# Sample Size Calculator

In order to successfully measure results, programme staff need to select appropriate sample sizes for surveys, often on a limited budget and without access to specialist expertise. The DCED’s publication, Practical Advice for Selecting Sample Sizes, provides simple guidelines to help programmes make appropriate decisions.

The calculator below accompanies the guidance by providing a simple, practical tool to help programmes using the DCED Standard to select the minimum sample sizes for quantitative surveys. For full guidance on how to use it, download the Practical Advice for Selecting Sample Sizes.

The right sample size is only one aspect of a good research strategy. To learn more, read the DCED’s Practical Guidelines on Conducting Research.

You can watch a webinar on the topic on the DCED’s youtube channel.

#### Type of Research

This calculator supports three different research options, described below. In order to use this guidance, decide which research option you want to use.

#### 1. Descriptive

In a descriptive study, the aim is to estimate the characteristics of a population.

###### Example Question:

How many hectares of wheat do farmers plant?

#### 2. Comparative

In a comparative study, the aim is to establish whether there are significant differences between two groups.

###### Example Question:

Do farmers who have participated in our intervention have a higher income than farmers who didn’t?

#### 3. Comparative (paired)

In a paired comparative study, the aim is to compare the same people at two points in time.

###### Example Question:

Do farmers who have participated in our intervention have a higher income than they did a year ago?

#### What range will 95% of your data fall in?

The ‘range’ is simply the difference between the highest value and the lowest value in your sample. Obviously, before you have done your survey, you will not know the range exactly. You will need to make the best guess you can, based on the evidence that you have available. Ask yourself the following two questions:

1. What is the lowest value that would typically occur? This will be the lowest value of the range.
2. What is the highest value that would typically occur? This will be the highest value of the range.

Note that you are not being asked for the highest value that would ever occur. You are being asked for the range of values that 95% of your data is likely to fall into. If you don’t know the answer, try asking a few specialists in the sector, such as practitioners or research institutes. The sample size calculator will assume that the average value of the sample is half way between the highest and the lowest.

This question asks about just one range, although a survey would typically assess multiple variables, each with different expected ranges. For example, a single survey might assess yields, land size, and costs. Consequently, you should select the most important variable in your study, (often an impact indicator, such as income) and use the range for that variable in the calculator. Alternatively, you could include ranges from several different variables and use the one which suggests the largest sample size.

If you are doing a comparative study, you are surveying two groups of people. You only need to enter the range for the baseline group, which is the group that has not received any intervention.

If you are doing a comparative (paired) study, the range does not refer to the range of values in the group. Instead, it refers to the range of differences between people.

Your margin of error is 5, which is 10% of 50, your implied mean.

#### Margin of Error Explanation

What margin of error do you require?

The margin of error is a measure of how precisely your sample can estimate the true average of the population.

Imagine that a survey found that respondents, on average, used 70 kilogrammes of improved seed per hectare, with a margin of error of 10. This means that the precision of the survey is 70 kilogrammes, plus or minus ten. In other words, the true population average for the amount of seed used is likely to be between 60 and 80 kilogrammes. If the margin of error had been 20, then the survey would have been much less accurate, even if the average finding was the same. With a margin of error of 20, all you would know is that the true population average is likely to be between 50 and 90 kilogrammes of seed per hectare. (Exactly how likely this is depends on the confidence level; see below.)

In general, a smaller margin of error requires a larger sample size. Select your margin of error by considering the purpose of the study. If the aim is to do a rapid scan of a population which will give a quick idea of their characteristics, a high margin of error is acceptable. If the aim is to get a more accurate understanding of a population, then a low margin of error would be better. A commonly used value is a margin of error of 10% of the expected average value.

In this calculator, enter the margin of error in the same units that you have given the range. (In other words, if your average is 40, and you want a margin of error of 10% of the average, then you need to enter ‘4’ into the sample size calculator.

#### Minimum Detectable Difference Explanation

What minimum detectable difference do you require?

The minimum detectable difference is the smallest difference between two groups that you want to detect in your study. The smaller the difference you want to detect, the larger your sample size would need to be.

In order to work out what the minimum detectable difference should be, you need to estimate what level of change you would be happy to see between the groups.

Imagine that a business environment reform programme wanted to compare two groups of business. One group of businesses used an online portal to lodge applications for importing and exporting goods, while the other group lodged offline applications. The programme wanted to know whether the businesses using an online portal had their applications approved faster than the other group. They hypothesise, based on stakeholder interviews, that the speed of approval might change from 36 hours (using offline applications) to 24 hours (using online applications.) This is a reduction in time taken of 12 hours. The programme decides, however, that it is not really interested in any change less than 6 hours. That is the minimum detectable difference.

In this calculator, enter the minimum detectable difference in the same units that you have given the range.

#### What confidence level do you need?

The confidence level is a measure of how confident you can be in your answer.

If the confidence level is 90%, then you can be 90% confident that the true population average lies within your margins of error.

We suggest using a confidence level of 90%, although 95% is often used in scientific research.

#### What is the population size?

Enter in the size of the population that you are sampling from.

Bigger population sizes typically require a bigger sample size. However, the sample size as a percentage of the population to be sampled reduces dramatically.

The sample size doesn't change much for populations larger than 20,000, so if in doubt use that figure.

Your minimum sample size is 68