# The Quantitative Research Confidence Interval Calculator

By Chris Martin

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One of the most misunderstood concepts of quantitative research is the confidence interval. However, it is a crucial step in finding out whether or not your survey results confirm your original hypothesis.

To simplify the process, we’ve created an interactive tool that automatically calculates the range within your result must fall to be considered a representative mean. We have also broken down the required variables and calculation itself for the more curious statisticians.

### Calculator Terms Defined

Not sure what values to use? This brief guide explains the terms used in our confidence interval calculator, in addition to providing recommended values for optimum results.

Confidence Interval: This is the output of the calculator. It is comprised of two values: the upper and lower bound. The range between these two values is the area in which your research result must fall to be considered representative of the population.

Sample Mean: The sample mean is defined as an unbiased estimation of the overall mean. In this case, it should be the hypothetical value you hypothesise will be the result, and are therefore testing. It is around this figure which the upper and lower confidence bounds will be calculated.

Sample Size: Your sample size is the amount of consumers in your target population that take part in your research project. A larger sample size leads to increased precision in measurement. Our quantitative sample calculator suggests the minimum amount of participants required to make your project statistically representative.

Confidence Level: A confidence level is defined as the statistical probability that the value of a parameter falls within a specified range of values. Therefore a confidence level of N% means you can be N% sure that your results contain the true mean average of the designated population.

In market research, the most commonly used confidence level is 95%. A higher confidence level indicates a higher probability that your results are accurate, but increasing it can dramatically increase the required sample size. Finding a balance between confidence and an achievable research goal is crucial.

In this calculation, each confidence level is translated to a z-score. A z-score is a statistical method for rescaling data that helps researchers draw comparisons easier. The following table details the z-score generated from each confidence level:

 Confidence Level z-score 90% 1.645 95% 1.96 99% 2.58

Standard Deviation: The standard deviation is a measure of how spread responses are. In this calculator, because the results are gathered from the sample (rather than the whole population), you should use the sample standard deviation.

### The DIY Confidence Interval Calculation

Want to work out your confidence interval manually? Our interactive calculator uses the following equation. Simply follow the steps below to work out the target range that your results must fall within to be representative of the population as a whole.

CI = x ± Za/2 * σ/√(n)

CI = confidence interval | = sample mean | Za/2 = confidence level | σ = standard deviation | n = sample size

Once you have calculated the upper and lower bounds of your confidence interval, you can compare the results of your quantitative research to discover whether or not the findings fall within a range that can confirms your initial hypothesis. So, how can this be applied in a business context? One effective use of confidence intervals is to confirm or deny predictions made by Big Data and machine learning analysis.

The following is a fictional, but realistic, example of this in practice. Your company is planning to launch a range of headphones marketed at owners of leading smartphones in the UK, but is struggling to decide on a price point. The company's data analysis team predict that smartphone owners spend an average of £41.50 each on headphones. To test this theory, you run a survey of 3,400 sample consumers. The result of your survey finds that consumers spend an average of £48.20 on headphones.

So, does this result confirm the initial prediction? To find out you'll need to use the confidence interval calculation to discover the upper and lower bounds. In this case, the range equals £33.13-£49.87. Because your prediction fall within this range - you can confirm that it was accurate and can be applied to the target population.

This is just one example of confidence intervals in practice. There are many more applications, limited only by your creativity. What are your best examples of confidence intervals to aid business decisions? Let us know in the comments below and join the conversation.

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### Chris Martin- Marketing Specialist

Personal Bio: With a relentless focus on consumer experience, Chris is uniquely skilled in managing online communication channels. Combined with an in-depth knowledge of the digital era and a sharp analytical mind, he is able to creatively develop the FlexMR brand in accordance with a constantly evolving industry.