This is a more technical lesson. Where we are going to describe the different methods, used to calculate a simple size. We're also going to describe a few inputs needed for that proposal. We already defined a few of them and we're going to see additional factors that are needed to calculate the sample size. Basically, we describe of emitted based on precision and also power base simple size calculations for equal sample and equal sample. Before presenting the different metadata typically use to calculate the sample size of household server, it is worth describing first this circle of influence. This circle of influence highlight the importance of re-sampling method. Along with the sample size to show how the truth is or should be in the population of reference. A good sampling method along with a good sample size are critical parameters considerations to produce the sample data representing the anterior populations and we shall also reduce the simple bias. Quality sampling is re-emitted that is typically recommended for household covered server. For which the sample can be calculated based on the power, based on the precision and sometime using both for precision and power. Lets describe a first precision-based sample size calculations, and then talk about the power base method. What is of the precision base sample size calculations? Let's first remember what we mean by precision. Precision is the closeness or level of confidence we wish a sample value can be expected to approximate the population value for a given indicators. Precision-based sample size calculation is therefore defined as an approach base on a desired level of precision, level of confidence to have in your sample point estimate. For any estimate, we expect a margin of error or uncertainty around it that will depend on the size of the sample and the underlying variability of the data. In that respect, the larger the sample size, the lower the uncertainty and better the precision of your sample. Before presenting the formula to calculate the precision-base of sample size, it's good to point out that the precision of the sample size depends on a few factor, which are typically target populations, also known as denominators. The desired precisions, also known as a margin of error. We estimate the frequency at the base line server of the reference group of your study and have design effect. We already have a defined some of these concepts in the previous sessions devoted to be key concept of sample size calculations. But it's good to point out that an estimated frequency of 50 percent represented the most conservative assumptions requiring the biggest sample size or over things being equal. In another thing the smaller of the desired precision, the larger the sample size. But we should expect a larger sample size or a bigger design effect. Target populations, as we already see. Specific to educate ourselves. The size of the target populations typically vary according to criteria of inclusions for data indicators. For instance, in indicators of our research the target population adolescent women aged 15-14 years will require a larger sample size. I mean that a larger or higher number of households to get the required number of adolescents as compared to another indicator also which target adult women aged 15-49, all other factor being equal. This slide presents the formula for precision-based calculation of a sample size for which a few inputs are required. In the previous slide, we already described a few of what was input, which were the desired precision, the estimated frequency, and the design effect. For a precision-based sample size calculation, there are additional input parameters which are the critical value of the normal distribution for which we typically use a value of 1.96 for a probability of committing a type one error of five percent. We also need a compliment to one of the desired precision as well as the survey non-response rate. Those different input can be estimated from other surveys with similar sampling design and which also were measuring similar indicators in a similar population. The power-based sample size calculation is the second options to calculate the sample size along with the precision. Power-based sample size calculation should be applied only when you are comparing estimator from two or more population or two or more points in time. This approach is based on the probability to detect a statistically significant minimum difference between different group or the change between different time point that a survey or a set of surveys will be able to detect with a given power error sample size. The power-based calculations is particularly influenced by the size and the survey design effect. A larger sample size provide greater power to detect differences between a population group or difference or change over time. As previously said for the precision-based sample size calculation, the target populations are specific to indicators and the size of the target population typically vary according to criteria of inclusions. To be able to detect a smaller magnitude of difference between your population group or between the time of point, you should plan increasing your survey sample size. The higher the design effect of your sample, the larger the sample size. A survey sample size also vary according to the estimated the precision for the reference population group or with baseline pointer. A frequency of 50 percent, as we said, is of a more so conservative assumptions on research require a larger sample size, all other factors equal. But let's see completely how we proceed to calculate a sample size based on the power. For power, base sample size calculation. We are able to calculate the sample size for equal sample size or for unequal sample size. This slide present the formula on how to calculate the sample size baseline of the power for equal sample size. More technically, the calculation of a sample size baseline on the power for equal sample size require the critical value of normal distribution for which the value of 1.96 is typically used and of which stands for the probability of committing a type I error of five percent. We also need a typical value of the normal distribution of probability of not committing a type II error which stand for with power. Typically people use a power of 80 percent and associate critical value of a normal distribution of 0.84. The estimated proportion at baseline or end line are estimated proportions of between your reference group 1 and group 2. For instance, I use to calculate the magnitude of change over time how to calculate the difference between population group. The design effect of the non-response rate. A long with the estimated proportion at baseline in the reference group can be estimated from over survey. We've a similar populations and also similar sampling design and indicators. You will see some example on where we can draw this input to calculate the sample size. In the previous slide, we described the formula and input needed for power baseline calculation of equal sample size. In the compare group time point. For time point comparison, it is highly recommended to have the same sample size and sampling design. However you may have a study for which you need a different sample size for the compared population group 1. Basically that happens when you have population group specific indicators. For instance, you may have some interventions which are specific to your reference group for which you need a larger sample size for the group ratio calculations. Compared to the comparison group for which we may need lower number for individual. There is a video where we're going to describe a concrete example of unequal sample size calculations. The additionally input for the power baseline calculation of unequal sample size is the key factor, which stands for the ratio of the sample size in group 2, to a sample size in a group 1. The overall parameters are the same as what we previously described for sample size based on power for equal sample size. We will see in a minute, what can be some example of unequal sample size, in the next lesson. For household converting Server, people use in general, multi-stage random sampling method. We review households as the last stage. Cluster, district or region can be some additional stage. We will do household as the last stage. That mean that you should therefore convert the number of target individual to number of household. All the target individual in a household should be eligible for your survey. The number of households typically vary according to the target population. For instance, a survey targeting adolescent women in the age of 15-19 years old will require to visit a higher number of household in order to get the required number of adolescent compared to a novel study of survey for which woman is 15-49 are the target population population. A conversion factors is therefore required to convert the target populations into number of household. Let's see how to populate this conversion factor, and how to use it to convert target population to number of household. The conversion factors in this formula represent the average number of individual in the denominator per household. For essence, the average number of woman with a life of birth in the last two years per household can be used as a conversion factor for a few indicators. The conversion factor varies by indicators and by setting, and can be estimated from previous survey in the same area or in similar settings. The required number of household is calculated using the number of target individual divided by the conversion factor which is the average number of target population that a household and obtain from previous survey. The number of individual in the denominator of the coverage indicators is obtained from the precision base or power base formula that had been previously described. That means that the formula will basically give you the number of individual, and you need Nano to use the conversion factor Nano to convert Nano with target populations to required number of household for your study. To get the conversion factor for your study, you need to use information from a benchmark survey conducted in the same area or similar settings. To calculate the conversion factor, which we defined as the average number of target individual per household for a given indicator, you need the number of target individual surveyed and the number of household which had been interviewed in the reference survey. Let's go through this example relating to the prevalence and care-seeking of acute respiratory infections. In Tanzania 2015, Demographic and Health Survey, we're going to use as an example. You'll be able to find the number for household interviewed. In the this table from the survey report appendix, we are able to see that for the survey in Tanzania, 12,563 household had been successfully interviewed during the study. This information will be used in addition to other information to calculate our conversion factor based on benchmark survey. In the previous slide, we saw how to get the total number of household interviewed. From another table in the survey report, you can find the total number of children and that is five, in this case, the blue column, which allow to calculate the average number of children under age five their household using the total number of interviewed household in the previous slide. That can be used as a conversion factor. For the prevalence of symptom of acute respiratory infections, as well as all indicate also for whether children under age five are the target population. Similarly, you can calculate the average number of children age under five years with symptom of acute respiratory infections of that household in order to calculate the required number of households in your survey sample. For care-seeking or treatment of acute respiratory infections. The last column in this example, we read the number of household [inaudible] from the previous table are required for calculation of the later convention factors. There are a few key steps to consider for calculating your sample size. For your indicators of interest, you need to think about the objective of your study and decide whether you care about point estimate I mean, precision or you care about the change or difference between a population group or between time point. But usually, with the precision base and power base calculation are commanded whether applicable. For each indicators, you should calculate the sample size based on the precision and base on the power considering living factor like the non-response rate or the design effect. After calculating the target number of populations you needed to convert now that number to household using a conversion factor, and also keeping in mind that not all the household will have a big target individual in the denominator for your indicator. After calculating the number of individuals and converting that number to household, you need to double-check both the number of individual and number of household you find along with the assumption, and the input that had been used for the calculations. Importantly, thinks about the requirement and a valuable resources to cover the sample you have calculated. The resources typically comprise the staff logistic, the time to implement your survey, and also the fund or money, you need to implement the survey based on the calculate sample size. If available resources are not sufficient to cover the sample, consider a way where you can live with lower precision or power. Double-check your assumption and input and recalculate your sample size with new precision or new power. Sample size and available resources are actually interrelated. In addition to statistical considerations, I mean, every precision and power, a valuable resources are also and even often more likely to guide the final sample size needed for your study. Let's now see two concrete examples of precision-based and power-based calculation. In this example, we want to calculate the sample size to measure skilled attendant at birth in the Lake Zone in Tanzania, with an estimated proportion of 51 percent. The precision of a five-percent. Also, from a previous benchmark survey, we found 1,146 women age of 15-49 years, with a live birth in the two-year prior to the survey from 2555 households. We seek for the required number of household to carry out our survey. For that proposal, you need first to calculator the required number of target populations. That is, the number of women age 15-49 with a live birth in the last two years prior to the survey. As input for your calculation, you already have this frequency that is 51 percent. That allow you also to populate the compliment to one of the estimator frequency, that is 49 percent in this example. The design effect, the number of women age of 15-49 with a live birth in two years prior to the survey. In number 8 and the number of household interviewed had derived from Orbit Tanzania 2015 demographic and health survey that we're going to use as a base marker survey. Using a particular value of normal distribution of 1.96, and also using the provided estimated frequency to compliment to one or to estimate frequency, the design effect of 1.99 and of a precision of five percentage of pointer, you are able to calculate of the required number of UDL. You can apply at this stage. We nonetheless phosphate are applied with respect to that later when you convert a number of loci and UDL or house under. The conversion factor is based on data from the base marker survey, which is of a Tanzania 2015 DHS. These professional factor was obtained by dividing the number of women age of 15 - 49 with a large barrier with two year period to a survey by the number of household or interview in that benchmark center. Using now the conversion factor and of the household response rate, you can calculate the finally, we'll call your number of household of survey received 1,846 household in this example. Let's see now another example based on the power. Using the same data as the previous example, you want now to carry out a power based simple set calculations. Since you are interested in comparing baseline and inline server for your study, you want a sample size which allow you to detect the minimum difference of 10 percent between your baseline and your end line up considering the estimate frequencies at baseline and end line. This difference of 10 percent is just the difference between the proportions for the population group 1 and also population group 2. They require number of a woman age of 15-49 with a live birth in the two-year prior to survey obtained using the critical value of normal distribution of a low probability of committing a type 1 error of five percent, which is the value of 1.96. We also use the value of 0.84, that is the critical value of a normal distribution for a power of 80 percent or the probability of not committing a type 2 error. You also need the estimated frequency at baseline, and the estimate frequency at end line, which will allow you also to populate over complimentary to one to each estimator frequency. You finally need to also take into account the magnitude of change over time, which is the difference between the estimator proportion for group 1 and estimator proportion for the group 2. Lastly, to also account for the designer effector. In total, you need 769 woman age of 15-49 with a live birth for two years of prior to survey as a required number of n UDL for your study. We said previously, this number of n [inaudible] need to be converted into the number of household. Using our housework conversion factor and of the household response rate from the benchmark survey, which is of Tanzania DHS of 2015, you can finally calculate the required number of household for your survey which is 1,857 households for each the baseline survey and also the end liner survey where both example was to show you how that can be completely done. We're going to use a additional tool, mainly the sample size calculator in one of the next session to show you also how you can easily calculate the sample size based on the power of base of the precision of both power and sample size calculation. Thank you.
