**What is Population Sample?**

A population sample is a set of elements that represent the total universe, that is, they are a fraction of the total number of individuals to be evaluated. To determine the size of this sample is equally as important as the sample size.

This is important because establishing a population sample will allow a credible study about the objective and the different characteristics of each population. Determining the sample size is economically advisable in addition to reducing the time taken to conduct any related market research activities that you are planning to do.

**What is Sample Size?**

A sample is a selection of respondents from a population in such a manner that the sample represents the total population as closely as possible. Once you have determined your sample, the total number of individuals in that particular sample is the sample size.

A large sample size can yield better and more accurate study results. A research is a multistep process, that allows you to achieve the desired results if all the steps are conducted in a systematic manner and the most important of all the steps is how many responses are actually required to be able to derive a conclusive result. Larger sample sizes tend to lead to an increased precision. For example, we want to know how the proportion of children infected with a certain pathogen, then we would generally get a more precise estimate of this proportion if we chose to sample 300 children rather than 50.

Here is another example, you are a market researcher stationed in the U.S and want to send out a survey or questionnaire to understand the response of your audience about a new cell phone you are about to launch.You want to know what people in the US think about the specification of the product if the product is too gender specific or neutral.

Hypothetically, you choose the population of New York, which is 8.49 million. Since you cannot send a survey to everyone in New York, you choose a sample of 500 individuals that fit into our consumer panel requirement and received responses from them. Through these responses received, you will be able to determine how your audience will react to the product.

No lesser emphasis can be put on the fact that using the right sample size is essential. Afterall, if your sample size is too big that can lead to waste of resources, time and money and if your sample size is too small then this will not allow you to gain maximum insights and this will lead to inconclusive results.

**Sample Size and Target Population**

Before you can calculate a sample size, a few terms need to be well defined that of the target population and the sample you need:

**Population Size:**Population size is how many people actually fit your demographic? For example, if you want to know about the doctors residing in the US, then the total number of doctors in the US will become your population size. Don’t worry! Your population size need not be that big at all times. Even if your population size is small it just needs to be the right fit.-
**Confidence Level:**Confidence level tells you how confident you are. It is always expressed in percentage and aligned to the confidence interval. For example, if your confidence level is 90% it is most likely that you are 90% accurate. **The Margin of Error (Confidence Interval):**No sample will be perfect, so you must decide how much error to allow. The confidence interval determines how much higher or lower than the population mean you are willing to let your sample mean fall. A margin of error describes how close we can reasonably expect a survey result to fall relative to the true population value.**Standard of Deviation:**Standard deviation is the measure of dispersion of a set of data from its mean. It measures the absolute variability of a distribution; the higher the dispersion or variability, the greater is the standard deviation and greater will be the magnitude of the deviation of the value from their mean. For example, you have already sent out your survey, how much variance do you expect in your responses, that variation in response is standard of deviation.

**Sample Size Calculation Formula**

Now that we have all the terms defined let us now understand how the sample size calculation works:

Your confidence level corresponds to a Z-score. This is a constant value needed for this equation. Here are the z-scores for the most common confidence levels:

90% – Z Score = 1.645

95% – Z Score = 1.96

99% – Z Score = 2.576

If you choose a different confidence level, there are various online tools that can help you find your score.

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

Here is an example of how the math works assuming you chose a 90% confidence level, .6 standard deviation, and a margin of error (confidence interval) of +/- 4%.

((1.64)2 x .6(.6)) / (.04)2

( 2.68x .0.36) / .0016

.9648 / .0016

603

603 respondents are needed and that becomes your sample size.

**How to Determine and Calculate Sample Size**

Determining the right sample size for your survey has become one of the most common questions. The process for determining the best sample size to collect so that you can make a good decision isn’t as complicated as you might think (or remember from your stats classes).

Because there is no magic bullet or single number, there are a few things you’ll want to have determined before you start figuring out what your sample size is:

**Your goals and objectives:** What do you hope to do with the survey. Are you planning on projecting the results onto a whole demographic or population? Do you just want to see how a specific group thinks? Are you trying to make a big decision or just set a direction? If you’re going to be projecting the results of your survey on a larger population — then sample size is critical and you’ll want to make sure that it’s balanced and reflects the population. If you’re just trying to get a feel for preferences – then it’s not as critical.

**How precise do you need or want to be?:** How close do you want the survey results to mimic what the true value would be — if everyone responded? Again, if this survey is going to determine how you’re going to spend millions of dollars — you want to be very precise. The more precise you want to be, the more sample you’re going to want to have and the more your sample will have to represent the overall population. So if your population is small, say 200 – then you may want to do a complete census rather than get just a sample.

**How confident or sure do you want to be in the results?: **Think of Confidence from the perspective of risk. How much risk are you willing to take on? This is where your Confidence interval numbers become important. How confident do you want to be? 98% confident? 95% confident. Understand that this confidence percentage that you choose has a big impact on the number of completions you’ll need and that can possibly increase the length of the survey, how many samples you ultimately have to get and that means increased costs to your survey. It helps to understand the actual numbers behind the percents and the costs associated with reaching them. For example – if you want to be 99% confident and that means collecting an additional 1000 respondents and this means paying for sample or keeping your survey running for an additional week or so — you will have to ask yourself if you’re willing to make that tradeoff for the precision.

**What kind of variability are you looking at?:** In other words, how similar or different is the population. If you are surveying consumers on a broad topic – then you may have lots of variabilities and will need more sample. But if you’re surveying a fairly homogenous population, then your variability will be less and you can sample fewer people. So more variability equals more sample and less variability equals less sample. If you’re not sure, you can start with 50% variability.

**Estimate your response rate:** Of course, you want everyone to respond to the survey, but we know that isn’t going to happen. Your response rate will depend on how engaged your sample or population is with your product, service organization or brand. The higher the response rate, the more engaged your list. Your base sample size is the number of responses you MUST get. In order to meet those goals, you will have to increase your list size, remind people to complete the survey and also look at your survey structure. Sometimes people will not respond to long surveys, for example. Then if you reduce the number of questions in your survey, your response rate may increase.

Before you decide on the exact number of individuals to include in your survey, there are a few factors that you should take into consideration. The section below explains these factors in depth and how to determine the best sample size for your survey, but you will find a basic rundown of the process below.

Factors to consider when you calculate sample size:

**The objective of the Survey: **If you are interested in using the results of your survey to make a big decision or you plan to project the results on a larger population, the sample size is critical. If, however, you are merely using the results to get a feel for a specific group’s preferences the size of your sample may not be as important.

**Diversity: **How diverse is the population of individuals or groups you wish to survey? While similar respondents can typically be surveyed using a smaller sample size, surveys that require a more diverse population will receive more accurate results with a larger sample size.

**Accuracy: **How critical is the accuracy of your survey results? Sample size and targeted audience can play a significant role in the accuracy of your survey. For example, if you are planning to use the results of your survey to make a large investment or make a decision that will affect a large population, the accuracy of your survey is likely extremely important and a larger sample size is essential.

**The Rate of Response: **In order to target the most effective sample size for your survey, you should first consider the number of respondents you will need as well as the willingness of your audience to participate in your survey. If you estimate that only 50% of your audience will respond, and you need at least 100 respondents, for example, you will likely need to target a minimum of 200 individuals.

**Audience: **Another factor that should be considered when it comes to how to calculate sample size is the audience itself. You wouldn’t want to target homeowners when surveying about the quality of local apartment life, for example. If you send out a survey that is targeted toward a specific audience that is qualified to provide accurate answers, your sample size may not need to be as large as it would be if you decided to survey random individuals in the area.