absolute or relative precision. This precision is the value which will be altered by the researcher in order to adjust the sample size. Here is one example. From a pilot study it was reported that 28% had anemia, it was decided to have 95% confidence interval and 10% variability in the estimated 28%. How many patients are necessary to conduct the study? So what is given here is the prevalence, 28% through a pilot study. This can be through a pilot study or through review of literature from the similar study. So q is 100 minus p which will yield 72%, z-alpha is 1.96 for alpha at 0.05, d is 10% of 28%, that is 2.8% because it is given as 10% variability in the estimated 28%. So it is going to be the relative precision of 10%. So the formula given here is n is equal to z-square pq by d-square. So substituting the values 987.8 as the required sample size. Now how to write up this in our protocol or the research article? So a sample size of 988 would be sufficient to observe 28% prevalence of anemia with 10% relative precision and 95% confidence interval. Now when mean is the parameter of our study, how to calculate the sample size? So the sample size, the formula is z-square instead of pq we have this standard deviation square divided by d-square. d is the difference between the mean or the clinically expected variation. So z is same standard normal deviation at the z value, s is sample standard deviation, d is clinically expected variation or the precision between the means. Here is the example for calculation of sample size for estimation of mean. In a health survey of school children it is found that the mean hemoglobin level of 55 boys is 10.2 per 100 ml, a standard deviation of 2.1, consider the precision as 0.8. So mean is given as 10.2, standard deviation is 2.1, z value is going to be 1.96, d is going to be 0.8, the formula is n is equal to z-square, standard deviation square divided by precision square, so substituting the values you will get 26 as the sample size. Now we are moving on to the next two scenarios that is when we are going to compare two groups for proportion and means. So when the proportion is the parameter of our study, the formula is n is equal to z-alpha and z-beta whole square into p into q into 2 divided by d-square, p is equal to average percentage between two groups, q is equal to 100 minus p, whereas d is the precision, here it is clinically meaningful difference between two groups. So here is one more example, prevalence or the combined prevalence of is given as 10.4 percentage, so q will become 100 minus p, so 89.6 percentage, z-alpha is 1.96, z-beta is 1.282 for beta error at 0.10, so substituting these values will yield 125 in each arm. So when mean is our parameter of our study, the formula is n is equal to z-alpha plus z-beta whole square into standard deviation square into 2 divided by d-square, where s is standard deviation between the two groups, d is the clinically meaningful difference. So here is an example for calculation, so mean duration of ICU in hours for a low dose is 61.7 and high dose is 33.2, standard deviation is given here. We are fixing alpha level at 0.05, beta level at 0.10, so substituting the formula we will get n is equal to 210, if we are keeping the beta error as 0.10 and if we are keeping the beta error as 0.20, then we will get 157 as required sample size. Now the fifth step is adjustments after calculating sample size, which usually researches miss while calculating sample size. We have three adjustments, finite population correction, design effect, response rate. This design effect and response rate is going to increase your calculated sample size, but finite population correction will decrease your required sample size. What is finite population correction? If the population is small, then the sample size can be reduced slightly. This is because a given sample size provides proportionately more information for a small population than a large population. Here is a formula for finite population correction. The new sample size is equal to the calculated sample size divided by 1 plus calculated sample size minus 1 divided by the total population size. Now the two factors which may increase the sample size is response rate and the design effect. For non-response rate, the sample size can be modified using this formula. The required sample size is equal to calculated sample size divided by response rate. Remember, here we are not using the non-response rate. Instead, we are dividing the response rate with the calculated sample size to yield the required sample size. Now the third adjustment is for the cluster designs, we should inflate the sample size based on the design effect. Now how to calculate the design effect? So design effect is going to be 1 plus b minus 1 into rate of homogeneity, where b is equal to the cluster size and RoH is rate of homogeneity, otherwise called as intracluster correlation, which will be ranged as below. And we have to remember, for sample size calculation of case control studies, survival analysis, and validation studies are going to be different. Validation studies are diagnostic studies. The formula for validation studies or diagnostic studies is given here. Those who are interested can pause the video and can check. Now I am going to demonstrate how to calculate sample size using online calculators. So I am using here cleancalc.com for the sample size calculation. So here all our four scenarios will be given. So you need to select between this study group, whether you are using one group or two group. So if suppose let me start with one group, and whether if we are dealing with the categorical or a dichotomous variable, or we are dealing with proportion. So we will click like this. The calculation will appear here. So here they are asking for non-population in order to have this finite population correction. And the study group prevalence they are asking. And all followers we can adjust. And based on that, they will apply the z value and calculate the sample size. Same way we can use for one group continuous variable. The calculations will be here. Same way we can compare between two independent study groups. And means can be calculated. So group one anticipated mean and group two anticipated mean has to be substituted. And alpha and power will be here. Same way two group dichotomous variables can be calculated through this online sample size calculator. Here is one more tool for online sample size calculation that is select-statistics.co.uk, where you can have these calculators comparing two mean sample size, population mean sample size, comparing two proportion sample size, population proportion sample size. In this tool, you can get the information about, if you have any doubt about the information which you are feeding, you can check this info icon. After substituting these values, we will get a sample size, calculated sample size. And in alternative scenarios, when we are adjusting this alpha and beta error, how the sample size will change also will appear. So from this written example, we can get an idea on how to write this in research paper or your proposal. Basically, the sample size calculators is for estimation of a population proportion, population mean, and estimating an odds ratio, which we have not discussed. That also can be calculated using this online sample size calculator and comparing two proportions and comparing two means. This select statistics.co.uk and cleancalc.com are easy to use. To summarize, we have five steps in sample size calculation. Step one is to identify the major study variable and its type, whether we are going to estimate a mean or a proportion. Step two is, after deciding on the major study variable, we are going to do a thorough review of literature. We are going to get a similar study and the expected frequency of the variable. Then the third step is to understand the parameters used for sample size calculation. And fourth is to calculate the sample size either by formula or online calculators or apps or software. And the fifth is the adjustments. There are three types of adjustments. One is the finite population correction. Number two is the design effect adjustment. And number three is the adjustment for the response rate. Thanks for watching this video. If you like this video, please share it to your friends and subscribe to our channel. Thank you very much.